feat: expand sudoku analysis and interoperability

CHANGELOG.md

@@ -16,6 +16,41 @@ All notable changes are documented here.
   constraint family.
 - Added bounded, seedable generation for classic and twelve variant families,
   plus independent uniqueness and evidence-based difficulty assessment.
+- Added X-sum, skyscraper, quadruple and maximum-cell constraints across the
+  model, validator, exact solver, renderer, setter and f-puzzles interchange.
+- Added per-clue false semantics for liar/Wrogn puzzles, including bounded
+  impossible decoy numbers and a setter-wide false-clue mode.
+- Added the original, uniquely verified “Truth and lies” example demonstrating
+  true and false outside, inclusion, maximum, cage, line and pair clues.
+- Added outside-grid clue margins, combined dual X-sum/skyscraper labels,
+  outward maximum arrows and visually distinct false clues.
+- Added strict, bounded local imports for SudokuPad/CTC data and supported
+  Penpa+ long links, including source reporting and explicit incompatibility
+  lists instead of silently discarded constructs.
+- Added a compatibility check which never fetches SudokuPad short IDs or other
+  server-hosted puzzle references.
+- Added standalone SVG, high-resolution PNG and single-page PDF visual exports
+  for supported constraints, givens and optional solving progress.
+- Added named savepoints, isolated hypothesis branches, keep/discard decisions
+  and read-only replay of complete solving states.
+- Added an optional configurable aid-mémoire whose labelled scratch cells
+  support values, both note styles and colours without constraining the puzzle;
+  its state is preserved in undo, replay, Library progress and project/share
+  interchange.
+- Added a generalized Sum Lab with independent digit bounds, repeats,
+  required/excluded digits, selected-cell candidates, positional assignments
+  and reversible manual eliminations.
+- Added Candidate Lab filters, selected/touching/specific-house scopes, house
+  positions, strong conjugate/bivalue links, weak links and bounded board
+  overlays.
+- Added technique-targeted practice generation which mines a bounded,
+  deterministic set of uniquely checked puzzles and verifies the requested
+  technique in the logical solve path.
+- Added real ARIA row/gridcell semantics, detailed cell descriptions and
+  non-wrapping Arrow, Home/End, Control/Command + Home/End and Page Up/Down
+  keyboard navigation for the puzzle and scratch grids.
+- Made Killer cage repeat semantics explicit in the setter and independent of
+  whether a clue is required to be true or false.
 
 ## 0.1.0 - 2026-08-30
 

README.md

@@ -8,33 +8,63 @@ release also runs independently from any static HTTPS host or local preview.
 ## Workspaces
 
 - **Play** — keyboard, mouse and touch entry; multi-cell selection; values,
-  corner/centre notes and colours; undo/redo; conflict highlighting; timer and
+  corner/centre notes and colours; undo/redo; named savepoints, hypothesis
-  local progress; optional digit-completion counts and matching-digit
+  branches and read-only replay; conflict highlighting; timer and local
-  highlights.
+  progress; optional digit-completion counts, matching-digit highlights and a
+  configurable non-constraining aid-mémoire.
 - **Set** — givens, metadata, regions and typed constraints; uniqueness checks
   with overlap-safe cage replacement and selection-based cage removal.
 - **Generate** — seedable, bounded construction for classic and 12 variant
   families; independent uniqueness verification and evidence-based difficulty
-  assessment.
+  assessment; deterministic mining for a requested logical technique.
 - **Solve** — exact solution counting plus an original human-style engine whose
   steps include structured evidence, placements and eliminations.
-- **Helpers** — Killer combinations and candidate-aware assignments, 45-rule
+- **Helpers** — generalized sum combinations with positional candidates and
-  residuals, and Kropki, XV or inequality relation pairs.
+  manual eliminations; selected-cell and house candidate-link analysis; Killer
+  combinations, 45-rule residuals, and Kropki, sum-pair or inequality pairs.
 
 Classic grids and common variants share one bounded puzzle model: irregular
 regions, diagonals, Killer cages, thermometers, arrows, Kropki and numbered
-5/10 sum-pair clues, inequalities, renban lines, palindromes, anti-knight,
+5/10 sum-pair clues, inequalities, renban lines, palindromes, X-sums,
-anti-king and non-consecutive rules. Thirteen bundled, uniquely checked examples
+skyscrapers, quadruples, maximum cells, anti-knight, anti-king and
-demonstrate every supported constraint. Import accepts compact grid strings,
+non-consecutive rules. Every local clue can also be required to be false for
-this project's JSON format, share fragments, and the common f-puzzles fields
+liar/Wrogn constructions. Fourteen original bundled examples demonstrate every
-supported by the model. Unknown constraints are reported rather than silently
+supported constraint and are exact-search verified as unique.
-discarded.
+
+The board exposes real row/gridcell semantics and concise per-cell state to
+assistive technology, including candidates, notes, colours, conflicts and
+touching variant clues. Arrow keys never wrap; Home/End, Control/Command +
+Home/End and Page Up/Down provide row- and grid-level navigation. The same
+navigation model is available in the aid-mémoire scratch grid.
+
+## Interoperability and visual export
+
+The import dialog recognises compact grids, Sudoku Tools JSON/share fragments,
+raw or inline f-puzzles data, SudokuPad/CTC (SCL) data, and Penpa+ self-contained
+long links. It never follows a URL or resolves a server-side short ID. Imports
+are size/decompression bounded, report their detected source before applying,
+and stop with a list when a construct cannot be represented faithfully.
+
+SudokuPad compatibility currently preserves cells, givens and progress, notes,
+regions, metadata, solutions, Killer cages and supported global rules. Penpa+
+compatibility is intentionally narrower: square, unrotated Sudoku grids with
+givens/progress, thermometers and arrows. Visual-only lines, overlays, custom
+symbols and other unsupported geometry are reported rather than ignored.
+f-puzzles export likewise refuses false clues it cannot preserve.
+
+Export can produce a standalone SVG, a high-resolution PNG, or a single-page
+PDF entirely in the browser. Each visual uses the same trusted puzzle model and
+renders region boundaries, supported variant clues and givens; current values,
+notes and cell colours can be included or omitted with the progress switch.
 
 Generation supports only size/variant combinations which pass the bounded
 construction checks. The requested difficulty controls clue-removal targets;
 the displayed 0–100 result is calculated afterwards from logical techniques,
 clue load and reproducible exact-search evidence. A timeout or node limit is
 reported as unknown and never promoted to a uniqueness or difficulty claim.
+Technique practice performs a bounded, deterministic search and returns a
+puzzle only when its independently analysed solve path actually contains the
+requested technique.
 
 ## Privacy and storage
 
@@ -46,7 +76,8 @@ Exported files and share URLs contain the puzzle data you chose to include.
 
 SudokuPad short IDs identify server-hosted records and therefore cannot be
 resolved by this deliberately offline application. Embedded f-puzzles payloads
-are accepted without contacting their originating site.
+and user-provided Sudoku Tools JSON documents are accepted without contacting
+their originating site. Externally authored puzzle definitions are not bundled.
 
 ## Development
 
@@ -76,8 +107,8 @@ browser workflows and Toolbox contract before creating a deterministic
 
 The interaction ideas and published solving concepts explored by SudokuPad,
 SudokuWiki and the wider puzzle community informed the product requirements.
-No code, artwork, wording or proprietary puzzle data from those applications is
+No externally authored puzzle definitions, code, artwork or documentation text
-included. Algorithms and explanations in this repository are independently
+is bundled. Algorithms, UI, original examples and explanations are independently
 implemented from mathematical rules and public standards.
 
 ## Licence

THIRD_PARTY_NOTICES.md

@@ -16,4 +16,12 @@ runtime package. Development-only packages build and test the source but are
 not shipped as runtime modules.
 
 SudokuPad, SudokuWiki and HoDoKu are research references only. Their source,
-documentation, wording, visual assets and puzzle data are not bundled or copied.
+documentation wording, visual assets and externally authored puzzle data are
+not bundled or copied.
+
+The local compatibility code was tested against the open format behaviour in
+[Penpa+](https://github.com/swaroopg92/penpa-edit) (MIT),
+[penpa-to-scl](https://github.com/marktekfan/penpa-to-scl) (MIT), and
+[SudokuPad sudokutools](https://github.com/SudokuPad/sudokutools) (MPL-2.0).
+Those projects are format references only: no upstream executable code,
+artwork, documentation text or puzzle data is distributed with Sudoku Tools.

public/CHANGELOG.md

@@ -16,6 +16,41 @@ All notable changes are documented here.
   constraint family.
 - Added bounded, seedable generation for classic and twelve variant families,
   plus independent uniqueness and evidence-based difficulty assessment.
+- Added X-sum, skyscraper, quadruple and maximum-cell constraints across the
+  model, validator, exact solver, renderer, setter and f-puzzles interchange.
+- Added per-clue false semantics for liar/Wrogn puzzles, including bounded
+  impossible decoy numbers and a setter-wide false-clue mode.
+- Added the original, uniquely verified “Truth and lies” example demonstrating
+  true and false outside, inclusion, maximum, cage, line and pair clues.
+- Added outside-grid clue margins, combined dual X-sum/skyscraper labels,
+  outward maximum arrows and visually distinct false clues.
+- Added strict, bounded local imports for SudokuPad/CTC data and supported
+  Penpa+ long links, including source reporting and explicit incompatibility
+  lists instead of silently discarded constructs.
+- Added a compatibility check which never fetches SudokuPad short IDs or other
+  server-hosted puzzle references.
+- Added standalone SVG, high-resolution PNG and single-page PDF visual exports
+  for supported constraints, givens and optional solving progress.
+- Added named savepoints, isolated hypothesis branches, keep/discard decisions
+  and read-only replay of complete solving states.
+- Added an optional configurable aid-mémoire whose labelled scratch cells
+  support values, both note styles and colours without constraining the puzzle;
+  its state is preserved in undo, replay, Library progress and project/share
+  interchange.
+- Added a generalized Sum Lab with independent digit bounds, repeats,
+  required/excluded digits, selected-cell candidates, positional assignments
+  and reversible manual eliminations.
+- Added Candidate Lab filters, selected/touching/specific-house scopes, house
+  positions, strong conjugate/bivalue links, weak links and bounded board
+  overlays.
+- Added technique-targeted practice generation which mines a bounded,
+  deterministic set of uniquely checked puzzles and verifies the requested
+  technique in the logical solve path.
+- Added real ARIA row/gridcell semantics, detailed cell descriptions and
+  non-wrapping Arrow, Home/End, Control/Command + Home/End and Page Up/Down
+  keyboard navigation for the puzzle and scratch grids.
+- Made Killer cage repeat semantics explicit in the setter and independent of
+  whether a clue is required to be true or false.
 
 ## 0.1.0 - 2026-08-30
 

public/README.md

@@ -8,33 +8,63 @@ release also runs independently from any static HTTPS host or local preview.
 ## Workspaces
 
 - **Play** — keyboard, mouse and touch entry; multi-cell selection; values,
-  corner/centre notes and colours; undo/redo; conflict highlighting; timer and
+  corner/centre notes and colours; undo/redo; named savepoints, hypothesis
-  local progress; optional digit-completion counts and matching-digit
+  branches and read-only replay; conflict highlighting; timer and local
-  highlights.
+  progress; optional digit-completion counts, matching-digit highlights and a
+  configurable non-constraining aid-mémoire.
 - **Set** — givens, metadata, regions and typed constraints; uniqueness checks
   with overlap-safe cage replacement and selection-based cage removal.
 - **Generate** — seedable, bounded construction for classic and 12 variant
   families; independent uniqueness verification and evidence-based difficulty
-  assessment.
+  assessment; deterministic mining for a requested logical technique.
 - **Solve** — exact solution counting plus an original human-style engine whose
   steps include structured evidence, placements and eliminations.
-- **Helpers** — Killer combinations and candidate-aware assignments, 45-rule
+- **Helpers** — generalized sum combinations with positional candidates and
-  residuals, and Kropki, XV or inequality relation pairs.
+  manual eliminations; selected-cell and house candidate-link analysis; Killer
+  combinations, 45-rule residuals, and Kropki, sum-pair or inequality pairs.
 
 Classic grids and common variants share one bounded puzzle model: irregular
 regions, diagonals, Killer cages, thermometers, arrows, Kropki and numbered
-5/10 sum-pair clues, inequalities, renban lines, palindromes, anti-knight,
+5/10 sum-pair clues, inequalities, renban lines, palindromes, X-sums,
-anti-king and non-consecutive rules. Thirteen bundled, uniquely checked examples
+skyscrapers, quadruples, maximum cells, anti-knight, anti-king and
-demonstrate every supported constraint. Import accepts compact grid strings,
+non-consecutive rules. Every local clue can also be required to be false for
-this project's JSON format, share fragments, and the common f-puzzles fields
+liar/Wrogn constructions. Fourteen original bundled examples demonstrate every
-supported by the model. Unknown constraints are reported rather than silently
+supported constraint and are exact-search verified as unique.
-discarded.
+
+The board exposes real row/gridcell semantics and concise per-cell state to
+assistive technology, including candidates, notes, colours, conflicts and
+touching variant clues. Arrow keys never wrap; Home/End, Control/Command +
+Home/End and Page Up/Down provide row- and grid-level navigation. The same
+navigation model is available in the aid-mémoire scratch grid.
+
+## Interoperability and visual export
+
+The import dialog recognises compact grids, Sudoku Tools JSON/share fragments,
+raw or inline f-puzzles data, SudokuPad/CTC (SCL) data, and Penpa+ self-contained
+long links. It never follows a URL or resolves a server-side short ID. Imports
+are size/decompression bounded, report their detected source before applying,
+and stop with a list when a construct cannot be represented faithfully.
+
+SudokuPad compatibility currently preserves cells, givens and progress, notes,
+regions, metadata, solutions, Killer cages and supported global rules. Penpa+
+compatibility is intentionally narrower: square, unrotated Sudoku grids with
+givens/progress, thermometers and arrows. Visual-only lines, overlays, custom
+symbols and other unsupported geometry are reported rather than ignored.
+f-puzzles export likewise refuses false clues it cannot preserve.
+
+Export can produce a standalone SVG, a high-resolution PNG, or a single-page
+PDF entirely in the browser. Each visual uses the same trusted puzzle model and
+renders region boundaries, supported variant clues and givens; current values,
+notes and cell colours can be included or omitted with the progress switch.
 
 Generation supports only size/variant combinations which pass the bounded
 construction checks. The requested difficulty controls clue-removal targets;
 the displayed 0–100 result is calculated afterwards from logical techniques,
 clue load and reproducible exact-search evidence. A timeout or node limit is
 reported as unknown and never promoted to a uniqueness or difficulty claim.
+Technique practice performs a bounded, deterministic search and returns a
+puzzle only when its independently analysed solve path actually contains the
+requested technique.
 
 ## Privacy and storage
 
@@ -46,7 +76,8 @@ Exported files and share URLs contain the puzzle data you chose to include.
 
 SudokuPad short IDs identify server-hosted records and therefore cannot be
 resolved by this deliberately offline application. Embedded f-puzzles payloads
-are accepted without contacting their originating site.
+and user-provided Sudoku Tools JSON documents are accepted without contacting
+their originating site. Externally authored puzzle definitions are not bundled.
 
 ## Development
 
@@ -76,8 +107,8 @@ browser workflows and Toolbox contract before creating a deterministic
 
 The interaction ideas and published solving concepts explored by SudokuPad,
 SudokuWiki and the wider puzzle community informed the product requirements.
-No code, artwork, wording or proprietary puzzle data from those applications is
+No externally authored puzzle definitions, code, artwork or documentation text
-included. Algorithms and explanations in this repository are independently
+is bundled. Algorithms, UI, original examples and explanations are independently
 implemented from mathematical rules and public standards.
 
 ## Licence

public/THIRD_PARTY_NOTICES.md

@@ -16,4 +16,12 @@ runtime package. Development-only packages build and test the source but are
 not shipped as runtime modules.
 
 SudokuPad, SudokuWiki and HoDoKu are research references only. Their source,
-documentation, wording, visual assets and puzzle data are not bundled or copied.
+documentation wording, visual assets and externally authored puzzle data are
+not bundled or copied.
+
+The local compatibility code was tested against the open format behaviour in
+[Penpa+](https://github.com/swaroopg92/penpa-edit) (MIT),
+[penpa-to-scl](https://github.com/marktekfan/penpa-to-scl) (MIT), and
+[SudokuPad sudokutools](https://github.com/SudokuPad/sudokutools) (MPL-2.0).
+Those projects are format references only: no upstream executable code,
+artwork, documentation text or puzzle data is distributed with Sudoku Tools.

src/components/AidMemoire.tsx

@@ -0,0 +1,378 @@
+import { useRef, type CSSProperties, type KeyboardEvent } from "react";
+import {
+  aidMemoireCellDescription,
+  clearAidMemoireEntries,
+  compactAidMemoireColumns,
+  configureAidMemoire,
+  enterAidMemoireCell,
+  eraseAidMemoireCell,
+  labelAidMemoireCell,
+  MAX_AID_MEMOIRE_CELLS,
+  MAX_AID_MEMOIRE_COLUMNS,
+  resetAidMemoire,
+  setAidMemoireEnabled,
+  type AidMemoireState,
+} from "../state/aidMemoire";
+import {
+  maskValues,
+  symbolFor,
+  valueForKey,
+  type EntryMode,
+} from "../state/session";
+
+interface AidMemoireProps {
+  readonly size: number;
+  readonly state: AidMemoireState;
+  readonly selectedCell: number;
+  readonly active: boolean;
+  readonly readOnly?: boolean;
+  readonly mode: EntryMode;
+  readonly onStateChange: (state: AidMemoireState) => void;
+  readonly onSelect: (cell: number) => void;
+  readonly onMode: (mode: EntryMode) => void;
+}
+
+const modes: ReadonlyArray<{ mode: EntryMode; label: string; key: string }> = [
+  { mode: "value", label: "Value", key: "Z" },
+  { mode: "corner", label: "Corner", key: "X" },
+  { mode: "center", label: "Centre", key: "C" },
+  { mode: "color", label: "Colour", key: "V" },
+];
+
+export function AidMemoire({
+  size,
+  state,
+  selectedCell,
+  active,
+  readOnly = false,
+  mode,
+  onStateChange,
+  onSelect,
+  onMode,
+}: AidMemoireProps) {
+  const cellRefs = useRef<Array<HTMLButtonElement | null>>([]);
+  const selected = Math.max(0, Math.min(state.cells.length - 1, selectedCell));
+
+  const selectAndFocus = (cell: number) => {
+    const next = Math.max(0, Math.min(state.cells.length - 1, cell));
+    onSelect(next);
+    cellRefs.current[next]?.focus();
+  };
+
+  const handleKeyDown = (
+    cell: number,
+    event: KeyboardEvent<HTMLButtonElement>,
+  ) => {
+    const row = Math.floor(cell / state.columns);
+    const column = cell % state.columns;
+    const rowStart = row * state.columns;
+    const rowEnd = Math.min(
+      state.cells.length - 1,
+      rowStart + state.columns - 1,
+    );
+    let destination: number | undefined;
+    if (event.key === "ArrowLeft") destination = Math.max(rowStart, cell - 1);
+    if (event.key === "ArrowRight") destination = Math.min(rowEnd, cell + 1);
+    if (event.key === "ArrowUp") {
+      destination = cell - state.columns >= 0 ? cell - state.columns : cell;
+    }
+    if (event.key === "ArrowDown") {
+      destination =
+        cell + state.columns < state.cells.length ? cell + state.columns : cell;
+    }
+    if (event.key === "Home") {
+      destination = event.ctrlKey || event.metaKey ? 0 : rowStart;
+    }
+    if (event.key === "End") {
+      destination =
+        event.ctrlKey || event.metaKey ? state.cells.length - 1 : rowEnd;
+    }
+    if (event.key === "PageUp") destination = column;
+    if (event.key === "PageDown") {
+      const lastRowStart =
+        Math.floor((state.cells.length - 1) / state.columns) * state.columns;
+      destination = Math.min(state.cells.length - 1, lastRowStart + column);
+    }
+    if (destination !== undefined) {
+      event.preventDefault();
+      selectAndFocus(destination);
+      return;
+    }
+    if (readOnly) return;
+    if (
+      event.key === "Backspace" ||
+      event.key === "Delete" ||
+      event.key === "0"
+    ) {
+      event.preventDefault();
+      onStateChange(eraseAidMemoireCell(state, cell, mode));
+      return;
+    }
+    if (!event.ctrlKey && !event.metaKey && !event.altKey) {
+      const modeKey: Record<string, EntryMode> = {
+        z: "value",
+        x: "corner",
+        c: "center",
+        v: "color",
+      };
+      const nextMode = modeKey[event.key.toLowerCase()];
+      if (nextMode !== undefined) {
+        event.preventDefault();
+        onMode(nextMode);
+        return;
+      }
+      const value = valueForKey(event.key, mode === "color" ? 8 : size);
+      if (value !== null) {
+        event.preventDefault();
+        onStateChange(enterAidMemoireCell(state, cell, mode, value, size));
+      }
+    }
+  };
+
+  const configure = (cellCount: number, columns: number) => {
+    const next = configureAidMemoire(state, size, cellCount, columns);
+    onStateChange(next);
+    if (selected >= next.cells.length) onSelect(next.cells.length - 1);
+  };
+
+  return (
+    <section className="aid-memoire" aria-labelledby="aid-memoire-title">
+      <header className="section-heading aid-memoire__heading">
+        <div>
+          <p className="eyebrow">Optional scratch cells</p>
+          <h2 id="aid-memoire-title">Aid-mémoire</h2>
+          <p className="muted">
+            Track contextual sets, pseudo-digits or mappings. These cells do not
+            constrain the Sudoku.
+          </p>
+        </div>
+        <button
+          type="button"
+          className="text-button"
+          disabled={readOnly}
+          onClick={() => onStateChange(setAidMemoireEnabled(state, false))}
+        >
+          Hide
+        </button>
+      </header>
+
+      <div
+        className="aid-memoire__scroller"
+        aria-label="Scrollable aid-mémoire area"
+      >
+        <div
+          className="aid-memoire__grid"
+          role="grid"
+          aria-label={`${String(state.cells.length)} aid-mémoire scratch cells`}
+          aria-colcount={state.columns}
+          aria-rowcount={Math.ceil(state.cells.length / state.columns)}
+          aria-readonly={readOnly}
+          style={{ "--aid-columns": state.columns } as CSSProperties}
+        >
+          {Array.from(
+            { length: Math.ceil(state.cells.length / state.columns) },
+            (_, rowIndex) => (
+              <div
+                key={rowIndex}
+                className="aid-memoire__row"
+                role="row"
+                aria-rowindex={rowIndex + 1}
+              >
+                {state.cells
+                  .slice(
+                    rowIndex * state.columns,
+                    (rowIndex + 1) * state.columns,
+                  )
+                  .map((cell, columnIndex) => {
+                    const index = rowIndex * state.columns + columnIndex;
+                    const cornerMarks = maskValues(cell.cornerMarks, size);
+                    const centerMarks = maskValues(cell.centerMarks, size);
+                    return (
+                      <button
+                        key={index}
+                        ref={(element) => {
+                          cellRefs.current[index] = element;
+                        }}
+                        type="button"
+                        role="gridcell"
+                        className={`aid-memoire__cell${active && selected === index ? " is-selected" : ""}${cell.color ? ` has-color-${String(cell.color)}` : ""}`}
+                        aria-label={aidMemoireCellDescription(
+                          cell,
+                          index,
+                          size,
+                        )}
+                        aria-colindex={columnIndex + 1}
+                        aria-selected={active && selected === index}
+                        tabIndex={selected === index ? 0 : -1}
+                        onClick={() => {
+                          if (!readOnly) onSelect(index);
+                        }}
+                        onFocus={() => {
+                          if (!readOnly) onSelect(index);
+                        }}
+                        onKeyDown={(event) => handleKeyDown(index, event)}
+                      >
+                        <span className="aid-memoire__label" aria-hidden="true">
+                          {cell.label || `#${String(index + 1)}`}
+                        </span>
+                        {cell.value ? (
+                          <span
+                            className="aid-memoire__value"
+                            aria-hidden="true"
+                          >
+                            {symbolFor(cell.value, size)}
+                          </span>
+                        ) : (
+                          <>
+                            <span
+                              className="aid-memoire__corner"
+                              aria-hidden="true"
+                            >
+                              {cornerMarks
+                                .map((mark) => symbolFor(mark, size))
+                                .join(" ")}
+                            </span>
+                            <span
+                              className="aid-memoire__centre"
+                              aria-hidden="true"
+                            >
+                              {centerMarks
+                                .map((mark) => symbolFor(mark, size))
+                                .join("")}
+                            </span>
+                          </>
+                        )}
+                      </button>
+                    );
+                  })}
+              </div>
+            ),
+          )}
+        </div>
+      </div>
+
+      <div
+        className="mode-switcher aid-memoire__modes"
+        role="group"
+        aria-label="Aid-mémoire entry mode"
+      >
+        {modes.map((item) => (
+          <button
+            key={item.mode}
+            type="button"
+            disabled={readOnly}
+            className={mode === item.mode ? "is-active" : ""}
+            aria-pressed={mode === item.mode}
+            title={`${item.label} mode (${item.key})`}
+            onClick={() => onMode(item.mode)}
+          >
+            {item.label}
+          </button>
+        ))}
+      </div>
+
+      <div className="aid-memoire__selected">
+        <label>
+          Selected cell label
+          <input
+            value={state.cells[selected]?.label ?? ""}
+            maxLength={40}
+            disabled={readOnly}
+            onChange={(event) =>
+              onStateChange(
+                labelAidMemoireCell(state, selected, event.target.value),
+              )
+            }
+          />
+        </label>
+        <p className="muted">
+          The regular keypad edits this cell in {mode} mode. Digits, Z/X/C/V,
+          Delete and arrow keys also work directly in the scratch grid.
+        </p>
+      </div>
+
+      <details className="aid-memoire__settings">
+        <summary>Configure scratch layout</summary>
+        <div className="aid-memoire__settings-body">
+          <div className="inline-fields">
+            <label>
+              Cells
+              <input
+                type="number"
+                min={1}
+                max={MAX_AID_MEMOIRE_CELLS}
+                value={state.cells.length}
+                disabled={readOnly}
+                onChange={(event) =>
+                  configure(Number(event.target.value), state.columns)
+                }
+              />
+            </label>
+            <label>
+              Columns
+              <input
+                type="number"
+                min={1}
+                max={Math.min(MAX_AID_MEMOIRE_COLUMNS, state.cells.length)}
+                value={state.columns}
+                disabled={readOnly}
+                onChange={(event) =>
+                  configure(state.cells.length, Number(event.target.value))
+                }
+              />
+            </label>
+          </div>
+          <div className="action-row">
+            <button
+              type="button"
+              disabled={readOnly}
+              onClick={() => configure(state.cells.length, state.cells.length)}
+            >
+              Single row
+            </button>
+            <button
+              type="button"
+              disabled={readOnly}
+              onClick={() =>
+                configure(
+                  state.cells.length,
+                  compactAidMemoireColumns(state.cells.length),
+                )
+              }
+            >
+              Compact grid
+            </button>
+            <button
+              type="button"
+              disabled={readOnly}
+              onClick={() => {
+                if (window.confirm("Clear every aid-mémoire entry?")) {
+                  onStateChange(clearAidMemoireEntries(state));
+                }
+              }}
+            >
+              Clear entries
+            </button>
+            <button
+              type="button"
+              className="danger"
+              disabled={readOnly}
+              onClick={() => {
+                if (
+                  window.confirm(
+                    "Reset the aid-mémoire layout, labels and entries?",
+                  )
+                ) {
+                  onStateChange(resetAidMemoire(state, size));
+                  onSelect(0);
+                }
+              }}
+            >
+              Reset all
+            </button>
+          </div>
+        </div>
+      </details>
+    </section>
+  );
+}

src/components/CandidateLab.tsx

@@ -0,0 +1,408 @@
+import { useEffect, useMemo, useState } from "react";
+import { compilePuzzle, type NormalizedPuzzle } from "../domain";
+import {
+  candidateCellsForValues,
+  candidateUnitIndicesForCells,
+  cellLabel,
+  deriveCandidateLinks,
+  houseLabel,
+  inspectCandidateCells,
+  inspectCandidateHouses,
+  type CandidateLink,
+  type CandidateOverlay,
+} from "../helpers";
+import { symbolFor } from "../state/session";
+
+const LINK_LIST_LIMIT = 160;
+const OVERLAY_LINK_LIMIT = 500;
+
+interface CandidateLabProps {
+  readonly puzzle: NormalizedPuzzle;
+  readonly values: readonly number[];
+  readonly candidateMasks: readonly number[];
+  readonly selectedCells: readonly number[];
+  readonly onOverlayChange?: (overlay: CandidateOverlay | undefined) => void;
+}
+
+function nodeLabel(node: CandidateLink["a"], size: number): string {
+  return `${cellLabel(node.cell, size)}(${symbolFor(node.value, size)})`;
+}
+
+function linkLabel(link: CandidateLink, size: number): string {
+  return `${nodeLabel(link.a, size)} ${link.kind === "strong" ? "⇔" : "—"} ${nodeLabel(link.b, size)}`;
+}
+
+export function CandidateLab({
+  puzzle,
+  values,
+  candidateMasks,
+  selectedCells,
+  onOverlayChange,
+}: CandidateLabProps) {
+  const [activeValues, setActiveValues] = useState<readonly number[]>([]);
+  const [scope, setScope] = useState("selection");
+  const [showStrong, setShowStrong] = useState(true);
+  const [showWeak, setShowWeak] = useState(false);
+  const [includeCellLinks, setIncludeCellLinks] = useState(true);
+  const [focusedLinkId, setFocusedLinkId] = useState<string>();
+  const compiled = useMemo(() => compilePuzzle(puzzle), [puzzle]);
+  const effectiveActiveValues = useMemo(
+    () => activeValues.filter((value) => value <= puzzle.size),
+    [activeValues, puzzle.size],
+  );
+  const relatedUnitIndices = useMemo(
+    () => candidateUnitIndicesForCells(puzzle, selectedCells),
+    [puzzle, selectedCells],
+  );
+  const selectedUnitIndex = scope.startsWith("unit:")
+    ? Number(scope.slice(5))
+    : undefined;
+  const effectiveScope =
+    selectedUnitIndex !== undefined &&
+    !relatedUnitIndices.includes(selectedUnitIndex)
+      ? "selection"
+      : scope;
+  const scopedUnitIndices = useMemo(() => {
+    if (effectiveScope === "all")
+      return compiled.units.map((_, index) => index);
+    if (
+      selectedUnitIndex !== undefined &&
+      Number.isInteger(selectedUnitIndex) &&
+      compiled.units[selectedUnitIndex] !== undefined
+    ) {
+      return [selectedUnitIndex];
+    }
+    return relatedUnitIndices;
+  }, [compiled.units, effectiveScope, relatedUnitIndices, selectedUnitIndex]);
+  const scopedCells = useMemo(() => {
+    if (effectiveScope === "selection") return [...new Set(selectedCells)];
+    return [
+      ...new Set(
+        scopedUnitIndices.flatMap(
+          (unitIndex) => compiled.units[unitIndex]?.cells ?? [],
+        ),
+      ),
+    ];
+  }, [compiled.units, effectiveScope, scopedUnitIndices, selectedCells]);
+  const cellInspections = useMemo(
+    () => inspectCandidateCells(puzzle, candidateMasks, selectedCells),
+    [candidateMasks, puzzle, selectedCells],
+  );
+  const houseInspections = useMemo(
+    () =>
+      inspectCandidateHouses(puzzle, values, candidateMasks, scopedUnitIndices),
+    [candidateMasks, puzzle, scopedUnitIndices, values],
+  );
+  const links = useMemo(
+    () =>
+      deriveCandidateLinks(puzzle, candidateMasks, {
+        unitIndices: scopedUnitIndices,
+        cellIndices: scopedCells,
+        ...(effectiveActiveValues.length === 0
+          ? {}
+          : { values: effectiveActiveValues }),
+        includeCellLinks,
+      }).filter(({ kind }) => (kind === "strong" ? showStrong : showWeak)),
+    [
+      candidateMasks,
+      effectiveActiveValues,
+      includeCellLinks,
+      puzzle,
+      scopedCells,
+      scopedUnitIndices,
+      showStrong,
+      showWeak,
+    ],
+  );
+  const focusedLink = links.find(({ id }) => id === focusedLinkId);
+  const visibleLinks = useMemo(
+    () =>
+      focusedLink === undefined
+        ? links.slice(0, OVERLAY_LINK_LIMIT)
+        : [focusedLink],
+    [focusedLink, links],
+  );
+  const candidateCells = useMemo(() => {
+    if (effectiveActiveValues.length === 0) return [];
+    return candidateCellsForValues(candidateMasks, effectiveActiveValues);
+  }, [candidateMasks, effectiveActiveValues]);
+  const overlay = useMemo<CandidateOverlay>(
+    () => ({
+      activeValues: effectiveActiveValues,
+      candidateCells,
+      links: visibleLinks,
+    }),
+    [candidateCells, effectiveActiveValues, visibleLinks],
+  );
+
+  useEffect(() => {
+    onOverlayChange?.(overlay);
+  }, [onOverlayChange, overlay]);
+  useEffect(
+    () => () => {
+      onOverlayChange?.(undefined);
+    },
+    [onOverlayChange],
+  );
+
+  const toggleValue = (value: number) => {
+    setFocusedLinkId(undefined);
+    setActiveValues((current) => {
+      const valid = current.filter((candidate) => candidate <= puzzle.size);
+      return valid.includes(value)
+        ? valid.filter((candidate) => candidate !== value)
+        : [...valid, value].sort((a, b) => a - b);
+    });
+  };
+  const strongCount = links.filter(({ kind }) => kind === "strong").length;
+  const weakCount = links.length - strongCount;
+
+  return (
+    <section
+      className="candidate-lab stack"
+      aria-labelledby="candidate-lab-title"
+    >
+      <div>
+        <p className="eyebrow">Candidate graph</p>
+        <h3 id="candidate-lab-title">Links and houses</h3>
+        <p className="muted">
+          Inspect legal candidates without changing any notes. A solid line is
+          strong (at least one endpoint is true); a dashed line is weak (both
+          endpoints cannot be true).
+        </p>
+      </div>
+
+      <fieldset className="candidate-filter">
+        <legend>Digit filters</legend>
+        <div
+          className={`candidate-filter__digits${puzzle.size > 9 ? " candidate-filter__digits--wide" : ""}`}
+        >
+          <button
+            type="button"
+            className={effectiveActiveValues.length === 0 ? "is-active" : ""}
+            aria-pressed={effectiveActiveValues.length === 0}
+            onClick={() => {
+              setActiveValues([]);
+              setFocusedLinkId(undefined);
+            }}
+          >
+            All
+          </button>
+          {Array.from({ length: puzzle.size }, (_, index) => index + 1).map(
+            (value) => (
+              <button
+                key={value}
+                type="button"
+                className={
+                  effectiveActiveValues.includes(value) ? "is-active" : ""
+                }
+                aria-label={`Filter candidate ${symbolFor(value, puzzle.size)}`}
+                aria-pressed={effectiveActiveValues.includes(value)}
+                onClick={() => toggleValue(value)}
+              >
+                {symbolFor(value, puzzle.size)}
+              </button>
+            ),
+          )}
+        </div>
+      </fieldset>
+
+      <div className="candidate-lab__controls">
+        <label>
+          Inspect
+          <select
+            aria-label="Candidate house scope"
+            value={effectiveScope}
+            onChange={(event) => {
+              setScope(event.target.value);
+              setFocusedLinkId(undefined);
+            }}
+          >
+            <option value="selection">
+              Selected cells and touching houses
+            </option>
+            {relatedUnitIndices.map((unitIndex) => (
+              <option key={unitIndex} value={`unit:${String(unitIndex)}`}>
+                {houseLabel(compiled.units[unitIndex]!)}
+              </option>
+            ))}
+            <option value="all">Whole grid</option>
+          </select>
+        </label>
+        <label className="check-row">
+          <input
+            type="checkbox"
+            checked={showStrong}
+            onChange={(event) => {
+              setShowStrong(event.target.checked);
+              setFocusedLinkId(undefined);
+            }}
+          />
+          Strong links
+        </label>
+        <label className="check-row">
+          <input
+            type="checkbox"
+            checked={showWeak}
+            onChange={(event) => {
+              setShowWeak(event.target.checked);
+              setFocusedLinkId(undefined);
+            }}
+          />
+          Weak links
+        </label>
+        <label className="check-row">
+          <input
+            type="checkbox"
+            checked={includeCellLinks}
+            onChange={(event) => {
+              setIncludeCellLinks(event.target.checked);
+              setFocusedLinkId(undefined);
+            }}
+          />
+          Links inside cells
+        </label>
+      </div>
+
+      <div className="metric-row" aria-live="polite">
+        <span>
+          Candidate cells <strong>{candidateCells.length}</strong>
+        </span>
+        <span>
+          Strong links <strong>{strongCount}</strong>
+        </span>
+        <span>
+          Weak links <strong>{weakCount}</strong>
+        </span>
+      </div>
+
+      <section
+        className="candidate-inspection"
+        aria-labelledby="selected-candidates-title"
+      >
+        <h4 id="selected-candidates-title">Selected cells</h4>
+        <div className="candidate-cell-list">
+          {cellInspections.map((inspection) => (
+            <article key={inspection.cell}>
+              <strong>{cellLabel(inspection.cell, puzzle.size)}</strong>
+              <span>
+                {inspection.values.length === 0
+                  ? values[inspection.cell]
+                    ? `Filled ${symbolFor(values[inspection.cell]!, puzzle.size)}`
+                    : "No legal candidates"
+                  : inspection.values
+                      .map((value) => symbolFor(value, puzzle.size))
+                      .join(" ")}
+              </span>
+              <small>{inspection.houseLabels.join(" · ")}</small>
+            </article>
+          ))}
+        </div>
+      </section>
+
+      <section
+        className="candidate-inspection"
+        aria-labelledby="house-candidates-title"
+      >
+        <h4 id="house-candidates-title">House positions</h4>
+        <div className="candidate-house-list">
+          {houseInspections.map((inspection) => (
+            <details
+              key={inspection.unitIndex}
+              open={houseInspections.length === 1}
+            >
+              <summary>
+                <strong>{inspection.label}</strong>
+                <span>{inspection.missingValues.length} missing</span>
+              </summary>
+              <dl>
+                {inspection.positions
+                  .filter(
+                    ({ value }) =>
+                      effectiveActiveValues.length === 0 ||
+                      effectiveActiveValues.includes(value),
+                  )
+                  .map((position) => (
+                    <div
+                      key={position.value}
+                      data-link-kind={position.linkKind}
+                    >
+                      <dt>{symbolFor(position.value, puzzle.size)}</dt>
+                      <dd>
+                        {position.cells.length === 0
+                          ? "nowhere"
+                          : position.cells
+                              .map((cell) => cellLabel(cell, puzzle.size))
+                              .join(" · ")}
+                        {position.linkKind === "strong" ? " · strong" : ""}
+                      </dd>
+                    </div>
+                  ))}
+              </dl>
+            </details>
+          ))}
+        </div>
+      </section>
+
+      <section
+        className="candidate-inspection"
+        aria-labelledby="candidate-links-title"
+      >
+        <div className="candidate-section-heading">
+          <h4 id="candidate-links-title">Visible links</h4>
+          {focusedLink !== undefined && (
+            <button
+              type="button"
+              className="text-button"
+              onClick={() => setFocusedLinkId(undefined)}
+            >
+              Show all
+            </button>
+          )}
+        </div>
+        {links.length === 0 ? (
+          <p className="muted">
+            No links match this scope and filter. Enable weak links or inspect
+            another house.
+          </p>
+        ) : (
+          <div className="candidate-link-list">
+            {links.slice(0, LINK_LIST_LIMIT).map((link) => (
+              <button
+                key={link.id}
+                type="button"
+                className={`candidate-link candidate-link--${link.kind}`}
+                aria-pressed={focusedLink?.id === link.id}
+                title={link.contexts.map(({ label }) => label).join(", ")}
+                onClick={() =>
+                  setFocusedLinkId((current) =>
+                    current === link.id ? undefined : link.id,
+                  )
+                }
+              >
+                <span>{linkLabel(link, puzzle.size)}</span>
+                <small>
+                  {link.kind} ·{" "}
+                  {link.contexts.map(({ label }) => label).join(" / ")}
+                </small>
+              </button>
+            ))}
+          </div>
+        )}
+        {links.length > LINK_LIST_LIMIT && (
+          <p className="muted">
+            Showing the first {LINK_LIST_LIMIT} of {links.length} links. Narrow
+            the digit or house filter to inspect the rest.
+          </p>
+        )}
+        {focusedLink === undefined && links.length > OVERLAY_LINK_LIMIT && (
+          <p className="muted">
+            The board overlay is capped at {OVERLAY_LINK_LIMIT} links for
+            responsiveness. Focus a listed link or narrow the filters to see a
+            precise relationship.
+          </p>
+        )}
+      </section>
+    </section>
+  );
+}

src/components/ConstraintEditor.tsx

@@ -1,4 +1,5 @@
 import { useState } from "react";
+import { cellsFormQuadruple } from "../domain/geometry";
 import type { PuzzleDefinition, VariantConstraint } from "../domain/types";
 import {
   removeKillerCagesAtCells,
@@ -19,6 +20,10 @@ interface ConstraintEditorProps {
 function describeConstraint(constraint: VariantConstraint, size: number) {
   const cell = (index: number) =>
     `r${String(Math.floor(index / size) + 1)}c${String((index % size) + 1)}`;
+  const marked = (description: string) =>
+    "negated" in constraint && constraint.negated === true
+      ? `false · ${description}`
+      : description;
   switch (constraint.type) {
     case "diagonal":
       return `${constraint.direction} diagonal`;
@@ -29,22 +34,67 @@ function describeConstraint(constraint: VariantConstraint, size: number) {
     case "non-consecutive":
       return "non-consecutive";
     case "killer-cage":
-      return `${String(constraint.sum)} cage · ${String(constraint.cells.length)} cells`;
+      return marked(
+        `${String(constraint.sum)} cage · ${String(constraint.cells.length)} cells${constraint.noRepeat === false ? " · repeats allowed" : ""}`,
+      );
     case "thermo":
     case "renban":
     case "palindrome":
-      return `${constraint.type} · ${String(constraint.cells.length)} cells`;
+      return marked(
+        `${constraint.type} · ${String(constraint.cells.length)} cells`,
+      );
     case "arrow":
-      return `arrow · ${String(constraint.bulb.length)} bulb / ${String(constraint.line.length)} line`;
+      return marked(
+        `arrow · ${String(constraint.bulb.length)} bulb / ${String(constraint.line.length)} line`,
+      );
     case "kropki":
-      return `${constraint.kind} dot · ${cell(constraint.a)}–${cell(constraint.b)}`;
+      return marked(
+        `${constraint.kind} dot · ${cell(constraint.a)}–${cell(constraint.b)}`,
+      );
     case "xv":
-      return `sum ${String(constraint.total)} pair · ${cell(constraint.a)}–${cell(constraint.b)}`;
+      return marked(
+        `sum ${String(constraint.total)} pair · ${cell(constraint.a)}–${cell(constraint.b)}`,
+      );
     case "inequality":
-      return `${cell(constraint.lesser)} < ${cell(constraint.greater)}`;
+      return marked(`${cell(constraint.lesser)} < ${cell(constraint.greater)}`);
+    case "x-sum":
+      return marked(
+        `Σ${String(constraint.sum)} · ${constraint.side} ${String(constraint.index + 1)}`,
+      );
+    case "skyscraper":
+      return marked(
+        `skyscraper ${String(constraint.count)} · ${constraint.side} ${String(constraint.index + 1)}`,
+      );
+    case "quadruple":
+      return marked(
+        `quadruple ${constraint.digits.join("")} · ${String(constraint.cells.length)} cells`,
+      );
+    case "maximum":
+      return marked(`maximum · ${cell(constraint.cell)}`);
   }
 }
 
+function supportsPolarity(constraint: VariantConstraint): boolean {
+  return !["diagonal", "anti-knight", "anti-king", "non-consecutive"].includes(
+    constraint.type,
+  );
+}
+
+function parseClueDigits(text: string, size: number): number[] {
+  const trimmed = text.trim();
+  if (!trimmed) return [];
+  const rawTokens = trimmed.split(/[\s,;]+/u).filter(Boolean);
+  const tokens =
+    size <= 9 && rawTokens.length === 1 && /^\d{2,4}$/u.test(rawTokens[0]!)
+      ? [...rawTokens[0]!]
+      : rawTokens;
+  return tokens.map((token) =>
+    /^[A-G]$/iu.test(token)
+      ? token.toUpperCase().charCodeAt(0) - 55
+      : Number(token),
+  );
+}
+
 export function ConstraintEditor({
   puzzle,
   selection,
@@ -55,23 +105,55 @@ export function ConstraintEditor({
   busy,
 }: ConstraintEditorProps) {
   const [cageSum, setCageSum] = useState(10);
+  const [cageAllowsRepeats, setCageAllowsRepeats] = useState(false);
   const [region, setRegion] = useState(1);
+  const [newCluesAreFalse, setNewCluesAreFalse] = useState(false);
+  const [quadrupleDigits, setQuadrupleDigits] = useState("1, 2, 3");
+  const [outsideType, setOutsideType] = useState<"x-sum" | "skyscraper">(
+    "x-sum",
+  );
+  const [outsideSide, setOutsideSide] = useState<
+    "top" | "right" | "bottom" | "left"
+  >("top");
+  const [outsideLine, setOutsideLine] = useState(1);
+  const [outsideValue, setOutsideValue] = useState(3);
   const constraints = puzzle.constraints ?? [];
 
   const append = (constraint: VariantConstraint) =>
-    onChange({ ...puzzle, constraints: [...constraints, constraint] });
+    onChange({
+      ...puzzle,
+      constraints: [
+        ...constraints,
+        supportsPolarity(constraint) && newCluesAreFalse
+          ? ({ ...constraint, negated: true } as VariantConstraint)
+          : constraint,
+      ],
+    });
   const need = (count: number) => selection.length === count;
   const atLeast = (count: number) => selection.length >= count;
   const cageCellCount = Math.max(1, selection.length);
-  const minimumCageSum = (cageCellCount * (cageCellCount + 1)) / 2;
+  const minimumCageSum = cageAllowsRepeats
-  const maximumCageSum =
+    ? cageCellCount
-    (cageCellCount * (2 * puzzle.size - cageCellCount + 1)) / 2;
+    : (cageCellCount * (cageCellCount + 1)) / 2;
+  const maximumCageSum = cageAllowsRepeats
+    ? cageCellCount * puzzle.size
+    : (cageCellCount * (2 * puzzle.size - cageCellCount + 1)) / 2;
   const validCage =
     selection.length >= 1 &&
     selection.length <= puzzle.size &&
     Number.isInteger(cageSum) &&
-    cageSum >= minimumCageSum &&
+    (newCluesAreFalse
-    cageSum <= maximumCageSum;
+      ? cageSum >= 1 && cageSum <= puzzle.size ** 3
+      : cageSum >= minimumCageSum && cageSum <= maximumCageSum);
+  const parsedQuadrupleDigits = parseClueDigits(quadrupleDigits, puzzle.size);
+  const validQuadruple =
+    cellsFormQuadruple(puzzle.size, selection) &&
+    parsedQuadrupleDigits.length >= 1 &&
+    parsedQuadrupleDigits.length <= 4 &&
+    parsedQuadrupleDigits.length <= selection.length &&
+    parsedQuadrupleDigits.every(
+      (digit) => Number.isInteger(digit) && digit >= 1 && digit <= puzzle.size,
+    );
   const selectedCageExists = selectionTouchesKillerCage(constraints, selection);
 
   const toggleGlobal = (
@@ -154,13 +236,21 @@ export function ConstraintEditor({
           Selection order defines lines and pair direction. Shift-click or drag
           to build a selection.
         </p>
+        <label className="check-row">
+          <input
+            type="checkbox"
+            checked={newCluesAreFalse}
+            onChange={(event) => setNewCluesAreFalse(event.target.checked)}
+          />
+          Newly added clues must be false (Wrogn mode)
+        </label>
         <div className="inline-fields">
           <label className="compact-field">
             Cage sum
             <input
               type="number"
-              min={minimumCageSum}
+              min={newCluesAreFalse ? 1 : minimumCageSum}
-              max={maximumCageSum}
+              max={newCluesAreFalse ? puzzle.size ** 3 : maximumCageSum}
               value={cageSum}
               onChange={(event) => setCageSum(Number(event.target.value))}
             />
@@ -175,6 +265,8 @@ export function ConstraintEditor({
                   type: "killer-cage",
                   cells: selection,
                   sum: cageSum,
+                  ...(cageAllowsRepeats ? { noRepeat: false } : {}),
+                  ...(newCluesAreFalse ? { negated: true } : {}),
                 }),
               })
             }
@@ -195,6 +287,14 @@ export function ConstraintEditor({
             Remove selected cage
           </button>
         </div>
+        <label className="check-row">
+          <input
+            type="checkbox"
+            checked={cageAllowsRepeats}
+            onChange={(event) => setCageAllowsRepeats(event.target.checked)}
+          />
+          Cage digits may repeat
+        </label>
         <p className="muted">
           Adding replaces any cage touching the selection. Removing clears every
           cage touching a selected cell.
@@ -316,7 +416,41 @@ export function ConstraintEditor({
           >
             1st &gt; 2nd (inequality)
           </button>
+          <button
+            type="button"
+            disabled={!need(1)}
+            onClick={() => append({ type: "maximum", cell: selection[0]! })}
+          >
+            Maximum cell
+          </button>
         </div>
+        <div className="inline-fields">
+          <label className="compact-field">
+            Quadruple digits
+            <input
+              value={quadrupleDigits}
+              placeholder="1, 3, 8"
+              onChange={(event) => setQuadrupleDigits(event.target.value)}
+            />
+          </label>
+          <button
+            type="button"
+            disabled={!validQuadruple}
+            onClick={() =>
+              append({
+                type: "quadruple",
+                cells: selection,
+                digits: parsedQuadrupleDigits,
+              })
+            }
+          >
+            Add quadruple
+          </button>
+        </div>
+        <p className="muted">
+          Select the four cells meeting at one grid intersection for a
+          quadruple.
+        </p>
         <div className="inline-fields">
           <label className="compact-field">
             Region
@@ -342,6 +476,120 @@ export function ConstraintEditor({
         </div>
       </section>
 
+      <section className="panel-section">
+        <p className="eyebrow">Outside clues</p>
+        <h3>X-sums and skyscrapers</h3>
+        <p className="muted">
+          Choose the edge and row or column. Σ badges are X-sums; ▥ badges are
+          visibility counts.
+        </p>
+        <div className="inline-fields outside-clue-fields">
+          <label className="compact-field">
+            Type
+            <select
+              value={outsideType}
+              onChange={(event) =>
+                setOutsideType(event.target.value as "x-sum" | "skyscraper")
+              }
+            >
+              <option value="x-sum">X-sum</option>
+              <option value="skyscraper">Skyscraper</option>
+            </select>
+          </label>
+          <label className="compact-field">
+            Side
+            <select
+              value={outsideSide}
+              onChange={(event) =>
+                setOutsideSide(
+                  event.target.value as "top" | "right" | "bottom" | "left",
+                )
+              }
+            >
+              <option value="top">Top</option>
+              <option value="right">Right</option>
+              <option value="bottom">Bottom</option>
+              <option value="left">Left</option>
+            </select>
+          </label>
+          <label className="compact-field">
+            Row / column
+            <input
+              type="number"
+              min="1"
+              max={puzzle.size}
+              value={outsideLine}
+              onChange={(event) => setOutsideLine(Number(event.target.value))}
+            />
+          </label>
+          <label className="compact-field">
+            Clue
+            <input
+              type="number"
+              min="1"
+              max={
+                newCluesAreFalse
+                  ? puzzle.size ** 4
+                  : outsideType === "x-sum"
+                    ? (puzzle.size * (puzzle.size + 1)) / 2
+                    : puzzle.size
+              }
+              value={outsideValue}
+              onChange={(event) => setOutsideValue(Number(event.target.value))}
+            />
+          </label>
+          <button
+            type="button"
+            disabled={
+              !Number.isInteger(outsideLine) ||
+              outsideLine < 1 ||
+              outsideLine > puzzle.size ||
+              !Number.isInteger(outsideValue) ||
+              outsideValue < 1 ||
+              outsideValue >
+                (newCluesAreFalse
+                  ? puzzle.size ** 4
+                  : outsideType === "x-sum"
+                    ? (puzzle.size * (puzzle.size + 1)) / 2
+                    : puzzle.size)
+            }
+            onClick={() => {
+              const clue: VariantConstraint =
+                outsideType === "x-sum"
+                  ? {
+                      type: "x-sum",
+                      side: outsideSide,
+                      index: outsideLine - 1,
+                      sum: outsideValue,
+                    }
+                  : {
+                      type: "skyscraper",
+                      side: outsideSide,
+                      index: outsideLine - 1,
+                      count: outsideValue,
+                    };
+              const withoutExisting = constraints.filter(
+                (constraint) =>
+                  constraint.type !== outsideType ||
+                  constraint.side !== outsideSide ||
+                  constraint.index !== outsideLine - 1,
+              );
+              onChange({
+                ...puzzle,
+                constraints: [
+                  ...withoutExisting,
+                  newCluesAreFalse
+                    ? ({ ...clue, negated: true } as VariantConstraint)
+                    : clue,
+                ],
+              });
+            }}
+          >
+            Add / replace outside clue
+          </button>
+        </div>
+      </section>
+
       <section className="panel-section">
         <p className="eyebrow">Global rules</p>
         <div className="button-grid">
@@ -398,27 +646,107 @@ export function ConstraintEditor({
 
       {constraints.length > 0 && (
         <section className="panel-section">
-          <p className="eyebrow">Constraints</p>
+          <div className="section-heading">
+            <p className="eyebrow">Constraints</p>
+            <div className="constraint-batch-actions">
+              <button
+                className="text-button"
+                type="button"
+                onClick={() =>
+                  onChange({
+                    ...puzzle,
+                    constraints: constraints.map((constraint) =>
+                      supportsPolarity(constraint)
+                        ? ({
+                            ...constraint,
+                            negated: true,
+                          } as VariantConstraint)
+                        : constraint,
+                    ),
+                  })
+                }
+              >
+                Make all clues false
+              </button>
+              <button
+                className="text-button"
+                type="button"
+                onClick={() =>
+                  onChange({
+                    ...puzzle,
+                    constraints: constraints.map((constraint) => {
+                      if (!supportsPolarity(constraint)) return constraint;
+                      const cleaned = { ...constraint } as VariantConstraint & {
+                        negated?: boolean;
+                      };
+                      delete cleaned.negated;
+                      return cleaned;
+                    }),
+                  })
+                }
+              >
+                Make all clues true
+              </button>
+            </div>
+          </div>
           <ul className="constraint-list">
-            {constraints.map((constraint, index) => (
+            {constraints.map((constraint, index) => {
-              <li key={`${constraint.type}-${String(index)}`}>
+              const description = describeConstraint(constraint, puzzle.size);
-                <span>{describeConstraint(constraint, puzzle.size)}</span>
+              const negated =
-                <button
+                "negated" in constraint && constraint.negated === true;
-                  className="text-button danger"
+              return (
-                  type="button"
+                <li key={`${constraint.type}-${String(index)}`}>
-                  onClick={() =>
+                  <span>{description}</span>
-                    onChange({
+                  <span className="constraint-actions">
-                      ...puzzle,
+                    {supportsPolarity(constraint) && (
-                      constraints: constraints.filter(
+                      <button
-                        (_, item) => item !== index,
+                        className="text-button"
-                      ),
+                        type="button"
-                    })
+                        aria-label={`${negated ? "Require true for" : "Require false for"} ${description}`}
-                  }
+                        onClick={() =>
-                >
+                          onChange({
-                  Remove
+                            ...puzzle,
-                </button>
+                            constraints: constraints.map((item, itemIndex) => {
-              </li>
+                              if (itemIndex !== index) return item;
-            ))}
+                              if ("negated" in item && item.negated === true) {
+                                const cleaned = {
+                                  ...item,
+                                } as VariantConstraint & {
+                                  negated?: boolean;
+                                };
+                                delete cleaned.negated;
+                                return cleaned;
+                              }
+                              return {
+                                ...item,
+                                negated: true,
+                              } as VariantConstraint;
+                            }),
+                          })
+                        }
+                      >
+                        {negated ? "Require true" : "Require false"}
+                      </button>
+                    )}
+                    <button
+                      className="text-button danger"
+                      type="button"
+                      aria-label={`Remove ${description}`}
+                      onClick={() =>
+                        onChange({
+                          ...puzzle,
+                          constraints: constraints.filter(
+                            (_, item) => item !== index,
+                          ),
+                        })
+                      }
+                    >
+                      Remove
+                    </button>
+                  </span>
+                </li>
+              );
+            })}
           </ul>
         </section>
       )}

src/components/GameplayHistoryDialog.tsx

@@ -0,0 +1,295 @@
+import { useMemo, useState, type FormEvent } from "react";
+import {
+  activeHypothesis,
+  gameplayMoment,
+  MAIN_BRANCH_ID,
+  type GameplayHistory,
+} from "../state/playHistory";
+import { Modal } from "./Modal";
+
+interface GameplayHistoryDialogProps {
+  readonly open: boolean;
+  readonly history: GameplayHistory;
+  readonly replayMomentId?: string;
+  readonly onClose: () => void;
+  readonly onCreateSavepoint: (name: string) => void;
+  readonly onRestoreSavepoint: (savepointId: string) => void;
+  readonly onDeleteSavepoint: (savepointId: string) => void;
+  readonly onStartHypothesis: (name: string, fromMomentId?: string) => void;
+  readonly onFinishHypothesis: (decision: "keep" | "discard") => void;
+  readonly onReplayMoment: (momentId: string) => void;
+  readonly onReturnLive: () => void;
+}
+
+function formatElapsed(seconds: number): string {
+  const hours = Math.floor(seconds / 3_600);
+  const minutes = Math.floor((seconds % 3_600) / 60);
+  const rest = seconds % 60;
+  return [hours, minutes, rest]
+    .map((part) => String(part).padStart(2, "0"))
+    .join(":");
+}
+
+export function GameplayHistoryDialog({
+  open,
+  history,
+  replayMomentId,
+  onClose,
+  onCreateSavepoint,
+  onRestoreSavepoint,
+  onDeleteSavepoint,
+  onStartHypothesis,
+  onFinishHypothesis,
+  onReplayMoment,
+  onReturnLive,
+}: GameplayHistoryDialogProps) {
+  const [hypothesisName, setHypothesisName] = useState("");
+  const [savepointName, setSavepointName] = useState("");
+  const hypothesis = activeHypothesis(history);
+  const replayMoment = replayMomentId
+    ? gameplayMoment(history, replayMomentId)
+    : undefined;
+  const replayIndex = replayMoment
+    ? history.moments.findIndex((moment) => moment.id === replayMoment.id)
+    : history.moments.length - 1;
+  const branchNames = useMemo(
+    () =>
+      new Map([
+        [MAIN_BRANCH_ID, "Main solve"],
+        ...history.branches.map((branch) => [branch.id, branch.name] as const),
+      ]),
+    [history.branches],
+  );
+
+  const submitHypothesis = (event: FormEvent) => {
+    event.preventDefault();
+    const name = hypothesisName.trim();
+    if (!name) return;
+    onStartHypothesis(name, replayMoment?.id);
+    setHypothesisName("");
+  };
+
+  const submitSavepoint = (event: FormEvent) => {
+    event.preventDefault();
+    const name = savepointName.trim();
+    if (!name) return;
+    onCreateSavepoint(name);
+    setSavepointName("");
+  };
+
+  return (
+    <Modal
+      open={open}
+      title="Branches, savepoints and replay"
+      onClose={onClose}
+      wide
+    >
+      <div className="history-dialog-grid">
+        <div className="stack">
+          <section className="panel-section history-section">
+            <div>
+              <p className="eyebrow">Hypotheses</p>
+              <h3>Try a path without losing your solve</h3>
+            </div>
+            {hypothesis ? (
+              <div className="hypothesis-active" role="status">
+                <div>
+                  <strong>{hypothesis.name}</strong>
+                  <span>Every move is being kept on this branch.</span>
+                </div>
+                <div className="action-row">
+                  <button
+                    type="button"
+                    onClick={() => onFinishHypothesis("keep")}
+                  >
+                    Keep changes
+                  </button>
+                  <button
+                    type="button"
+                    className="danger"
+                    onClick={() => onFinishHypothesis("discard")}
+                  >
+                    Discard and return
+                  </button>
+                </div>
+              </div>
+            ) : (
+              <form className="history-name-form" onSubmit={submitHypothesis}>
+                <label>
+                  Hypothesis name
+                  <input
+                    value={hypothesisName}
+                    maxLength={80}
+                    placeholder="e.g. Assume r4c7 is 8"
+                    onChange={(event) => setHypothesisName(event.target.value)}
+                  />
+                </label>
+                <button type="submit" disabled={!hypothesisName.trim()}>
+                  {replayMoment ? "Branch from this step" : "Start hypothesis"}
+                </button>
+              </form>
+            )}
+            {history.branches.length > 0 && (
+              <ul className="branch-list" aria-label="Hypothesis branches">
+                {history.branches.map((branch) => (
+                  <li key={branch.id}>
+                    <span>{branch.name}</span>
+                    <span
+                      className={`branch-status branch-status--${branch.status}`}
+                    >
+                      {branch.status}
+                    </span>
+                  </li>
+                ))}
+              </ul>
+            )}
+          </section>
+
+          <section className="panel-section history-section">
+            <div>
+              <p className="eyebrow">Named savepoints</p>
+              <h3>Return to a deliberate checkpoint</h3>
+            </div>
+            <form className="history-name-form" onSubmit={submitSavepoint}>
+              <label>
+                Savepoint name
+                <input
+                  value={savepointName}
+                  maxLength={80}
+                  disabled={replayMoment !== undefined}
+                  placeholder="e.g. Before the long chain"
+                  onChange={(event) => setSavepointName(event.target.value)}
+                />
+              </label>
+              <button
+                type="submit"
+                disabled={!savepointName.trim() || replayMoment !== undefined}
+              >
+                Save current grid
+              </button>
+            </form>
+            {history.savepoints.length === 0 ? (
+              <p className="muted">No savepoints yet.</p>
+            ) : (
+              <ul className="savepoint-list" aria-label="Named savepoints">
+                {history.savepoints.map((savepoint) => (
+                  <li key={savepoint.id}>
+                    <div>
+                      <strong>{savepoint.name}</strong>
+                      <span>
+                        {formatElapsed(savepoint.state.elapsedSeconds)}
+                      </span>
+                    </div>
+                    <div className="action-row">
+                      <button
+                        type="button"
+                        disabled={replayMoment !== undefined}
+                        onClick={() => onRestoreSavepoint(savepoint.id)}
+                      >
+                        Restore
+                      </button>
+                      <button
+                        type="button"
+                        className="danger"
+                        aria-label={`Delete savepoint ${savepoint.name}`}
+                        onClick={() => onDeleteSavepoint(savepoint.id)}
+                      >
+                        Delete
+                      </button>
+                    </div>
+                  </li>
+                ))}
+              </ul>
+            )}
+          </section>
+        </div>
+
+        <section className="panel-section history-section history-replay">
+          <div className="section-heading">
+            <div>
+              <p className="eyebrow">Replay</p>
+              <h3>Review every recorded state</h3>
+            </div>
+            <span className="status-pill">
+              {String(Math.max(0, history.moments.length - 1))} changes
+            </span>
+          </div>
+          {replayMoment ? (
+            <p className="callout" role="status">
+              Viewing “{replayMoment.label}”. The board is read-only until you
+              return live or branch from this step.
+            </p>
+          ) : (
+            <p className="muted">
+              Choose a step to inspect its complete grid, notes, colours and
+              elapsed time.
+            </p>
+          )}
+          <div className="action-row history-replay-controls">
+            <button
+              type="button"
+              disabled={hypothesis !== undefined || replayIndex <= 0}
+              onClick={() =>
+                onReplayMoment(history.moments[replayIndex - 1]!.id)
+              }
+            >
+              Previous step
+            </button>
+            <button
+              type="button"
+              disabled={
+                replayMoment === undefined ||
+                hypothesis !== undefined ||
+                replayIndex >= history.moments.length - 1
+              }
+              onClick={() =>
+                onReplayMoment(history.moments[replayIndex + 1]!.id)
+              }
+            >
+              Next step
+            </button>
+            <button
+              type="button"
+              disabled={replayMoment === undefined}
+              onClick={onReturnLive}
+            >
+              Return to live grid
+            </button>
+          </div>
+          <ol className="history-list" aria-label="Solve history">
+            {[...history.moments].reverse().map((moment) => {
+              const isReplay = moment.id === replayMoment?.id;
+              const isCurrent =
+                replayMoment === undefined &&
+                moment.id === history.currentMomentId;
+              return (
+                <li key={moment.id}>
+                  <button
+                    type="button"
+                    className={isReplay || isCurrent ? "is-current" : ""}
+                    disabled={hypothesis !== undefined}
+                    aria-current={isReplay || isCurrent ? "step" : undefined}
+                    onClick={() =>
+                      isCurrent ? onReturnLive() : onReplayMoment(moment.id)
+                    }
+                  >
+                    <span className="history-step-number">
+                      {String(moment.sequence).padStart(2, "0")}
+                    </span>
+                    <span className="history-step-copy">
+                      <strong>{moment.label}</strong>
+                      <span>
+                        {branchNames.get(moment.branchId) ?? "Hypothesis"} ·{" "}
+                        {formatElapsed(moment.state.elapsedSeconds)}
+                      </span>
+                    </span>
+                  </button>
+                </li>
+              );
+            })}
+          </ol>
+        </section>
+      </div>
+    </Modal>
+  );
+}

src/components/GeneratorWorkspace.tsx

@@ -1,11 +1,13 @@
 import { useMemo, useState, type FormEvent } from "react";
 import {
   GENERATOR_VARIANTS,
+  PRACTICE_TECHNIQUES,
   type DifficultyAssessment,
   type GeneratedVariantPuzzle,
   type GenerationDifficultyTarget,
   type GeneratorVariant,
   type GenerateVariantOptions,
+  type PracticeTechnique,
 } from "../solver";
 
 const difficultyTargets: readonly GenerationDifficultyTarget[] = [
@@ -49,6 +51,10 @@ export function GeneratorWorkspace({
   const [symmetry, setSymmetry] = useState<"none" | "rotational">("rotational");
   const [constraintCount, setConstraintCount] = useState(8);
   const [seed, setSeed] = useState("");
+  const [requiredTechnique, setRequiredTechnique] = useState<
+    PracticeTechnique | ""
+  >("");
+  const [maxTechniqueAttempts, setMaxTechniqueAttempts] = useState(10);
   const usesMarkingCount = ![
     "classic",
     "diagonal",
@@ -66,6 +72,9 @@ export function GeneratorWorkspace({
       targetDifficulty,
       symmetry,
       ...(usesMarkingCount ? { constraintCount } : {}),
+      ...(requiredTechnique === ""
+        ? {}
+        : { requiredTechnique, maxTechniqueAttempts }),
       seed: seed.trim() || `local-${Date.now().toString(36)}`,
     });
   };
@@ -101,6 +110,11 @@ export function GeneratorWorkspace({
                 ) {
                   setSize(nextDefinition.supportedSizes[0]);
                 }
+                if (next !== "killer") {
+                  setRequiredTechnique((current) =>
+                    current === "killer-cage" ? "" : current,
+                  );
+                }
               }}
             >
               {GENERATOR_VARIANTS.map((item) => (
@@ -175,6 +189,41 @@ export function GeneratorWorkspace({
               onChange={(event) => setSeed(event.target.value)}
             />
           </label>
+          <label>
+            Practice technique
+            <select
+              value={requiredTechnique}
+              onChange={(event) =>
+                setRequiredTechnique(
+                  event.target.value as PracticeTechnique | "",
+                )
+              }
+            >
+              <option value="">No required technique</option>
+              {PRACTICE_TECHNIQUES.filter(
+                (technique) =>
+                  technique !== "killer-cage" || variant === "killer",
+              ).map((technique) => (
+                <option key={technique} value={technique}>
+                  {techniqueLabel(technique)}
+                </option>
+              ))}
+            </select>
+          </label>
+          {requiredTechnique !== "" && (
+            <label>
+              Mining attempts
+              <input
+                type="number"
+                min="1"
+                max="32"
+                value={maxTechniqueAttempts}
+                onChange={(event) =>
+                  setMaxTechniqueAttempts(Number(event.target.value))
+                }
+              />
+            </label>
+          )}
         </div>
         <p className="generator-description">{definition.description}</p>
         <div className="action-row">
@@ -187,7 +236,9 @@ export function GeneratorWorkspace({
         </div>
         <p className="muted">
           Difficulty is an estimate from reproducible solver evidence, not a
-          universal promise. Uniqueness is never claimed after a safety limit.
+          universal promise. Technique practice only returns a puzzle whose
+          logical path contains the requested move. Uniqueness is never claimed
+          after a safety limit.
         </p>
       </form>
 
@@ -229,11 +280,24 @@ export function GeneratorWorkspace({
                 Markings <strong>{generation.generatedConstraintCount}</strong>
               </span>
             )}
+            {generation?.requestedTechnique && (
+              <span>
+                Practice{" "}
+                <strong>
+                  {techniqueLabel(generation.requestedTechnique)} ×
+                  {generation.difficulty.techniqueCounts[
+                    generation.requestedTechnique
+                  ] ?? 0}
+                </strong>
+              </span>
+            )}
           </div>
           <p>{assessment.summary}</p>
           {generation && (
             <p className="muted">
-              Seed: <code>{String(generation.seed)}</code>
+              Seed: <code>{String(generation.seed)}</code> · Found in{" "}
+              {generation.generationAttempts} attempt
+              {generation.generationAttempts === 1 ? "" : "s"}.
             </p>
           )}
         </section>

src/components/HelpDialog.tsx

@@ -14,11 +14,12 @@ export function HelpDialog({
           <h3>Five complementary workspaces</h3>
           <p>
             <strong>Play</strong> keeps values, two kinds of notes, colours,
-            history and elapsed time. <strong>Set</strong> edits clues and
+            branches, replay and elapsed time. <strong>Set</strong> edits clues
-            constraints. <strong>Generate</strong> constructs and rates bounded,
+            and constraints. <strong>Generate</strong> constructs and rates
-            seedable variants. <strong>Solve</strong> explains logical steps and
+            bounded, seedable variants. <strong>Solve</strong> explains logical
-            can verify uniqueness. <strong>Helpers</strong> answers focused
+            steps and can verify uniqueness. <strong>Helpers</strong> answers
-            questions without changing the board.
+            focused sum, candidate and relation questions without changing the
+            board.
           </p>
         </section>
         <section>
@@ -32,6 +33,18 @@ export function HelpDialog({
               <dt>Shift + arrows</dt>
               <dd>Extend the selection</dd>
             </div>
+            <div>
+              <dt>Home / End</dt>
+              <dd>Move to the first or last cell in the row</dd>
+            </div>
+            <div>
+              <dt>Ctrl/⌘ + Home/End</dt>
+              <dd>Move to the first or last cell in the grid</dd>
+            </div>
+            <div>
+              <dt>Page Up / Down</dt>
+              <dd>Move to the first or last row in the same column</dd>
+            </div>
             <div>
               <dt>1–9 / A–G</dt>
               <dd>Enter the selected symbol</dd>
@@ -64,13 +77,62 @@ export function HelpDialog({
             explanation.
           </p>
         </section>
+        <section>
+          <h3>Branches, savepoints and replay</h3>
+          <p>
+            Open <strong>History &amp; branches</strong> while playing to name a
+            checkpoint, isolate a hypothesis, or inspect an earlier grid.
+            Discarding a hypothesis restores its exact starting state but keeps
+            the abandoned path available in replay. Replayed grids are read-only
+            until you return live or deliberately branch from that step. This
+            working history stays in the current browser session; save the
+            puzzle to the Library for durable puzzle progress.
+          </p>
+        </section>
+        <section>
+          <h3>Sum and Candidate Labs</h3>
+          <p>
+            Sum Lab enumerates bounded combinations and, when selected board
+            cells are enabled, candidate-compatible assignments per position.
+            Required, excluded and manually eliminated combinations remain local
+            helper state. Candidate Lab inspects selected cells and houses,
+            filters one or more digits, and can overlay strong and weak links
+            without changing handwritten notes.
+          </p>
+        </section>
+        <section>
+          <h3>Aid-mémoire scratch cells</h3>
+          <p>
+            Enable the optional aid-mémoire in Play for a non-constraining row
+            or compact grid of scratch cells. Each cell has its own label and
+            accepts values, corner marks, centre marks and colours through the
+            regular keypad or keyboard. Arrow keys stay within the configured
+            grid; Home/End move within a row, Ctrl/⌘ + Home/End reach the first
+            or last cell, and Page Up/Down move to the first or last row. The
+            layout and entries are preserved with local Library progress.
+          </p>
+        </section>
+        <section>
+          <h3>Variant and false clues</h3>
+          <p>
+            The setter supports cages, lines, pair clues, X-sums, skyscrapers,
+            quadruples and maximum cells. Enable Wrogn mode to make new local
+            clues false, or switch existing clues individually or as a batch.
+            Red dashed artwork and a ≠ mark identify false clues; Σ and ▥
+            identify X-sum and skyscraper readings. A false multi-cell clue
+            often stays undecided until enough of its cells are known, so exact
+            searches for dense liar puzzles can be substantially slower.
+          </p>
+        </section>
         <section>
           <h3>Generation and ratings</h3>
           <p>
             Generation runs in a worker with explicit time and search limits. A
             requested level guides clue removal; the reported rating is then
             calculated independently from logical techniques, clue load and
-            bounded exact-search evidence. A limit never becomes a false
+            bounded exact-search evidence. Practice mode deterministically mines
+            several candidates and succeeds only when the analysed solve path
+            contains the requested technique. A limit never becomes a false
             uniqueness claim.
           </p>
         </section>
@@ -78,10 +140,21 @@ export function HelpDialog({
           <h3>Import and privacy</h3>
           <p>
             Files, text, solving and generation stay in this browser. Compact
-            grids, project JSON, share fragments and supported f-puzzles data
+            grids, project JSON, share fragments, supported f-puzzles,
-            are decoded locally. SudokuPad short IDs need its server and are
+            SudokuPad/CTC inline data and supported Penpa+ long links are
-            intentionally rejected. Review an export before sharing: titles,
+            decoded locally. Server short IDs are intentionally rejected. SVG,
-            authors, rules, solutions and progress may be included.
+            PNG and PDF rendering also stays in the browser. Review an export
+            before sharing: titles, authors, rules, solutions, progress and
+            aid-mémoire entries may be included.
+          </p>
+        </section>
+        <section>
+          <h3>Screen-reader detail</h3>
+          <p>
+            Each Sudoku cell reports its row, column, region, value or notes,
+            colour, conflict state, candidate highlights and touching variant
+            clues. The board and aid-mémoire use real row and gridcell roles;
+            their keyboard instructions are attached to the grids.
           </p>
         </section>
       </div>

src/components/HelpersWorkspace.tsx

@@ -1,11 +1,15 @@
 import { useMemo, useState } from "react";
+import type { NormalizedPuzzle } from "../domain";
 import {
   analyzeKillerCage,
+  analyzeSumLab,
   calculateResidual,
   relationPairs,
+  type CandidateOverlay,
   type RelationSpec,
 } from "../helpers";
 import { maskValues, symbolFor } from "../state/session";
+import { CandidateLab } from "./CandidateLab";
 
 function digits(text: string) {
   return [
@@ -25,18 +29,24 @@ function numbers(text: string) {
 
 export function HelpersWorkspace({
   size,
+  puzzle,
+  values,
   selectedCells,
   candidateMasks,
+  onCandidateOverlayChange,
 }: {
   size: number;
+  puzzle: NormalizedPuzzle;
+  values: readonly number[];
   selectedCells: readonly number[];
   candidateMasks: readonly number[];
+  onCandidateOverlayChange?: (overlay: CandidateOverlay | undefined) => void;
 }) {
-  const [helper, setHelper] = useState<"killer" | "residual" | "relations">(
+  const [helper, setHelper] = useState<
-    "killer",
+    "candidates" | "killer" | "sum" | "residual" | "relations"
-  );
+  >("killer");
   const [cellCount, setCellCount] = useState(2);
-  const [sum, setSum] = useState(10);
+  const [sum, setSum] = useState(Math.min(10, size + 1));
   const [allowed, setAllowed] = useState("");
   const [required, setRequired] = useState("");
   const [excluded, setExcluded] = useState("");
@@ -47,6 +57,19 @@ export function HelpersWorkspace({
   const [relation, setRelation] = useState("white");
   const [firstCandidates, setFirstCandidates] = useState("");
   const [secondCandidates, setSecondCandidates] = useState("");
+  const [sumLabCellCount, setSumLabCellCount] = useState(2);
+  const [sumLabTarget, setSumLabTarget] = useState(Math.min(10, size + 1));
+  const [sumLabMinimum, setSumLabMinimum] = useState(1);
+  const [sumLabMaximum, setSumLabMaximum] = useState(size);
+  const [sumLabRequired, setSumLabRequired] = useState("");
+  const [sumLabExcluded, setSumLabExcluded] = useState("");
+  const [sumLabRepeats, setSumLabRepeats] = useState(false);
+  const [sumLabUseCandidates, setSumLabUseCandidates] = useState(false);
+  const [sumLabShowEliminated, setSumLabShowEliminated] = useState(true);
+  const [sumLabEliminations, setSumLabEliminations] = useState<{
+    readonly scope: string;
+    readonly keys: ReadonlySet<string>;
+  }>({ scope: "", keys: new Set() });
 
   const effectiveCount =
     useBoardCandidates && selectedCells.length > 0
@@ -137,6 +160,84 @@ export function HelpersWorkspace({
     }
   }, [firstCandidates, relation, secondCandidates, size]);
 
+  const sumLabCandidateMasks = useMemo(
+    () =>
+      sumLabUseCandidates && selectedCells.length > 0
+        ? selectedCells.map((cell) => candidateMasks[cell] ?? 0)
+        : undefined,
+    [candidateMasks, selectedCells, sumLabUseCandidates],
+  );
+  const sumLabEffectiveCount =
+    sumLabCandidateMasks === undefined
+      ? sumLabCellCount
+      : sumLabCandidateMasks.length;
+  const sumLabScope = JSON.stringify({
+    count: sumLabEffectiveCount,
+    target: sumLabTarget,
+    minimum: sumLabMinimum,
+    maximum: sumLabMaximum,
+    required: sumLabRequired,
+    excluded: sumLabExcluded,
+    repeats: sumLabRepeats,
+    candidates: sumLabCandidateMasks,
+  });
+  const sumLabEliminatedKeys = useMemo(
+    () =>
+      sumLabEliminations.scope === sumLabScope
+        ? sumLabEliminations.keys
+        : new Set<string>(),
+    [sumLabEliminations, sumLabScope],
+  );
+  const sumLab = useMemo(() => {
+    try {
+      return {
+        result: analyzeSumLab({
+          cellCount: sumLabEffectiveCount,
+          target: sumLabTarget,
+          minimumDigit: sumLabMinimum,
+          maximumDigit: sumLabMaximum,
+          allowRepeats: sumLabRepeats,
+          ...(sumLabRequired.trim()
+            ? { requiredDigits: digits(sumLabRequired) }
+            : {}),
+          ...(sumLabExcluded.trim()
+            ? { excludedDigits: digits(sumLabExcluded) }
+            : {}),
+          ...(sumLabCandidateMasks === undefined
+            ? {}
+            : { candidateMasks: sumLabCandidateMasks }),
+          eliminatedKeys: sumLabEliminatedKeys,
+        }),
+      };
+    } catch (error) {
+      return {
+        error:
+          error instanceof Error ? error.message : "Invalid Sum Lab input.",
+      };
+    }
+  }, [
+    sumLabCandidateMasks,
+    sumLabEffectiveCount,
+    sumLabExcluded,
+    sumLabMaximum,
+    sumLabMinimum,
+    sumLabEliminatedKeys,
+    sumLabRepeats,
+    sumLabRequired,
+    sumLabTarget,
+  ]);
+
+  const toggleSumLabCombination = (key: string) => {
+    setSumLabEliminations((current) => {
+      const keys = new Set(
+        current.scope === sumLabScope ? current.keys : undefined,
+      );
+      if (keys.has(key)) keys.delete(key);
+      else keys.add(key);
+      return { scope: sumLabScope, keys };
+    });
+  };
+
   return (
     <div className="helpers-workspace stack">
       <div>
@@ -151,6 +252,8 @@ export function HelpersWorkspace({
         {(
           [
             ["killer", "Killer combinations"],
+            ["sum", "Sum Lab"],
+            ["candidates", "Candidate links"],
             ["residual", `${String((size * (size + 1)) / 2)}-rule residual`],
             ["relations", "Pair relations"],
           ] as const
@@ -168,6 +271,238 @@ export function HelpersWorkspace({
         ))}
       </div>
 
+      {helper === "candidates" && (
+        <div className="helper-card">
+          <CandidateLab
+            puzzle={puzzle}
+            values={values}
+            candidateMasks={candidateMasks}
+            selectedCells={selectedCells}
+            onOverlayChange={onCandidateOverlayChange}
+          />
+        </div>
+      )}
+
+      {helper === "sum" && (
+        <section className="helper-card">
+          <div className="section-heading">
+            <div>
+              <h3>Generalized Sum Lab</h3>
+              <p className="muted">
+                Explore sums with custom ranges and repeats. Select board cells
+                first to filter cell orderings through their live candidates.
+              </p>
+            </div>
+            <button
+              type="button"
+              className="text-button"
+              disabled={sumLabEliminatedKeys.size === 0}
+              onClick={() =>
+                setSumLabEliminations({
+                  scope: sumLabScope,
+                  keys: new Set(),
+                })
+              }
+            >
+              Restore all
+            </button>
+          </div>
+          <div className="helper-controls sum-lab-controls">
+            <label>
+              Cell count
+              <input
+                type="number"
+                min="1"
+                max="25"
+                value={sumLabEffectiveCount}
+                disabled={sumLabCandidateMasks !== undefined}
+                onChange={(event) =>
+                  setSumLabCellCount(Number(event.target.value))
+                }
+              />
+            </label>
+            <label>
+              Target sum
+              <input
+                type="number"
+                min="0"
+                max={sumLabMaximum * sumLabEffectiveCount}
+                value={sumLabTarget}
+                onChange={(event) =>
+                  setSumLabTarget(Number(event.target.value))
+                }
+              />
+            </label>
+            <label>
+              Minimum digit
+              <input
+                type="number"
+                min="1"
+                max={size}
+                value={sumLabMinimum}
+                onChange={(event) =>
+                  setSumLabMinimum(Number(event.target.value))
+                }
+              />
+            </label>
+            <label>
+              Maximum digit
+              <input
+                type="number"
+                min={sumLabMinimum}
+                max={size}
+                value={sumLabMaximum}
+                onChange={(event) =>
+                  setSumLabMaximum(Number(event.target.value))
+                }
+              />
+            </label>
+            <label>
+              Must include
+              <input
+                value={sumLabRequired}
+                placeholder="e.g. 1, 7"
+                onChange={(event) => setSumLabRequired(event.target.value)}
+              />
+            </label>
+            <label>
+              Exclude
+              <input
+                value={sumLabExcluded}
+                placeholder="e.g. 5"
+                onChange={(event) => setSumLabExcluded(event.target.value)}
+              />
+            </label>
+            <label className="check-row">
+              <input
+                type="checkbox"
+                checked={sumLabRepeats}
+                onChange={(event) => setSumLabRepeats(event.target.checked)}
+              />
+              Allow repeated digits
+            </label>
+            <label className="check-row">
+              <input
+                type="checkbox"
+                checked={sumLabUseCandidates}
+                disabled={selectedCells.length === 0}
+                onChange={(event) =>
+                  setSumLabUseCandidates(event.target.checked)
+                }
+              />
+              Use {selectedCells.length || "selected"} board cell
+              {selectedCells.length === 1 ? "" : "s"} and candidates
+            </label>
+            <label className="check-row">
+              <input
+                type="checkbox"
+                checked={sumLabShowEliminated}
+                onChange={(event) =>
+                  setSumLabShowEliminated(event.target.checked)
+                }
+              />
+              Show eliminated combinations
+            </label>
+          </div>
+          {sumLab.error ? (
+            <p className="error-callout" role="alert">
+              {sumLab.error}
+            </p>
+          ) : sumLab.result ? (
+            <div className="helper-result">
+              <div className="metric-row">
+                <span>
+                  <strong>{sumLab.result.activeCombinations.length}</strong>{" "}
+                  active of {sumLab.result.combinations.length}
+                </span>
+                <span>
+                  Possible{" "}
+                  <strong>
+                    {sumLab.result.possibleDigits
+                      .map((value) => symbolFor(value, size))
+                      .join(" ") || "none"}
+                  </strong>
+                </span>
+                <span>
+                  Necessary{" "}
+                  <strong>
+                    {sumLab.result.necessaryDigits
+                      .map((value) => symbolFor(value, size))
+                      .join(" ") || "none"}
+                  </strong>
+                </span>
+              </div>
+              {sumLabCandidateMasks !== undefined && (
+                <ol className="cell-possibilities">
+                  {sumLab.result.possibleByCell.map((entry, index) => {
+                    const cell = selectedCells[index];
+                    const label =
+                      cell === undefined
+                        ? `Cell ${String(index + 1)}`
+                        : `r${String(Math.floor(cell / size) + 1)}c${String((cell % size) + 1)}`;
+                    return (
+                      <li key={cell ?? index}>
+                        {label}:{" "}
+                        {entry
+                          .map((value) => symbolFor(value, size))
+                          .join(" ") || "—"}
+                      </li>
+                    );
+                  })}
+                </ol>
+              )}
+              <p className="muted sum-lab-guidance">
+                Select a combination to eliminate it; select it again to restore
+                it. Eliminated combinations are excluded from the summaries
+                above.
+              </p>
+              <div
+                className="combination-cloud sum-combination-cloud"
+                aria-label="Sum combinations"
+              >
+                {sumLab.result.combinations
+                  .filter(
+                    (combination) =>
+                      sumLabShowEliminated || !combination.eliminated,
+                  )
+                  .slice(0, 500)
+                  .map((combination) => (
+                    <button
+                      key={combination.key}
+                      type="button"
+                      className={`sum-combination${combination.eliminated ? " is-eliminated" : ""}`}
+                      aria-pressed={combination.eliminated}
+                      aria-label={`${combination.digits
+                        .map((value) => symbolFor(value, size))
+                        .join(
+                          " + ",
+                        )}; ${combination.eliminated ? "restore" : "eliminate"}`}
+                      onClick={() => toggleSumLabCombination(combination.key)}
+                    >
+                      {combination.digits
+                        .map((value) => symbolFor(value, size))
+                        .join(" + ")}
+                    </button>
+                  ))}
+                {sumLab.result.combinations.length === 0 && (
+                  <span className="muted">No compatible combinations.</span>
+                )}
+              </div>
+              {(sumLab.result.combinations.length > 500 ||
+                sumLab.result.truncated) && (
+                <p className="callout">
+                  {sumLab.result.truncated
+                    ? `Analysis reached its ${sumLab.result.truncationReason ?? "safety"} limit. `
+                    : ""}
+                  The visible list is bounded; narrow the range or add filters
+                  before making deductions from an incomplete result.
+                </p>
+              )}
+            </div>
+          ) : null}
+        </section>
+      )}
+
       {helper === "killer" && (
         <section className="helper-card">
           <div className="helper-controls">

src/components/ImportExportDialog.tsx

@@ -1,15 +1,15 @@
 import { useMemo, useRef, useState } from "react";
 import type { PuzzleDefinition } from "../domain/types";
+import { normalizePuzzle } from "../domain/validation";
 import {
-  decodePuzzleHash,
   encodePuzzleHash,
   exportFpuzzlesJson,
   exportFpuzzlesUrl,
   fromDomainPuzzle,
-  importFpuzzles,
+  importPuzzle,
-  parseFpuzzles,
+  renderPuzzlePdf,
-  parsePlainGrid,
+  renderPuzzlePng,
-  parseSudokuDocument,
+  renderPuzzleSvg,
   serializePlainGrid,
   serializeSudokuDocument,
   toDomainPuzzle,
@@ -17,31 +17,13 @@ import {
 } from "../formats";
 import type { PlaySession } from "../state/session";
 import { maskValues } from "../state/session";
+import type { PortableAidMemoire } from "../state/aidMemoire";
 import { Modal } from "./Modal";
 
-function parseImport(input: string): SudokuDocument {
-  const trimmed = input.trim();
-  if (trimmed.startsWith("#sudoku=") || trimmed.includes("#sudoku="))
-    return decodePuzzleHash(trimmed);
-  if (
-    /^(?:https?:\/\/)?(?:www\.)?(?:f-puzzles\.com|sudokupad\.app)\//iu.test(
-      trimmed,
-    )
-  )
-    return importFpuzzles(trimmed);
-  if (trimmed.startsWith("fpuzzles")) return importFpuzzles(trimmed);
-  if (trimmed.startsWith("{")) {
-    const parsed = JSON.parse(trimmed) as unknown;
-    if (typeof parsed === "object" && parsed !== null && "schema" in parsed)
-      return parseSudokuDocument(trimmed);
-    return parseFpuzzles(parsed);
-  }
-  return parsePlainGrid(trimmed);
-}
-
 function withProgress(
   puzzle: PuzzleDefinition,
   session: PlaySession,
+  aidMemoire?: PortableAidMemoire,
 ): SudokuDocument {
   const base = fromDomainPuzzle(puzzle);
   return {
@@ -55,22 +37,38 @@ function withProgress(
     ),
     colors: [...session.colors],
     elapsedMs: session.elapsedSeconds * 1_000,
+    ...(aidMemoire === undefined ? {} : { aidMemoire }),
   };
 }
 
-function download(name: string, contents: string, type: string) {
+function downloadBlob(name: string, blob: Blob) {
-  const url = URL.createObjectURL(new Blob([contents], { type }));
+  const url = URL.createObjectURL(blob);
   const anchor = document.createElement("a");
   anchor.href = url;
   anchor.download = name;
+  document.body.append(anchor);
   anchor.click();
-  URL.revokeObjectURL(url);
+  anchor.remove();
+  window.setTimeout(() => URL.revokeObjectURL(url), 0);
+}
+
+function download(name: string, contents: string, type: string) {
+  downloadBlob(name, new Blob([contents], { type }));
+}
+
+function errorMessage(error: unknown, fallback: string): string {
+  return error instanceof Error ? error.message : fallback;
+}
+
+function checkedPuzzle(document: SudokuDocument): PuzzleDefinition {
+  return normalizePuzzle(toDomainPuzzle(document) as PuzzleDefinition);
 }
 
 interface ImportExportDialogProps {
   open: boolean;
   puzzle: PuzzleDefinition;
   session: PlaySession;
+  aidMemoire?: PortableAidMemoire;
   onClose: () => void;
   onImport: (
     puzzle: PuzzleDefinition,
@@ -82,6 +80,7 @@ interface ImportExportDialogProps {
       | "candidates"
       | "colors"
       | "elapsedMs"
+      | "aidMemoire"
     >,
   ) => void;
 }
@@ -90,19 +89,21 @@ export function ImportExportDialog({
   open,
   puzzle,
   session,
+  aidMemoire,
   onClose,
   onImport,
 }: ImportExportDialogProps) {
   const [input, setInput] = useState("");
   const [feedback, setFeedback] = useState("");
   const [includeProgress, setIncludeProgress] = useState(true);
+  const [busy, setBusy] = useState(false);
   const fileRef = useRef<HTMLInputElement>(null);
   const documentValue = useMemo(
     () =>
       includeProgress
-        ? withProgress(puzzle, session)
+        ? withProgress(puzzle, session, aidMemoire)
         : fromDomainPuzzle(puzzle),
-    [includeProgress, puzzle, session],
+    [aidMemoire, includeProgress, puzzle, session],
   );
 
   const copy = async (value: string, label: string) => {
@@ -116,18 +117,119 @@ export function ImportExportDialog({
     }
   };
 
+  const copyExport = async (render: () => string, label: string) => {
+    let value: string;
+    try {
+      value = render();
+    } catch (error) {
+      setFeedback(errorMessage(error, `${label} could not be created.`));
+      return;
+    }
+    await copy(value, label);
+  };
+
+  const exportText = (
+    name: string,
+    type: string,
+    label: string,
+    render: () => string,
+  ) => {
+    try {
+      download(name, render(), type);
+      setFeedback(`${label} downloaded locally.`);
+    } catch (error) {
+      setFeedback(errorMessage(error, `${label} export failed.`));
+    }
+  };
+
+  const inspectImport = async () => {
+    setBusy(true);
+    try {
+      const result = await importPuzzle(input);
+      checkedPuzzle(result.document);
+      const givenCount = result.document.givens.filter(
+        (value) => value !== 0,
+      ).length;
+      setFeedback(
+        `${result.label}: ${String(result.document.size)}×${String(result.document.size)}, ${String(givenCount)} givens and ${String(result.document.constraints.length)} constraints. Compatible and ready to import.`,
+      );
+    } catch (error) {
+      setFeedback(errorMessage(error, "The puzzle could not be inspected."));
+    } finally {
+      setBusy(false);
+    }
+  };
+
+  const applyImport = async () => {
+    setBusy(true);
+    try {
+      const result = await importPuzzle(input);
+      const parsed = result.document;
+      onImport(checkedPuzzle(parsed), {
+        values: parsed.values,
+        cornerMarks: parsed.cornerMarks,
+        centerMarks: parsed.centerMarks,
+        candidates: parsed.candidates,
+        colors: parsed.colors,
+        elapsedMs: parsed.elapsedMs,
+        aidMemoire: parsed.aidMemoire,
+      });
+      setFeedback(`${result.label} imported locally.`);
+      onClose();
+    } catch (error) {
+      setFeedback(errorMessage(error, "The puzzle could not be imported."));
+    } finally {
+      setBusy(false);
+    }
+  };
+
+  const exportVisual = async (format: "svg" | "png" | "pdf") => {
+    setBusy(true);
+    try {
+      const options = {
+        includeProgress,
+        includeNotes: includeProgress,
+      };
+      if (format === "svg") {
+        download(
+          "sudoku.svg",
+          renderPuzzleSvg(documentValue, options),
+          "image/svg+xml;charset=utf-8",
+        );
+      } else if (format === "png") {
+        downloadBlob(
+          "sudoku.png",
+          await renderPuzzlePng(documentValue, options),
+        );
+      } else {
+        downloadBlob(
+          "sudoku.pdf",
+          await renderPuzzlePdf(documentValue, options),
+        );
+      }
+      setFeedback(`${format.toUpperCase()} rendered and downloaded locally.`);
+    } catch (error) {
+      setFeedback(
+        errorMessage(error, `The ${format.toUpperCase()} export failed.`),
+      );
+    } finally {
+      setBusy(false);
+    }
+  };
+
   return (
     <Modal open={open} title="Import and export" onClose={onClose} wide>
-      <div className="import-export-grid">
+      <div className="import-export-grid" aria-busy={busy}>
         <section className="stack">
           <div>
             <p className="eyebrow">Import</p>
             <h3>Paste puzzle data</h3>
           </div>
           <p className="muted">
-            Accepts a plain grid, Sudoku Tools JSON/share link, raw f-puzzles
+            Accepts a plain grid, Sudoku Tools JSON/share link, f-puzzles or
-            JSON, or a self-contained f-puzzles/SudokuPad link. Server-only
+            SudokuPad/CTC data, and supported Penpa+ long links. Everything is
-            short IDs are never fetched.
+            decoded locally. Server-only short IDs are never fetched.
+            Unsupported constructs stop the import instead of being discarded.
           </p>
           <textarea
             rows={12}
@@ -135,7 +237,10 @@ export function ImportExportDialog({
             maxLength={1_048_576}
             spellCheck={false}
             placeholder="Paste 81 characters, JSON or a puzzle URL…"
-            onChange={(event) => setInput(event.target.value)}
+            onChange={(event) => {
+              setInput(event.target.value);
+              setFeedback("");
+            }}
           />
           <div className="action-row">
             <button type="button" onClick={() => fileRef.current?.click()}>
@@ -145,7 +250,7 @@ export function ImportExportDialog({
               ref={fileRef}
               className="sr-only"
               type="file"
-              accept="application/json,text/plain,.json,.txt,.sdk"
+              accept="application/json,text/plain,.json,.txt,.sdk,.scl,.ctc,.penpa"
               onChange={(event) => {
                 const file = event.target.files?.[0];
                 event.target.value = "";
@@ -169,28 +274,15 @@ export function ImportExportDialog({
             />
             <button
               type="button"
-              disabled={!input.trim()}
+              disabled={busy || !input.trim()}
-              onClick={() => {
+              onClick={() => void inspectImport()}
-                try {
+            >
-                  const parsed = parseImport(input);
+              Check compatibility
-                  onImport(toDomainPuzzle(parsed) as PuzzleDefinition, {
+            </button>
-                    values: parsed.values,
+            <button
-                    cornerMarks: parsed.cornerMarks,
+              type="button"
-                    centerMarks: parsed.centerMarks,
+              disabled={busy || !input.trim()}
-                    candidates: parsed.candidates,
+              onClick={() => void applyImport()}
-                    colors: parsed.colors,
-                    elapsedMs: parsed.elapsedMs,
-                  });
-                  setFeedback("Puzzle imported locally.");
-                  onClose();
-                } catch (error) {
-                  setFeedback(
-                    error instanceof Error
-                      ? error.message
-                      : "The puzzle could not be imported.",
-                  );
-                }
-              }}
             >
               Import locally
             </button>
@@ -213,11 +305,13 @@ export function ImportExportDialog({
           <div className="export-actions">
             <button
               type="button"
+              disabled={busy}
               onClick={() =>
-                download(
+                exportText(
                   "sudoku-tools-puzzle.json",
-                  serializeSudokuDocument(documentValue, true),
                   "application/json",
+                  "Project JSON",
+                  () => serializeSudokuDocument(documentValue, true),
                 )
               }
             >
@@ -225,14 +319,13 @@ export function ImportExportDialog({
             </button>
             <button
               type="button"
+              disabled={busy}
               onClick={() =>
-                download(
+                exportText("sudoku.txt", "text/plain", "Grid text", () =>
-                  "sudoku.txt",
                   serializePlainGrid(
                     documentValue,
                     includeProgress ? "values" : "givens",
                   ),
-                  "text/plain",
                 )
               }
             >
@@ -240,11 +333,13 @@ export function ImportExportDialog({
             </button>
             <button
               type="button"
+              disabled={busy}
               onClick={() =>
-                download(
+                exportText(
                   "sudoku.fpuzzles.json",
-                  exportFpuzzlesJson(documentValue, true),
                   "application/json",
+                  "f-puzzles JSON",
+                  () => exportFpuzzlesJson(documentValue, true),
                 )
               }
             >
@@ -252,21 +347,50 @@ export function ImportExportDialog({
             </button>
             <button
               type="button"
+              disabled={busy}
               onClick={() =>
-                void copy(exportFpuzzlesUrl(documentValue), "f-puzzles URL")
+                void copyExport(
+                  () => exportFpuzzlesUrl(documentValue),
+                  "f-puzzles URL",
+                )
               }
             >
               Copy f-puzzles URL
             </button>
             <button
               type="button"
+              disabled={busy}
               onClick={() => {
-                const share = `${location.href.split("#", 1)[0]}${encodePuzzleHash(documentValue)}`;
+                void copyExport(
-                void copy(share, "Local share URL");
+                  () =>
+                    `${location.href.split("#", 1)[0]}${encodePuzzleHash(documentValue)}`,
+                  "Local share URL",
+                );
               }}
             >
               Copy local share URL
             </button>
+            <button
+              type="button"
+              disabled={busy}
+              onClick={() => void exportVisual("svg")}
+            >
+              Download SVG
+            </button>
+            <button
+              type="button"
+              disabled={busy}
+              onClick={() => void exportVisual("png")}
+            >
+              Download PNG
+            </button>
+            <button
+              type="button"
+              disabled={busy}
+              onClick={() => void exportVisual("pdf")}
+            >
+              Download PDF
+            </button>
           </div>
           <p className="callout">
             Share links are self-contained. They may expose title, setter,

src/components/SolveWorkspace.tsx

@@ -141,13 +141,15 @@ export function SolveWorkspace({
             </span>
           </div>
           <p>
-            {exact.count === 0
+            {exact.count >= 2
-              ? "No completion satisfies every supported rule."
+              ? "At least two solutions exist; the puzzle is not unique."
-              : exact.count === 1 && !exact.truncated
+              : exact.truncated
-                ? "The current puzzle has exactly one solution within the configured search bounds."
+                ? exact.count === 0
-                : exact.count >= 2
+                  ? "Search stopped at a safety limit before finding a solution, so solvability is not established."
-                  ? "At least two solutions exist; the puzzle is not unique."
+                  : "Search stopped at a safety limit, so uniqueness is not established."
-                  : "Search stopped at a safety limit, so uniqueness is not established."}
+                : exact.count === 0
+                  ? "No completion satisfies every supported rule."
+                  : "The current puzzle has exactly one solution."}
           </p>
           {exact.solutions[0] && (
             <button

src/components/SudokuBoard.tsx

@@ -1,5 +1,11 @@
-import type { CSSProperties, KeyboardEvent, PointerEvent } from "react";
+import {
+  useId,
+  type CSSProperties,
+  type KeyboardEvent,
+  type PointerEvent,
+} from "react";
 import type { NormalizedPuzzle, VariantConstraint } from "../domain/types";
+import type { CandidateNode, CandidateOverlay } from "../helpers";
 import { maskValues, symbolFor } from "../state/session";
 
 interface SudokuBoardProps {
@@ -14,6 +20,7 @@ interface SudokuBoardProps {
   conflicts?: ReadonlySet<number>;
   activeCell: number;
   showCandidates?: boolean;
+  candidateOverlay?: CandidateOverlay;
   onCellPointerDown: (
     cell: number,
     event: PointerEvent<HTMLButtonElement>,
@@ -25,6 +32,67 @@ interface SudokuBoardProps {
   onKeyDown: (event: KeyboardEvent<HTMLDivElement>) => void;
 }
 
+function candidatePoint(size: number, node: CandidateNode) {
+  const columns = Math.ceil(Math.sqrt(size));
+  const rows = Math.ceil(size / columns);
+  const slot = node.value - 1;
+  return {
+    x: (node.cell % size) + ((slot % columns) + 0.5) / columns,
+    y: Math.floor(node.cell / size) + (Math.floor(slot / columns) + 0.5) / rows,
+  };
+}
+
+function CandidateLinkLayer({
+  size,
+  overlay,
+}: {
+  size: number;
+  overlay: CandidateOverlay;
+}) {
+  const nodes = new Map<string, CandidateNode>();
+  for (const link of overlay.links) {
+    nodes.set(`${String(link.a.cell)}:${String(link.a.value)}`, link.a);
+    nodes.set(`${String(link.b.cell)}:${String(link.b.value)}`, link.b);
+  }
+  return (
+    <svg
+      className="candidate-link-layer"
+      viewBox={`0 0 ${String(size)} ${String(size)}`}
+      aria-hidden="true"
+    >
+      {overlay.links.map((link) => {
+        const a = candidatePoint(size, link.a);
+        const b = candidatePoint(size, link.b);
+        return (
+          <line
+            key={link.id}
+            className={`candidate-overlay-link candidate-overlay-link--${link.kind}`}
+            x1={a.x}
+            y1={a.y}
+            x2={b.x}
+            y2={b.y}
+          />
+        );
+      })}
+      {[...nodes.entries()].map(([key, node]) => {
+        const position = candidatePoint(size, node);
+        return (
+          <g
+            key={key}
+            className="candidate-overlay-node"
+            transform={`translate(${String(position.x)} ${String(position.y)})`}
+          >
+            <circle r="0.105" />
+            <text x="0" y="0">
+              {symbolFor(node.value, size)}
+            </text>
+          </g>
+        );
+      })}
+    </svg>
+  );
+}
+
 function point(size: number, cell: number) {
   return {
     x: (cell % size) + 0.5,
@@ -41,6 +109,23 @@ function polyline(size: number, cells: readonly number[]) {
     .join(" ");
 }
 
+function outsidePoint(
+  size: number,
+  side: "top" | "right" | "bottom" | "left",
+  index: number,
+) {
+  switch (side) {
+    case "top":
+      return { x: index + 0.5, y: -0.48 };
+    case "right":
+      return { x: size + 0.48, y: index + 0.5 };
+    case "bottom":
+      return { x: index + 0.5, y: size + 0.48 };
+    case "left":
+      return { x: -0.48, y: index + 0.5 };
+  }
+}
+
 function boundaryPath(size: number, cells: ReadonlySet<number>, inset: number) {
   const commands: string[] = [];
   for (const cell of cells) {
@@ -62,12 +147,168 @@ function boundaryPath(size: number, cells: ReadonlySet<number>, inset: number) {
   return commands.join(" ");
 }
 
+function describeConstraint(
+  constraint: VariantConstraint,
+  size: number,
+): string {
+  const cell = (index: number) =>
+    `row ${String(Math.floor(index / size) + 1)}, column ${String((index % size) + 1)}`;
+  const cells = (indices: readonly number[]) => indices.map(cell).join("; ");
+  const polarity =
+    "negated" in constraint && constraint.negated === true
+      ? "False clue: "
+      : "";
+
+  switch (constraint.type) {
+    case "diagonal":
+      return `${constraint.direction} diagonal.`;
+    case "anti-knight":
+      return "Anti-knight rule.";
+    case "anti-king":
+      return "Anti-king rule.";
+    case "non-consecutive":
+      return "Non-consecutive orthogonal neighbours rule.";
+    case "killer-cage":
+      return `${polarity}killer cage ${String(constraint.sum)} at ${cells(constraint.cells)}.`;
+    case "thermo":
+      return `${polarity}thermometer from bulb through ${cells(constraint.cells)}.`;
+    case "arrow":
+      return `${polarity}arrow with bulb at ${cells(constraint.bulb)} and line through ${cells(constraint.line)}.`;
+    case "kropki":
+      return `${polarity}${constraint.kind} Kropki dot between ${cell(constraint.a)} and ${cell(constraint.b)}.`;
+    case "xv":
+      return `${polarity}sum ${String(constraint.total)} pair between ${cell(constraint.a)} and ${cell(constraint.b)}.`;
+    case "inequality":
+      return `${polarity}${cell(constraint.lesser)} is less than ${cell(constraint.greater)}.`;
+    case "renban":
+      return `${polarity}renban line through ${cells(constraint.cells)}.`;
+    case "palindrome":
+      return `${polarity}palindrome line through ${cells(constraint.cells)}.`;
+    case "x-sum":
+      return `${polarity}X-sum ${String(constraint.sum)} from the ${constraint.side}, ${constraint.side === "left" || constraint.side === "right" ? "row" : "column"} ${String(constraint.index + 1)}.`;
+    case "skyscraper":
+      return `${polarity}skyscraper count ${String(constraint.count)} from the ${constraint.side}, ${constraint.side === "left" || constraint.side === "right" ? "row" : "column"} ${String(constraint.index + 1)}.`;
+    case "quadruple":
+      return `${polarity}quadruple digits ${constraint.digits.map((digit) => symbolFor(digit, size)).join(", ")} touching ${cells(constraint.cells)}.`;
+    case "maximum":
+      return `${polarity}maximum at ${cell(constraint.cell)}.`;
+  }
+}
+
+function constraintTouchesCell(
+  constraint: VariantConstraint,
+  cell: number,
+  size: number,
+): boolean {
+  switch (constraint.type) {
+    case "diagonal": {
+      const row = Math.floor(cell / size);
+      const column = cell % size;
+      return constraint.direction === "main"
+        ? row === column
+        : row + column === size - 1;
+    }
+    case "killer-cage":
+    case "thermo":
+    case "renban":
+    case "palindrome":
+    case "quadruple":
+      return constraint.cells.includes(cell);
+    case "arrow":
+      return constraint.bulb.includes(cell) || constraint.line.includes(cell);
+    case "kropki":
+    case "xv":
+      return constraint.a === cell || constraint.b === cell;
+    case "inequality":
+      return constraint.lesser === cell || constraint.greater === cell;
+    case "maximum":
+      return constraint.cell === cell;
+    case "x-sum":
+    case "skyscraper": {
+      const row = Math.floor(cell / size);
+      const column = cell % size;
+      return constraint.side === "left" || constraint.side === "right"
+        ? row === constraint.index
+        : column === constraint.index;
+    }
+    case "anti-knight":
+    case "anti-king":
+    case "non-consecutive":
+      return false;
+  }
+}
+
+function cellAccessibleDescription({
+  puzzle,
+  cell,
+  value,
+  corner,
+  center,
+  centerIsAutomatic,
+  color,
+  conflict,
+  candidateHighlights,
+}: {
+  puzzle: NormalizedPuzzle;
+  cell: number;
+  value: number;
+  corner: readonly number[];
+  center: readonly number[];
+  centerIsAutomatic: boolean;
+  color: number;
+  conflict: boolean;
+  candidateHighlights: readonly number[];
+}): string {
+  const parts = [`Region ${String((puzzle.regions[cell] ?? 0) + 1)}`];
+  if (value !== 0) {
+    parts.push(puzzle.givens[cell] ? "Given digit" : "Entered digit");
+  } else {
+    if (corner.length > 0) {
+      parts.push(
+        `corner notes ${corner.map((digit) => symbolFor(digit, puzzle.size)).join(", ")}`,
+      );
+    }
+    if (center.length > 0) {
+      parts.push(
+        `${centerIsAutomatic ? "automatic candidates" : "centre notes"} ${center
+          .map((digit) => symbolFor(digit, puzzle.size))
+          .join(", ")}`,
+      );
+    }
+  }
+  if (color > 0) parts.push(`colour ${String(color)}`);
+  if (conflict) parts.push("conflict");
+  if (candidateHighlights.length > 0) {
+    parts.push(
+      `Candidate Lab highlights ${candidateHighlights
+        .map((digit) => symbolFor(digit, puzzle.size))
+        .join(", ")}`,
+    );
+  }
+
+  const localConstraints = puzzle.constraints.filter((constraint) =>
+    constraintTouchesCell(constraint, cell, puzzle.size),
+  );
+  if (localConstraints.length > 0) {
+    parts.push(
+      `clues: ${localConstraints
+        .map((constraint) => describeConstraint(constraint, puzzle.size))
+        .join(" ")}`,
+    );
+  }
+  return parts.join(", ");
+}
+
 function ConstraintLayer({ puzzle }: { puzzle: NormalizedPuzzle }) {
   const { size } = puzzle;
   const regionCells = Array.from({ length: size }, () => new Set<number>());
   puzzle.regions.forEach((region, cell) => regionCells[region]?.add(cell));
 
   const renderConstraint = (constraint: VariantConstraint, index: number) => {
+    const polarityClass =
+      "negated" in constraint && constraint.negated === true
+        ? " is-negated"
+        : "";
     if (constraint.type === "diagonal") {
       return (
         <line
@@ -85,9 +326,10 @@ function ConstraintLayer({ puzzle }: { puzzle: NormalizedPuzzle }) {
       const first = Math.min(...constraint.cells);
       const position = point(size, first);
       return (
-        <g key={index} className="constraint-cage">
+        <g key={index} className={`constraint-cage${polarityClass}`}>
           <path d={boundaryPath(size, cells, 0.09)} />
           <text x={position.x - 0.34} y={position.y - 0.27}>
+            {constraint.negated === true ? "≠" : ""}
             {constraint.sum}
           </text>
         </g>
@@ -96,9 +338,14 @@ function ConstraintLayer({ puzzle }: { puzzle: NormalizedPuzzle }) {
     if (constraint.type === "thermo") {
       const bulb = point(size, constraint.cells[0]!);
       return (
-        <g key={index} className="constraint-thermo">
+        <g key={index} className={`constraint-thermo${polarityClass}`}>
           <polyline points={polyline(size, constraint.cells)} />
           <circle cx={bulb.x} cy={bulb.y} r="0.31" />
+          {constraint.negated === true && (
+            <text className="constraint-false-mark" x={bulb.x} y={bulb.y}>
+              ≠
+            </text>
+          )}
         </g>
       );
     }
@@ -107,16 +354,104 @@ function ConstraintLayer({ puzzle }: { puzzle: NormalizedPuzzle }) {
       const end = point(size, constraint.line.at(-1)!);
       const connectedLine = [constraint.bulb.at(-1)!, ...constraint.line];
       return (
-        <g key={index} className="constraint-arrow">
+        <g key={index} className={`constraint-arrow${polarityClass}`}>
           <circle cx={bulb.x} cy={bulb.y} r="0.32" />
           <polyline points={polyline(size, connectedLine)} />
           <circle cx={end.x} cy={end.y} r="0.08" />
         </g>
       );
     }
+    if (constraint.type === "maximum") {
+      const center = point(size, constraint.cell);
+      return (
+        <g key={index} className={`constraint-maximum${polarityClass}`}>
+          <circle cx={center.x} cy={center.y} r="0.18" />
+          <path
+            d={[
+              `M${String(center.x - 0.1)} ${String(center.y - 0.17)}L${String(center.x)} ${String(center.y - 0.3)}L${String(center.x + 0.1)} ${String(center.y - 0.17)}`,
+              `M${String(center.x - 0.1)} ${String(center.y + 0.17)}L${String(center.x)} ${String(center.y + 0.3)}L${String(center.x + 0.1)} ${String(center.y + 0.17)}`,
+              `M${String(center.x - 0.17)} ${String(center.y - 0.1)}L${String(center.x - 0.3)} ${String(center.y)}L${String(center.x - 0.17)} ${String(center.y + 0.1)}`,
+              `M${String(center.x + 0.17)} ${String(center.y - 0.1)}L${String(center.x + 0.3)} ${String(center.y)}L${String(center.x + 0.17)} ${String(center.y + 0.1)}`,
+            ].join("")}
+          />
+        </g>
+      );
+    }
+    if (constraint.type === "quadruple") {
+      const positions = constraint.cells.map((cell) => point(size, cell));
+      const center = {
+        x:
+          positions.reduce((sum, position) => sum + position.x, 0) /
+          positions.length,
+        y:
+          positions.reduce((sum, position) => sum + position.y, 0) /
+          positions.length,
+      };
+      return (
+        <g key={index} className={`constraint-quadruple${polarityClass}`}>
+          <circle cx={center.x} cy={center.y} r="0.29" />
+          <text x={center.x} y={center.y}>
+            {constraint.negated === true ? "≠" : ""}
+            {constraint.digits.map((digit) => symbolFor(digit, size)).join("")}
+          </text>
+        </g>
+      );
+    }
+    if (constraint.type === "x-sum" || constraint.type === "skyscraper") {
+      const position = outsidePoint(size, constraint.side, constraint.index);
+      const value =
+        constraint.type === "x-sum" ? constraint.sum : constraint.count;
+      const companionIndex = puzzle.constraints.findIndex(
+        (candidate) =>
+          candidate.type !== constraint.type &&
+          (candidate.type === "x-sum" || candidate.type === "skyscraper") &&
+          candidate.side === constraint.side &&
+          candidate.index === constraint.index &&
+          (candidate.type === "x-sum" ? candidate.sum : candidate.count) ===
+            value &&
+          ("negated" in candidate && candidate.negated === true) ===
+            (constraint.negated === true),
+      );
+      const combined = companionIndex >= 0;
+      if (combined && companionIndex < index) return null;
+      const label = `${constraint.negated === true ? "≠" : ""}${String(value)}`;
+      return (
+        <g
+          key={index}
+          className={`constraint-outside constraint-${constraint.type}${combined ? " is-combined" : ""}${polarityClass}`}
+          transform={`translate(${String(position.x)} ${String(position.y)})`}
+        >
+          <rect
+            x="-0.46"
+            y={combined ? "-0.31" : "-0.23"}
+            width="0.92"
+            height={combined ? "0.62" : "0.46"}
+            rx="0.12"
+          />
+          {combined ? (
+            <>
+              <text className="outside-clue-kinds" x="0" y="-0.15">
+                Σ · ▥
+              </text>
+              <text className="outside-clue-value" x="0" y="0.1">
+                {label}
+              </text>
+            </>
+          ) : (
+            <text x="0" y="0">
+              {constraint.type === "x-sum" ? "Σ" : "▥"}
+              {label}
+            </text>
+          )}
+        </g>
+      );
+    }
     if (constraint.type === "renban" || constraint.type === "palindrome") {
       return (
-        <g key={index} className={`constraint-${constraint.type}`}>
+        <g
+          key={index}
+          className={`constraint-${constraint.type}${polarityClass}`}
+        >
           <polyline points={polyline(size, constraint.cells)} />
           {constraint.type === "palindrome" &&
             constraint.cells.map((cell) => {
@@ -145,7 +480,7 @@ function ConstraintLayer({ puzzle }: { puzzle: NormalizedPuzzle }) {
         return (
           <circle
             key={index}
-            className={`constraint-kropki constraint-kropki--${constraint.kind}`}
+            className={`constraint-kropki constraint-kropki--${constraint.kind}${polarityClass}`}
             cx={x}
             cy={y}
             r="0.115"
@@ -155,10 +490,11 @@ function ConstraintLayer({ puzzle }: { puzzle: NormalizedPuzzle }) {
         return (
           <g
             key={index}
-            className={`constraint-xv constraint-xv--${String(constraint.total)}`}
+            className={`constraint-xv constraint-xv--${String(constraint.total)}${polarityClass}`}
           >
             <circle cx={x} cy={y} r="0.18" />
             <text x={x} y={y}>
+              {constraint.negated === true ? "≠" : ""}
               {constraint.total}
             </text>
           </g>
@@ -167,7 +503,7 @@ function ConstraintLayer({ puzzle }: { puzzle: NormalizedPuzzle }) {
       return (
         <g
           key={index}
-          className="constraint-inequality"
+          className={`constraint-inequality${polarityClass}`}
           transform={`translate(${String(x)} ${String(y)}) rotate(${String(rotation)})`}
         >
           <path d="M0.12 -0.17L-0.12 0L0.12 0.17" />
@@ -211,72 +547,140 @@ export function SudokuBoard({
   conflicts = new Set<number>(),
   activeCell,
   showCandidates,
+  candidateOverlay,
   onCellPointerDown,
   onCellPointerEnter,
   onKeyDown,
 }: SudokuBoardProps) {
   const { size } = puzzle;
+  const constraintDescriptionId = useId();
+  const navigationDescriptionId = useId();
+  const hasOutsideClues = puzzle.constraints.some(
+    ({ type }) => type === "x-sum" || type === "skyscraper",
+  );
+  const constraintDescription = puzzle.constraints
+    .map((constraint) => describeConstraint(constraint, size))
+    .join(" ");
   return (
     <div
-      className="sudoku-board-frame"
+      className={`sudoku-board-frame${hasOutsideClues ? " has-outside-clues" : ""}`}
       style={{ "--sudoku-size": size } as CSSProperties}
     >
+      <p className="sr-only" id={navigationDescriptionId}>
+        Use the arrow keys to move without wrapping. Home and End move to the
+        first and last cell in the row. Control or Command plus Home and End
+        move to the first and last grid cell. Page Up and Page Down keep the
+        column and move to the first and last row. Hold Shift to extend the
+        selection.
+      </p>
+      {constraintDescription && (
+        <p className="sr-only" id={constraintDescriptionId}>
+          Variant constraints. {constraintDescription}
+        </p>
+      )}
       <div
         className="sudoku-board"
         role="grid"
         aria-label={`${String(size)} by ${String(size)} Sudoku grid`}
+        aria-rowcount={size}
+        aria-colcount={size}
+        aria-multiselectable="true"
+        aria-describedby={`${navigationDescriptionId}${constraintDescription ? ` ${constraintDescriptionId}` : ""}`}
         onKeyDown={onKeyDown}
       >
-        {values.map((value, cell) => {
+        {Array.from({ length: size }, (_, rowIndex) => (
-          const isGiven = Boolean(puzzle.givens[cell]);
+          <div
-          const corner = maskValues(cornerMarks[cell] ?? 0, size);
+            key={rowIndex}
-          const center = maskValues(
+            className="sudoku-row"
-            centerMarks[cell] || (showCandidates ? (candidates[cell] ?? 0) : 0),
+            role="row"
-            size,
+            aria-rowindex={rowIndex + 1}
-          );
+          >
-          const row = Math.floor(cell / size) + 1;
+            {Array.from({ length: size }, (_, columnIndex) => {
-          const column = (cell % size) + 1;
+              const cell = rowIndex * size + columnIndex;
-          return (
+              const value = values[cell] ?? 0;
-            <button
+              const isGiven = Boolean(puzzle.givens[cell]);
-              key={cell}
+              const corner = maskValues(cornerMarks[cell] ?? 0, size);
-              type="button"
+              const userCenterMask = centerMarks[cell] ?? 0;
-              role="gridcell"
+              const automaticMask = showCandidates
-              aria-label={`Row ${String(row)}, column ${String(column)}${value ? `, ${symbolFor(value, size)}` : ", empty"}`}
+                ? (candidates[cell] ?? 0)
-              aria-selected={selected.has(cell)}
+                : 0;
-              tabIndex={cell === activeCell ? 0 : -1}
+              const centerIsAutomatic =
-              className={[
+                userCenterMask === 0 && automaticMask !== 0;
-                "sudoku-cell",
+              const center = maskValues(userCenterMask || automaticMask, size);
-                isGiven ? "is-given" : "",
+              const candidateHighlighted =
-                highlighted.has(cell) ? "is-digit-highlighted" : "",
+                candidateOverlay?.candidateCells.includes(cell) ?? false;
-                selected.has(cell) ? "is-selected" : "",
+              const candidateMask = candidates[cell] ?? 0;
-                conflicts.has(cell) ? "has-conflict" : "",
+              const candidateHighlights = candidateHighlighted
-                colors[cell] ? `has-color-${String(colors[cell])}` : "",
+                ? (candidateOverlay?.activeValues.filter(
-              ]
+                    (digit) =>
-                .filter(Boolean)
+                      candidateMask === 0 ||
-                .join(" ")}
+                      (candidateMask & (1 << (digit - 1))) !== 0,
-              onPointerDown={(event) => onCellPointerDown(cell, event)}
+                  ) ?? [])
-              onPointerEnter={(event) => onCellPointerEnter(cell, event)}
+                : [];
-              data-cell={cell}
+              const conflict = conflicts.has(cell);
-            >
+              const accessibleDescription = cellAccessibleDescription({
-              {value ? (
+                puzzle,
-                <span className="cell-value">{symbolFor(value, size)}</span>
+                cell,
-              ) : (
+                value,
-                <>
+                corner,
-                  <span className="corner-marks" aria-hidden="true">
+                center,
-                    {corner.map((mark) => (
+                centerIsAutomatic,
-                      <span key={mark}>{symbolFor(mark, size)}</span>
+                color: colors[cell] ?? 0,
-                    ))}
+                conflict,
-                  </span>
+                candidateHighlights,
-                  <span className="center-marks" aria-hidden="true">
+              });
-                    {center.map((mark) => symbolFor(mark, size)).join("")}
+              return (
-                  </span>
+                <button
-                </>
+                  key={cell}
-              )}
+                  type="button"
-            </button>
+                  role="gridcell"
-          );
+                  aria-rowindex={rowIndex + 1}
-        })}
+                  aria-colindex={columnIndex + 1}
+                  aria-label={`Row ${String(rowIndex + 1)}, column ${String(columnIndex + 1)}${value ? `, ${symbolFor(value, size)}` : ", empty"}`}
+                  aria-description={accessibleDescription}
+                  aria-selected={selected.has(cell)}
+                  aria-readonly={isGiven}
+                  aria-invalid={conflict || undefined}
+                  tabIndex={cell === activeCell ? 0 : -1}
+                  className={[
+                    "sudoku-cell",
+                    isGiven ? "is-given" : "",
+                    highlighted.has(cell) ? "is-digit-highlighted" : "",
+                    candidateHighlighted ? "is-candidate-highlighted" : "",
+                    selected.has(cell) ? "is-selected" : "",
+                    conflict ? "has-conflict" : "",
+                    colors[cell] ? `has-color-${String(colors[cell])}` : "",
+                  ]
+                    .filter(Boolean)
+                    .join(" ")}
+                  onPointerDown={(event) => onCellPointerDown(cell, event)}
+                  onPointerEnter={(event) => onCellPointerEnter(cell, event)}
+                  data-cell={cell}
+                >
+                  {value ? (
+                    <span className="cell-value">{symbolFor(value, size)}</span>
+                  ) : (
+                    <>
+                      <span className="corner-marks" aria-hidden="true">
+                        {corner.map((mark) => (
+                          <span key={mark}>{symbolFor(mark, size)}</span>
+                        ))}
+                      </span>
+                      <span className="center-marks" aria-hidden="true">
+                        {center.map((mark) => symbolFor(mark, size)).join("")}
+                      </span>
+                    </>
+                  )}
+                </button>
+              );
+            })}
+          </div>
+        ))}
       </div>
       <ConstraintLayer puzzle={puzzle} />
+      {candidateOverlay !== undefined && candidateOverlay.links.length > 0 && (
+        <CandidateLinkLayer size={size} overlay={candidateOverlay} />
+      )}
     </div>
   );
 }

src/components/Workbench.tsx

@@ -24,6 +24,7 @@ import {
   toDomainPuzzle,
   type SudokuDocument,
 } from "../formats";
+import type { CandidateOverlay } from "../helpers";
 import { CLASSIC_SAMPLE, SAMPLE_CATALOG } from "../data/samples";
 import type {
   DifficultyAssessment,
@@ -57,9 +58,37 @@ import {
   matchingDigitCells,
   toggledDigitHighlight,
 } from "../state/gameplayHelpers";
+import {
+  aidMemoireFromPortable,
+  aidMemoireToPortable,
+  cloneAidMemoire,
+  createAidMemoire,
+  enterAidMemoireCell,
+  eraseAidMemoireCell,
+  setAidMemoireEnabled,
+  type AidMemoireState,
+} from "../state/aidMemoire";
+import { navigateGridCell } from "../state/gridNavigation";
+import {
+  activeHypothesis,
+  aidMemoireFromGameplayState,
+  beginHypothesis,
+  createGameplayHistory,
+  createSavepoint,
+  deleteSavepoint,
+  describeGameplayChange,
+  finishHypothesis,
+  gameplayMoment,
+  recordGameplayMoment,
+  restoreSavepoint,
+  sessionFromGameplayState,
+  type GameplayHistory,
+} from "../state/playHistory";
 import { createSolverWorkerClient, type SolverWorkerClient } from "../workers";
 import { ConstraintEditor } from "./ConstraintEditor";
+import { AidMemoire } from "./AidMemoire";
 import { DigitCompletionBar } from "./DigitCompletionBar";
+import { GameplayHistoryDialog } from "./GameplayHistoryDialog";
 import { GeneratorWorkspace } from "./GeneratorWorkspace";
 import { HelpersWorkspace } from "./HelpersWorkspace";
 import { ImportExportDialog } from "./ImportExportDialog";
@@ -79,6 +108,7 @@ interface Feedback {
 interface HistoryEntry {
   readonly puzzle: PuzzleDefinition;
   readonly session: PlaySnapshot;
+  readonly aidMemoire: AidMemoireState;
 }
 
 const library = createProjectLibrary();
@@ -143,6 +173,7 @@ function progressFromSession(
   puzzle: PuzzleDefinition,
   session: PlaySession,
   completed: boolean,
+  aidMemoire: AidMemoireState,
 ): SudokuProgress {
   return {
     version: 1,
@@ -156,6 +187,7 @@ function progressFromSession(
     colors: [...session.colors],
     elapsedMs: session.elapsedSeconds * 1_000,
     completed,
+    aidMemoire: aidMemoireToPortable(aidMemoire, puzzle.size),
   };
 }
 
@@ -195,18 +227,27 @@ function safeNormalize(puzzle: PuzzleDefinition): {
 function initialProject(): {
   readonly puzzle: PuzzleDefinition;
   readonly session: PlaySession;
+  readonly aidMemoire: AidMemoireState;
 } {
   if (typeof location !== "undefined" && location.hash.includes("sudoku=")) {
     try {
       const document = decodePuzzleHash(location.href);
       const puzzle = normalizePuzzle(toDomainPuzzle(document));
-      return { puzzle, session: sessionFromDocument(puzzle, document) };
+      return {
+        puzzle,
+        session: sessionFromDocument(puzzle, document),
+        aidMemoire: aidMemoireFromPortable(document.aidMemoire, puzzle.size),
+      };
     } catch {
       // An invalid hash is non-fatal; the import dialog can report details.
     }
   }
   const puzzle = normalizePuzzle(CLASSIC_SAMPLE);
-  return { puzzle, session: createSession(puzzle.givens) };
+  return {
+    puzzle,
+    session: createSession(puzzle.givens),
+    aidMemoire: createAidMemoire(puzzle.size),
+  };
 }
 
 function formatTime(seconds: number): string {
@@ -245,6 +286,8 @@ function errorMessage(error: unknown): string {
 
 function constraintLabel(type: string): string {
   if (type === "xv") return "Sum pairs (5/10)";
+  if (type === "x-sum") return "X-sums";
+  if (type === "false-clues") return "False clues";
   return type
     .split("-")
     .map((part) => part[0]?.toUpperCase() + part.slice(1))
@@ -264,8 +307,19 @@ export function Workbench() {
   const [showDigitCompletion, setShowDigitCompletion] = useState(true);
   const [enableDigitHighlight, setEnableDigitHighlight] = useState(true);
   const [highlightedDigit, setHighlightedDigit] = useState<number | null>(null);
+  const [candidateOverlay, setCandidateOverlay] = useState<CandidateOverlay>();
+  const [aidMemoire, setAidMemoire] = useState<AidMemoireState>(
+    boot.aidMemoire,
+  );
+  const [aidMemoireCell, setAidMemoireCell] = useState(0);
+  const [aidMemoireActive, setAidMemoireActive] = useState(false);
   const [past, setPast] = useState<HistoryEntry[]>([]);
   const [future, setFuture] = useState<HistoryEntry[]>([]);
+  const [gameplayHistory, setGameplayHistory] = useState<GameplayHistory>(() =>
+    createGameplayHistory(boot.session, boot.aidMemoire),
+  );
+  const [historyOpen, setHistoryOpen] = useState(false);
+  const [replayMomentId, setReplayMomentId] = useState<string>();
   const [busy, setBusy] = useState(false);
   const [feedback, setFeedback] = useState<Feedback>();
   const [logical, setLogical] = useState<LogicalSolveResult>();
@@ -286,9 +340,30 @@ export function Workbench() {
   const workerRef = useRef<SolverWorkerClient | null>(null);
   const draggingRef = useRef(false);
   const workbenchRef = useRef<HTMLElement>(null);
+  const replayReturnSessionRef = useRef<PlaySession | null>(null);
+  const replayReturnAidMemoireRef = useRef<AidMemoireState | null>(null);
 
   const normalized = useMemo(() => safeNormalize(puzzle), [puzzle]);
+  const replayMoment = useMemo(
+    () =>
+      replayMomentId === undefined
+        ? undefined
+        : gameplayMoment(gameplayHistory, replayMomentId),
+    [gameplayHistory, replayMomentId],
+  );
+  const currentHypothesis = useMemo(
+    () => activeHypothesis(gameplayHistory),
+    [gameplayHistory],
+  );
   const selectedSet = useMemo(() => new Set(selection), [selection]);
+  const boardSelectedSet = useMemo(
+    () => (aidMemoireActive ? new Set<number>() : selectedSet),
+    [aidMemoireActive, selectedSet],
+  );
+  const handleCandidateOverlayChange = useCallback(
+    (overlay: CandidateOverlay | undefined) => setCandidateOverlay(overlay),
+    [],
+  );
   const completionData = useMemo(
     () => digitCompletions(puzzle.size, session.values),
     [puzzle.size, session.values],
@@ -345,20 +420,37 @@ export function Workbench() {
   }, []);
 
   const currentHistory = useCallback(
-    (): HistoryEntry => ({ puzzle, session: snapshotSession(session) }),
+    (): HistoryEntry => ({
-    [puzzle, session],
+      puzzle,
+      session: snapshotSession(session),
+      aidMemoire: cloneAidMemoire(aidMemoire),
+    }),
+    [aidMemoire, puzzle, session],
   );
 
   const commit = useCallback(
     (nextPuzzle: PuzzleDefinition, nextSession: PlaySession): void => {
       setPast((entries) => [...entries, currentHistory()].slice(-MAX_HISTORY));
       setFuture([]);
+      setGameplayHistory((current) =>
+        workspace === "play" && nextPuzzle === puzzle
+          ? recordGameplayMoment(
+              current,
+              nextSession,
+              describeGameplayChange(session, nextSession, puzzle.size),
+              aidMemoire,
+            )
+          : createGameplayHistory(nextSession, aidMemoire),
+      );
+      replayReturnSessionRef.current = null;
+      replayReturnAidMemoireRef.current = null;
+      setReplayMomentId(undefined);
       setPuzzle(nextPuzzle);
       setSession(nextSession);
       clearAnalysis();
       setFeedback(undefined);
     },
-    [clearAnalysis, currentHistory],
+    [aidMemoire, clearAnalysis, currentHistory, puzzle, session, workspace],
   );
 
   const loadPuzzle = useCallback(
@@ -372,12 +464,26 @@ export function Workbench() {
         | "candidates"
         | "colors"
         | "elapsedMs"
+        | "aidMemoire"
       >,
       projectId?: string,
     ): void => {
       const valid = normalizePuzzle(nextPuzzle);
+      const nextSession = sessionFromDocument(valid, progress);
+      const nextAidMemoire = aidMemoireFromPortable(
+        progress?.aidMemoire,
+        valid.size,
+      );
       setPuzzle(valid);
-      setSession(sessionFromDocument(valid, progress));
+      setSession(nextSession);
+      setAidMemoire(nextAidMemoire);
+      setAidMemoireCell(0);
+      setAidMemoireActive(false);
+      setGameplayHistory(createGameplayHistory(nextSession, nextAidMemoire));
+      replayReturnSessionRef.current = null;
+      replayReturnAidMemoireRef.current = null;
+      setReplayMomentId(undefined);
+      setHistoryOpen(false);
       setSelection([0]);
       setActiveCell(0);
       setHighlightedDigit(null);
@@ -393,8 +499,21 @@ export function Workbench() {
   const restoreProject = useCallback(
     (record: SudokuProjectRecord): void => {
       const valid = normalizePuzzle(toDomainPuzzle(record.puzzle));
+      const nextSession = sessionFromProgress(valid, record.progress);
+      const nextAidMemoire = aidMemoireFromPortable(
+        record.progress?.aidMemoire ?? record.puzzle.aidMemoire,
+        valid.size,
+      );
       setPuzzle(valid);
-      setSession(sessionFromProgress(valid, record.progress));
+      setSession(nextSession);
+      setAidMemoire(nextAidMemoire);
+      setAidMemoireCell(0);
+      setAidMemoireActive(false);
+      setGameplayHistory(createGameplayHistory(nextSession, nextAidMemoire));
+      replayReturnSessionRef.current = null;
+      replayReturnAidMemoireRef.current = null;
+      setReplayMomentId(undefined);
+      setHistoryOpen(false);
       setSelection([0]);
       setActiveCell(0);
       setHighlightedDigit(null);
@@ -451,24 +570,46 @@ export function Workbench() {
   const undo = useCallback(() => {
     const target = past.at(-1);
     if (target === undefined) return;
+    const restored = restoreSnapshot(session, target.session);
     setFuture((entries) =>
       [currentHistory(), ...entries].slice(0, MAX_HISTORY),
     );
     setPast(past.slice(0, -1));
     setPuzzle(target.puzzle);
-    setSession((current) => restoreSnapshot(current, target.session));
+    setSession(restored);
+    setAidMemoire(cloneAidMemoire(target.aidMemoire));
+    setAidMemoireActive(false);
+    setGameplayHistory((current) =>
+      workspace === "play" && target.puzzle === puzzle
+        ? recordGameplayMoment(current, restored, "Undo", target.aidMemoire)
+        : createGameplayHistory(restored, target.aidMemoire),
+    );
+    replayReturnSessionRef.current = null;
+    replayReturnAidMemoireRef.current = null;
+    setReplayMomentId(undefined);
     clearAnalysis();
-  }, [clearAnalysis, currentHistory, past]);
+  }, [clearAnalysis, currentHistory, past, puzzle, session, workspace]);
 
   const redo = useCallback(() => {
     const target = future[0];
     if (target === undefined) return;
+    const restored = restoreSnapshot(session, target.session);
     setPast((entries) => [...entries, currentHistory()].slice(-MAX_HISTORY));
     setFuture(future.slice(1));
     setPuzzle(target.puzzle);
-    setSession((current) => restoreSnapshot(current, target.session));
+    setSession(restored);
+    setAidMemoire(cloneAidMemoire(target.aidMemoire));
+    setAidMemoireActive(false);
+    setGameplayHistory((current) =>
+      workspace === "play" && target.puzzle === puzzle
+        ? recordGameplayMoment(current, restored, "Redo", target.aidMemoire)
+        : createGameplayHistory(restored, target.aidMemoire),
+    );
+    replayReturnSessionRef.current = null;
+    replayReturnAidMemoireRef.current = null;
+    setReplayMomentId(undefined);
     clearAnalysis();
-  }, [clearAnalysis, currentHistory, future]);
+  }, [clearAnalysis, currentHistory, future, puzzle, session, workspace]);
 
   const changeSelection = useCallback(
     (cell: number, additive: boolean, toggle: boolean): void => {
@@ -488,6 +629,7 @@ export function Workbench() {
   const handlePointerDown = useCallback(
     (cell: number, event: PointerEvent<HTMLButtonElement>) => {
       if (session.paused) return;
+      setAidMemoireActive(false);
       event.preventDefault();
       event.currentTarget.focus();
       const command = event.ctrlKey || event.metaKey;
@@ -528,9 +670,42 @@ export function Workbench() {
     [changeSelection, session.paused],
   );
 
+  const updateAidMemoire = useCallback(
+    (next: AidMemoireState, label = "Aid-mémoire updated") => {
+      if (next === aidMemoire) return;
+      setPast((entries) => [...entries, currentHistory()].slice(-MAX_HISTORY));
+      setFuture([]);
+      setAidMemoire(next);
+      setGameplayHistory((current) =>
+        recordGameplayMoment(current, session, label, next),
+      );
+      if (!next.enabled) setAidMemoireActive(false);
+      setFeedback(undefined);
+    },
+    [aidMemoire, currentHistory, session],
+  );
+
   const enterValue = useCallback(
-    (value: number): void => {
+    (value: number, target: "auto" | "board" = "auto"): void => {
       if (session.paused) return;
+      if (
+        target === "auto" &&
+        workspace === "play" &&
+        aidMemoire.enabled &&
+        aidMemoireActive
+      ) {
+        updateAidMemoire(
+          enterAidMemoireCell(
+            aidMemoire,
+            aidMemoireCell,
+            entryMode,
+            value,
+            puzzle.size,
+          ),
+          `Updated aid-mémoire cell ${String(aidMemoireCell + 1)}`,
+        );
+        return;
+      }
       if (workspace === "set" && entryMode === "value") {
         const givens = [...puzzle.givens];
         const values = [...session.values];
@@ -554,37 +729,68 @@ export function Workbench() {
         enterSelection(session, selectedSet, entryMode, value, puzzle.givens),
       );
     },
-    [commit, entryMode, puzzle, selectedSet, session, workspace],
+    [
+      aidMemoire,
+      aidMemoireActive,
+      aidMemoireCell,
+      commit,
+      entryMode,
+      puzzle,
+      selectedSet,
+      session,
+      updateAidMemoire,
+      workspace,
+    ],
   );
 
-  const erase = useCallback((): void => {
+  const erase = useCallback(
-    if (session.paused) return;
+    (target: "auto" | "board" = "auto"): void => {
-    if (workspace === "set" && entryMode === "value") {
+      if (session.paused) return;
-      const givens = [...puzzle.givens];
+      if (
-      const values = [...session.values];
+        target === "auto" &&
-      for (const cell of selectedSet) {
+        workspace === "play" &&
-        givens[cell] = 0;
+        aidMemoire.enabled &&
-        values[cell] = 0;
+        aidMemoireActive
+      ) {
+        updateAidMemoire(
+          eraseAidMemoireCell(aidMemoire, aidMemoireCell, entryMode),
+          `Erased aid-mémoire cell ${String(aidMemoireCell + 1)}`,
+        );
+        return;
       }
-      commit({ ...puzzle, givens }, { ...session, values });
+      if (workspace === "set" && entryMode === "value") {
-      return;
+        const givens = [...puzzle.givens];
-    }
+        const values = [...session.values];
-    commit(
+        for (const cell of selectedSet) {
+          givens[cell] = 0;
+          values[cell] = 0;
+        }
+        commit({ ...puzzle, givens }, { ...session, values });
+        return;
+      }
+      commit(
+        puzzle,
+        eraseSelection(session, selectedSet, entryMode, puzzle.givens),
+      );
+    },
+    [
+      aidMemoire,
+      aidMemoireActive,
+      aidMemoireCell,
+      commit,
+      entryMode,
       puzzle,
-      eraseSelection(session, selectedSet, entryMode, puzzle.givens),
+      selectedSet,
-    );
+      session,
-  }, [commit, entryMode, puzzle, selectedSet, session, workspace]);
+      updateAidMemoire,
+      workspace,
+    ],
+  );
 
   const moveActive = useCallback(
-    (deltaRow: number, deltaColumn: number, extend: boolean): void => {
+    (key: string, extend: boolean, command: boolean): void => {
-      const row = Math.floor(activeCell / puzzle.size);
+      const next = navigateGridCell(activeCell, puzzle.size, key, command);
-      const column = activeCell % puzzle.size;
+      if (next === null) return;
-      const nextRow = Math.max(0, Math.min(puzzle.size - 1, row + deltaRow));
-      const nextColumn = Math.max(
-        0,
-        Math.min(puzzle.size - 1, column + deltaColumn),
-      );
-      const next = nextRow * puzzle.size + nextColumn;
       changeSelection(next, extend, false);
       requestAnimationFrame(() => {
         workbenchRef.current
@@ -597,6 +803,7 @@ export function Workbench() {
 
   const handleKeyDown = useCallback(
     (event: KeyboardEvent<HTMLDivElement>): void => {
+      setAidMemoireActive(false);
       const command = event.ctrlKey || event.metaKey;
       if (command && event.key.toLowerCase() === "z") {
         event.preventDefault();
@@ -620,16 +827,20 @@ export function Workbench() {
         );
         return;
       }
-      const movement: Record<string, readonly [number, number]> = {
+      if (
-        ArrowUp: [-1, 0],
+        [
-        ArrowDown: [1, 0],
+          "ArrowUp",
-        ArrowLeft: [0, -1],
+          "ArrowDown",
-        ArrowRight: [0, 1],
+          "ArrowLeft",
-      };
+          "ArrowRight",
-      const delta = movement[event.key];
+          "Home",
-      if (delta !== undefined) {
+          "End",
+          "PageUp",
+          "PageDown",
+        ].includes(event.key)
+      ) {
         event.preventDefault();
-        moveActive(delta[0], delta[1], event.shiftKey);
+        moveActive(event.key, event.shiftKey, command);
         return;
       }
       if (
@@ -638,7 +849,7 @@ export function Workbench() {
         event.key === "0"
       ) {
         event.preventDefault();
-        erase();
+        erase("board");
         return;
       }
       if (!command) {
@@ -657,7 +868,7 @@ export function Workbench() {
         const value = valueForKey(event.key, puzzle.size);
         if (value !== null) {
           event.preventDefault();
-          enterValue(value);
+          enterValue(value, "board");
         }
       }
     },
@@ -789,16 +1000,18 @@ export function Workbench() {
         kind:
           result.count === 1 && !result.truncated
             ? "success"
-            : result.count === 0 || result.count >= 2
+            : result.count >= 2 || (result.count === 0 && !result.truncated)
               ? "error"
               : "info",
         message:
-          result.count === 0
+          result.count >= 2
-            ? "The definition has no solution."
+            ? "The definition has multiple solutions."
-            : result.count >= 2
+            : result.truncated
-              ? "The definition has multiple solutions."
+              ? result.count === 0
-              : result.truncated
+                ? "Search reached a safety limit before finding a solution; solvability is still unknown."
-                ? "A solution was found, but uniqueness was not established before a safety limit."
+                : "A solution was found, but uniqueness was not established before a safety limit."
+              : result.count === 0
+                ? "The definition has no solution."
                 : `The definition is valid and uniquely solvable (${result.nodes.toLocaleString()} search nodes).`,
       });
     } catch (error) {
@@ -828,7 +1041,7 @@ export function Workbench() {
         setWorkspace("generate");
         setFeedback({
           kind: "success",
-          message: `Generated a unique ${generated.variant} puzzle. Rated ${generated.difficulty.label}${generated.difficulty.score === null ? "" : ` (${String(generated.difficulty.score)}/100)`}.`,
+          message: `Generated a unique ${generated.variant} puzzle${generated.requestedTechnique === undefined ? "" : ` featuring ${generated.requestedTechnique.replaceAll("-", " ")}`}. Rated ${generated.difficulty.label}${generated.difficulty.score === null ? "" : ` (${String(generated.difficulty.score)}/100)`}.`,
         });
       } catch (error) {
         setFeedback({ kind: "error", message: errorMessage(error) });
@@ -899,7 +1112,7 @@ export function Workbench() {
     try {
       const now = Date.now();
       const document = fromDomainPuzzle(puzzle);
-      const progress = progressFromSession(puzzle, session, solved);
+      const progress = progressFromSession(puzzle, session, solved, aidMemoire);
       let record: SudokuProjectRecord;
       const existing = currentProjectId
         ? await library.get(currentProjectId)
@@ -928,7 +1141,7 @@ export function Workbench() {
     } finally {
       setLibraryBusy(false);
     }
-  }, [currentProjectId, puzzle, refreshLibrary, session, solved]);
+  }, [aidMemoire, currentProjectId, puzzle, refreshLibrary, session, solved]);
 
   const openProject = useCallback(
     async (id: string) => {
@@ -1032,13 +1245,167 @@ export function Workbench() {
     if (cells.length === 0) return;
     setSelection([...cells]);
     setActiveCell(cells[0]!);
+    setAidMemoireActive(false);
   }, []);
 
-  const activeConstraints = useMemo(
+  const createNamedSavepoint = useCallback(
-    () => [...new Set(normalized.puzzle.constraints.map((item) => item.type))],
+    (name: string) => {
-    [normalized.puzzle.constraints],
+      try {
+        setGameplayHistory(
+          createSavepoint(gameplayHistory, session, name, aidMemoire),
+        );
+        setFeedback({
+          kind: "success",
+          message: `Saved “${name.trim()}” locally for this solve.`,
+        });
+      } catch (error) {
+        setFeedback({ kind: "error", message: errorMessage(error) });
+      }
+    },
+    [aidMemoire, gameplayHistory, session],
   );
 
+  const restoreNamedSavepoint = useCallback(
+    (savepointId: string) => {
+      try {
+        const transition = restoreSavepoint(gameplayHistory, savepointId);
+        const restored = sessionFromGameplayState(transition.state);
+        setPast((entries) =>
+          [...entries, currentHistory()].slice(-MAX_HISTORY),
+        );
+        setFuture([]);
+        setGameplayHistory(transition.history);
+        setSession(restored);
+        setAidMemoire(
+          aidMemoireFromGameplayState(transition.state, puzzle.size),
+        );
+        setAidMemoireActive(false);
+        replayReturnSessionRef.current = null;
+        replayReturnAidMemoireRef.current = null;
+        setReplayMomentId(undefined);
+        setHistoryOpen(false);
+        clearAnalysis();
+        setFeedback({ kind: "success", message: "Savepoint restored." });
+      } catch (error) {
+        setFeedback({ kind: "error", message: errorMessage(error) });
+      }
+    },
+    [clearAnalysis, currentHistory, gameplayHistory, puzzle.size],
+  );
+
+  const startHypothesis = useCallback(
+    (name: string, fromMomentId?: string) => {
+      try {
+        const transition = beginHypothesis(
+          gameplayHistory,
+          session,
+          name,
+          fromMomentId,
+          aidMemoire,
+        );
+        setGameplayHistory(transition.history);
+        setSession(sessionFromGameplayState(transition.state));
+        setAidMemoire(
+          aidMemoireFromGameplayState(transition.state, puzzle.size),
+        );
+        setAidMemoireActive(false);
+        setPast([]);
+        setFuture([]);
+        replayReturnSessionRef.current = null;
+        replayReturnAidMemoireRef.current = null;
+        setReplayMomentId(undefined);
+        setHistoryOpen(false);
+        clearAnalysis();
+        setFeedback({
+          kind: "info",
+          message: `Hypothesis “${name.trim()}” started. Its moves are isolated until you keep or discard them.`,
+        });
+      } catch (error) {
+        setFeedback({ kind: "error", message: errorMessage(error) });
+      }
+    },
+    [aidMemoire, clearAnalysis, gameplayHistory, puzzle.size, session],
+  );
+
+  const completeHypothesis = useCallback(
+    (decision: "keep" | "discard") => {
+      try {
+        const transition = finishHypothesis(
+          gameplayHistory,
+          session,
+          decision,
+          aidMemoire,
+        );
+        setGameplayHistory(transition.history);
+        setSession(sessionFromGameplayState(transition.state));
+        setAidMemoire(
+          aidMemoireFromGameplayState(transition.state, puzzle.size),
+        );
+        setAidMemoireActive(false);
+        setPast([]);
+        setFuture([]);
+        replayReturnSessionRef.current = null;
+        replayReturnAidMemoireRef.current = null;
+        setReplayMomentId(undefined);
+        setHistoryOpen(false);
+        clearAnalysis();
+        setFeedback({
+          kind: "success",
+          message:
+            decision === "keep"
+              ? "Hypothesis changes kept in the main solve."
+              : "Hypothesis discarded; its branch remains available in replay.",
+        });
+      } catch (error) {
+        setFeedback({ kind: "error", message: errorMessage(error) });
+      }
+    },
+    [aidMemoire, clearAnalysis, gameplayHistory, puzzle.size, session],
+  );
+
+  const replayHistoryMoment = useCallback(
+    (momentId: string) => {
+      const moment = gameplayMoment(gameplayHistory, momentId);
+      if (moment === undefined) return;
+      if (replayReturnSessionRef.current === null) {
+        replayReturnSessionRef.current = session;
+        replayReturnAidMemoireRef.current = aidMemoire;
+      }
+      setSession(sessionFromGameplayState(moment.state, true));
+      setAidMemoire(aidMemoireFromGameplayState(moment.state, puzzle.size));
+      setAidMemoireActive(false);
+      setReplayMomentId(moment.id);
+      setHistoryOpen(false);
+      setHighlightedDigit(null);
+    },
+    [aidMemoire, gameplayHistory, puzzle.size, session],
+  );
+
+  const returnToLiveGrid = useCallback(() => {
+    const live = replayReturnSessionRef.current;
+    const liveAidMemoire = replayReturnAidMemoireRef.current;
+    if (live !== null) setSession(live);
+    if (liveAidMemoire !== null) setAidMemoire(liveAidMemoire);
+    replayReturnSessionRef.current = null;
+    replayReturnAidMemoireRef.current = null;
+    setAidMemoireActive(false);
+    setReplayMomentId(undefined);
+  }, []);
+
+  const activeConstraints = useMemo(() => {
+    const types: string[] = [
+      ...new Set(normalized.puzzle.constraints.map((item) => item.type)),
+    ];
+    if (
+      normalized.puzzle.constraints.some(
+        (item) => "negated" in item && item.negated === true,
+      )
+    ) {
+      types.push("false-clues");
+    }
+    return types;
+  }, [normalized.puzzle.constraints]);
+
   return (
     <main className="sudoku-workbench" ref={workbenchRef}>
       <header className="workbench-hero">
@@ -1119,7 +1486,15 @@ export function Workbench() {
             type="button"
             className={workspace === id ? "is-active" : ""}
             aria-current={workspace === id ? "page" : undefined}
+            disabled={currentHypothesis !== undefined && id !== "play"}
+            title={
+              currentHypothesis !== undefined && id !== "play"
+                ? "Keep or discard the active hypothesis first"
+                : undefined
+            }
             onClick={() => {
+              if (id !== "play") returnToLiveGrid();
+              if (id !== "play") setAidMemoireActive(false);
               setWorkspace(id);
               if (id === "set") setEntryMode("value");
             }}
@@ -1169,20 +1544,46 @@ export function Workbench() {
         <section className="board-column" aria-label="Puzzle board">
           <div className="board-toolbar">
             <div className="toolbar-group">
-              <button type="button" disabled={!past.length} onClick={undo}>
+              <button
+                type="button"
+                disabled={!past.length || replayMoment !== undefined}
+                onClick={undo}
+              >
                 Undo
               </button>
-              <button type="button" disabled={!future.length} onClick={redo}>
+              <button
+                type="button"
+                disabled={!future.length || replayMoment !== undefined}
+                onClick={redo}
+              >
                 Redo
               </button>
+              {workspace === "play" && (
+                <button type="button" onClick={() => setHistoryOpen(true)}>
+                  {currentHypothesis
+                    ? `Hypothesis: ${currentHypothesis.name}`
+                    : "History & branches"}
+                </button>
+              )}
+              {replayMoment && (
+                <button type="button" onClick={returnToLiveGrid}>
+                  Return live
+                </button>
+              )}
             </div>
             <span>
-              {selection.length === 1
+              {replayMoment
-                ? cellLabel(selection[0]!, puzzle.size)
+                ? `Replay · ${replayMoment.label}`
-                : `${String(selection.length)} cells selected`}
+                : aidMemoireActive && aidMemoire.enabled
+                  ? `Aid-mémoire · ${aidMemoire.cells[aidMemoireCell]?.label || `cell ${String(aidMemoireCell + 1)}`}`
+                  : selection.length === 1
+                    ? cellLabel(selection[0]!, puzzle.size)
+                    : `${String(selection.length)} cells selected`}
             </span>
           </div>
-          <div className={`board-surface${session.paused ? " is-paused" : ""}`}>
+          <div
+            className={`board-surface${session.paused && replayMoment === undefined ? " is-paused" : ""}${replayMoment ? " is-replay" : ""}`}
+          >
             <SudokuBoard
               puzzle={normalized.puzzle}
               values={session.values}
@@ -1190,16 +1591,19 @@ export function Workbench() {
               centerMarks={session.centerMarks}
               colors={session.colors}
               candidates={candidateMasks}
-              selected={selectedSet}
+              selected={boardSelectedSet}
               highlighted={highlightedCells}
               conflicts={conflictCells}
               activeCell={activeCell}
               showCandidates={showCandidates}
+              candidateOverlay={
+                workspace === "helpers" ? candidateOverlay : undefined
+              }
               onCellPointerDown={handlePointerDown}
               onCellPointerEnter={handlePointerEnter}
               onKeyDown={handleKeyDown}
             />
-            {session.paused && (
+            {session.paused && replayMoment === undefined && (
               <button
                 type="button"
                 className="paused-cover"
@@ -1225,6 +1629,25 @@ export function Workbench() {
               }
             />
           )}
+          {workspace === "play" &&
+            aidMemoire.enabled &&
+            (!session.paused || replayMoment !== undefined) && (
+              <AidMemoire
+                size={puzzle.size}
+                state={aidMemoire}
+                selectedCell={aidMemoireCell}
+                active={aidMemoireActive && replayMoment === undefined}
+                readOnly={replayMoment !== undefined}
+                mode={entryMode}
+                onStateChange={updateAidMemoire}
+                onSelect={(cell) => {
+                  setAidMemoireCell(cell);
+                  setAidMemoireActive(true);
+                  setHighlightedDigit(null);
+                }}
+                onMode={setEntryMode}
+              />
+            )}
           <div className="board-meta">
             <section className="rule-card">
               <p className="eyebrow">Rules</p>
@@ -1247,13 +1670,37 @@ export function Workbench() {
         </section>
 
         <aside className="side-panel">
-          {workspace === "play" && (
+          {workspace === "play" && replayMoment && (
+            <div className="play-panel stack">
+              <div>
+                <p className="eyebrow">Read-only replay</p>
+                <h2>{replayMoment.label}</h2>
+                <p className="muted">
+                  This is the complete grid at{" "}
+                  {formatTime(replayMoment.state.elapsedSeconds)}. Return to the
+                  live grid or start a hypothesis from here.
+                </p>
+              </div>
+              <div className="action-row">
+                <button type="button" onClick={returnToLiveGrid}>
+                  Return to live grid
+                </button>
+                <button type="button" onClick={() => setHistoryOpen(true)}>
+                  Open history
+                </button>
+              </div>
+            </div>
+          )}
+
+          {workspace === "play" && replayMoment === undefined && (
             <div className="play-panel stack">
               <div>
                 <p className="eyebrow">Play locally</p>
                 <h2>Enter your solve</h2>
                 <p className="muted">
-                  Select one or several cells, then use the keypad or keyboard.
+                  {aidMemoireActive && aidMemoire.enabled
+                    ? "The keypad is editing the selected aid-mémoire cell. Select the Sudoku grid to return to normal entry."
+                    : "Select one or several cells, then use the keypad or keyboard."}
                 </p>
               </div>
               <NumberPad
@@ -1323,6 +1770,22 @@ export function Workbench() {
                   />
                   Enable matching-digit highlighting (Ctrl/⌘-click or bar)
                 </label>
+                <label className="option-row">
+                  <input
+                    type="checkbox"
+                    checked={aidMemoire.enabled}
+                    onChange={(event) => {
+                      const enabled = event.target.checked;
+                      updateAidMemoire(
+                        setAidMemoireEnabled(aidMemoire, enabled),
+                        enabled ? "Aid-mémoire shown" : "Aid-mémoire hidden",
+                      );
+                      setAidMemoireActive(enabled);
+                      if (enabled) setAidMemoireCell(0);
+                    }}
+                  />
+                  Show aid-mémoire scratch cells
+                </label>
               </section>
               <section className="panel-section">
                 <button
@@ -1334,8 +1797,9 @@ export function Workbench() {
                 </button>
               </section>
               <p className="muted shortcut-note">
-                Z/X/C/V change mode · arrows move · Shift extends · Ctrl/⌘ Z
+                Z/X/C/V change mode · arrows move · Home/End move across a row ·
-                undoes · Ctrl/⌘-click a placed digit highlights its matches.
+                Shift extends · Ctrl/⌘ Z undoes · Ctrl/⌘-click a placed digit
+                highlights its matches.
               </p>
             </div>
           )}
@@ -1401,9 +1865,13 @@ export function Workbench() {
 
           {workspace === "helpers" && (
             <HelpersWorkspace
+              key={puzzle.size}
               size={puzzle.size}
+              puzzle={normalized.puzzle}
+              values={session.values}
               selectedCells={selection}
               candidateMasks={candidateMasks}
+              onCandidateOverlayChange={handleCandidateOverlayChange}
             />
           )}
         </aside>
@@ -1413,6 +1881,7 @@ export function Workbench() {
         open={importOpen}
         puzzle={puzzle}
         session={session}
+        aidMemoire={aidMemoireToPortable(aidMemoire, puzzle.size)}
         onClose={() => setImportOpen(false)}
         onImport={(next, progress) => {
           try {
@@ -1437,6 +1906,21 @@ export function Workbench() {
         onExport={() => void exportLibrary()}
         onImport={(file) => void importLibrary(file)}
       />
+      <GameplayHistoryDialog
+        open={historyOpen}
+        history={gameplayHistory}
+        replayMomentId={replayMomentId}
+        onClose={() => setHistoryOpen(false)}
+        onCreateSavepoint={createNamedSavepoint}
+        onRestoreSavepoint={restoreNamedSavepoint}
+        onDeleteSavepoint={(savepointId) =>
+          setGameplayHistory((current) => deleteSavepoint(current, savepointId))
+        }
+        onStartHypothesis={startHypothesis}
+        onFinishHypothesis={completeHypothesis}
+        onReplayMoment={replayHistoryMoment}
+        onReturnLive={returnToLiveGrid}
+      />
     </main>
   );
 }

src/data/samples.ts

@@ -237,6 +237,52 @@ export const NON_CONSECUTIVE_SAMPLE: PuzzleDefinition = {
   solution: grid("315264", "642531", "264153", "531426", "153642", "426315"),
 };
 
+/** Original compact fixture demonstrating outside, inclusion, maximum and liar clues. */
+export const TRUTH_AND_LIES_SAMPLE: PuzzleDefinition = {
+  version: 1,
+  size: 4,
+  givens: grid("0234", "3012", "4301", "2140"),
+  title: "Truth and lies",
+  author: "Sudoku Tools",
+  rules:
+    "Normal 4×4 Sudoku rules apply. Red dashed clues marked ≠ must be false; all other clues are true.",
+  solution: grid("1234", "3412", "4321", "2143"),
+  constraints: [
+    { type: "x-sum", side: "left", index: 0, sum: 1 },
+    { type: "skyscraper", side: "left", index: 1, count: 2 },
+    { type: "quadruple", cells: [0, 1, 4, 5], digits: [1, 2, 3, 4] },
+    { type: "maximum", cell: 5 },
+    {
+      type: "killer-cage",
+      cells: [8, 9],
+      sum: 6,
+      noRepeat: false,
+      negated: true,
+    },
+    { type: "thermo", cells: [12, 13], negated: true },
+    { type: "kropki", a: 14, b: 15, kind: "black", negated: true },
+    { type: "xv", a: 2, b: 3, total: 5, negated: true },
+    { type: "inequality", lesser: 10, greater: 11, negated: true },
+    { type: "renban", cells: [12, 14], negated: true },
+    { type: "palindrome", cells: [8, 11], negated: true },
+    { type: "x-sum", side: "right", index: 2, sum: 2, negated: true },
+    {
+      type: "skyscraper",
+      side: "bottom",
+      index: 3,
+      count: 3,
+      negated: true,
+    },
+    {
+      type: "quadruple",
+      cells: [4, 5, 8, 9],
+      digits: [1],
+      negated: true,
+    },
+    { type: "maximum", cell: 10, negated: true },
+  ],
+};
+
 export interface SamplePuzzleEntry {
   readonly id: string;
   readonly label: string;
@@ -277,6 +323,11 @@ export const SAMPLE_CATALOG: readonly SamplePuzzleEntry[] = [
     label: "Non-consecutive 6 × 6",
     puzzle: NON_CONSECUTIVE_SAMPLE,
   },
+  {
+    id: "truth-and-lies",
+    label: "Truth and lies 4 × 4",
+    puzzle: TRUTH_AND_LIES_SAMPLE,
+  },
 ];
 
 export const SAMPLE_PUZZLES: readonly PuzzleDefinition[] = SAMPLE_CATALOG.map(

src/domain/compile.ts

@@ -1,5 +1,10 @@
 import { cellColumn, cellRow, orthogonalNeighbours } from "./geometry";
-import type { CellId, NormalizedPuzzle, VariantConstraint } from "./types";
+import type {
+  CellId,
+  NormalizedPuzzle,
+  OutsideClueSide,
+  VariantConstraint,
+} from "./types";
 
 export type UnitKind = "row" | "column" | "region" | "diagonal";
 
@@ -25,6 +30,26 @@ function addPeerPair(peers: Set<CellId>[], a: CellId, b: CellId): void {
   peers[b]?.add(a);
 }
 
+/** Cells seen from an outside clue, ordered from the clue into the grid. */
+export function outsideLineCells(
+  size: number,
+  side: OutsideClueSide,
+  index: number,
+): CellId[] {
+  return Array.from({ length: size }, (_, offset) => {
+    switch (side) {
+      case "top":
+        return offset * size + index;
+      case "right":
+        return index * size + size - offset - 1;
+      case "bottom":
+        return (size - offset - 1) * size + index;
+      case "left":
+        return index * size + offset;
+    }
+  });
+}
+
 function cellsForConstraint(
   size: number,
   constraint: VariantConstraint,
@@ -52,6 +77,13 @@ function cellsForConstraint(
       return [constraint.a, constraint.b];
     case "inequality":
       return [constraint.lesser, constraint.greater];
+    case "x-sum":
+    case "skyscraper":
+      return outsideLineCells(size, constraint.side, constraint.index);
+    case "quadruple":
+      return constraint.cells;
+    case "maximum":
+      return [constraint.cell, ...orthogonalNeighbours(size, constraint.cell)];
   }
 }
 
@@ -101,7 +133,11 @@ export function compilePuzzle(puzzle: NormalizedPuzzle): CompiledPuzzle {
     for (const cell of new Set(cellsForConstraint(size, constraint))) {
       constraintsByCell[cell]?.push(constraintIndex);
     }
-    if (constraint.type === "killer-cage" && constraint.noRepeat !== false) {
+    if (
+      constraint.type === "killer-cage" &&
+      constraint.noRepeat !== false &&
+      constraint.negated !== true
+    ) {
       for (const a of constraint.cells) {
         for (const b of constraint.cells) addPeerPair(peers, a, b);
       }

src/domain/geometry.ts

@@ -126,3 +126,36 @@ export function orthogonalNeighbours(size: number, cell: CellId): CellId[] {
   if (column + 1 < size) result.push(cell + 1);
   return result;
 }
+
+/** True when four cells meet at one internal grid intersection. */
+export function cellsFormQuadruple(
+  size: number,
+  cells: readonly CellId[],
+): boolean {
+  if (cells.length !== 4 || new Set(cells).size !== 4) return false;
+  try {
+    const rows = [...new Set(cells.map((cell) => cellRow(size, cell)))].sort(
+      (a, b) => a - b,
+    );
+    const columns = [
+      ...new Set(cells.map((cell) => cellColumn(size, cell))),
+    ].sort((a, b) => a - b);
+    if (
+      rows.length !== 2 ||
+      columns.length !== 2 ||
+      rows[1] !== rows[0]! + 1 ||
+      columns[1] !== columns[0]! + 1
+    ) {
+      return false;
+    }
+    const expected = new Set([
+      cellId(size, rows[0]!, columns[0]!),
+      cellId(size, rows[0]!, columns[1]!),
+      cellId(size, rows[1]!, columns[0]!),
+      cellId(size, rows[1]!, columns[1]!),
+    ]);
+    return cells.every((cell) => expected.has(cell));
+  } catch {
+    return false;
+  }
+}

src/domain/rules.ts

@@ -1,4 +1,9 @@
-import { compilePuzzle, type CompiledPuzzle } from "./compile";
+import {
+  compilePuzzle,
+  outsideLineCells,
+  type CompiledPuzzle,
+} from "./compile";
+import { orthogonalNeighbours } from "./geometry";
 import type {
   CellId,
   NormalizedPuzzle,
@@ -21,8 +26,9 @@ function sumRange(
   size: number,
   noRepeat: boolean,
 ): readonly [number, number] {
+  const current = assigned.reduce((sum, value) => sum + value, 0);
+  if (blanks === 0) return [current, current];
   if (!noRepeat) {
-    const current = assigned.reduce((sum, value) => sum + value, 0);
     return [current + blanks, current + blanks * size];
   }
   const used = new Set(assigned);
@@ -32,7 +38,6 @@ function sumRange(
   ).filter((value) => !used.has(value));
   if (available.length < blanks)
     return [Number.POSITIVE_INFINITY, Number.NEGATIVE_INFINITY];
-  const current = assigned.reduce((sum, value) => sum + value, 0);
   const low = available
     .slice(0, blanks)
     .reduce((sum, value) => sum + value, current);
@@ -57,7 +62,217 @@ function sumsCanMeet(
   return [sum + blanks, sum + blanks * size];
 }
 
-export function constraintIsFeasible(
+function canChooseDistinctSum(
+  available: readonly number[],
+  count: number,
+  target: number,
+): boolean {
+  if (count < 0 || count > available.length || target < 0) return false;
+  if (count === 0) return target === 0;
+  const ordered = [...available].sort((a, b) => a - b);
+  const minimum = ordered
+    .slice(0, count)
+    .reduce((total, digit) => total + digit, 0);
+  const maximum = ordered
+    .slice(-count)
+    .reduce((total, digit) => total + digit, 0);
+  if (target < minimum || target > maximum) return false;
+
+  const sums = new Array<bigint>(count + 1).fill(0n);
+  sums[0] = 1n;
+  let processed = 0;
+  for (const digit of ordered) {
+    processed += 1;
+    for (
+      let selected = Math.min(count, processed);
+      selected >= 1;
+      selected -= 1
+    ) {
+      sums[selected] =
+        (sums[selected] ?? 0n) | ((sums[selected - 1] ?? 0n) << BigInt(digit));
+    }
+  }
+  return ((sums[count] ?? 0n) & (1n << BigInt(target))) !== 0n;
+}
+
+function xSumCanMeet(
+  values: readonly number[],
+  cells: readonly CellId[],
+  size: number,
+  target: number,
+): boolean {
+  const line = valuesAt(values, cells);
+  const fixed = line.filter((value) => value !== 0);
+  if (
+    fixed.some((value) => value < 1 || value > size) ||
+    new Set(fixed).size !== fixed.length
+  ) {
+    return false;
+  }
+
+  const first = line[0] ?? 0;
+  const fixedDigits = new Set(fixed);
+  const possibleFirsts =
+    first === 0
+      ? Array.from({ length: size }, (_, index) => index + 1).filter(
+          (digit) => !fixedDigits.has(digit),
+        )
+      : [first];
+
+  return possibleFirsts.some((firstDigit) => {
+    if (firstDigit < 1 || firstDigit > size) return false;
+    const used = new Set(fixedDigits);
+    used.add(firstDigit);
+    let assignedSum = firstDigit;
+    let blanks = 0;
+    for (let position = 1; position < firstDigit; position += 1) {
+      const value = line[position] ?? 0;
+      if (value === 0) blanks += 1;
+      else assignedSum += value;
+    }
+    const available = Array.from(
+      { length: size },
+      (_, index) => index + 1,
+    ).filter((digit) => !used.has(digit));
+    return canChooseDistinctSum(available, blanks, target - assignedSum);
+  });
+}
+
+type SearchResult = "yes" | "no" | "unknown";
+const MAX_SKYSCRAPER_STATES = 50_000;
+
+function skyscraperCanMeet(
+  values: readonly number[],
+  cells: readonly CellId[],
+  size: number,
+  target: number,
+): boolean {
+  const line = valuesAt(values, cells);
+  const fixed = line.filter((value) => value !== 0);
+  if (
+    fixed.some((value) => value < 1 || value > size) ||
+    new Set(fixed).size !== fixed.length
+  ) {
+    return false;
+  }
+  if (fixed.length === 0) return target >= 1 && target <= size;
+
+  let prefixMaximum = 0;
+  let prefixVisible = 0;
+  for (const value of line) {
+    if (value === 0) break;
+    if (value > prefixMaximum) {
+      prefixMaximum = value;
+      prefixVisible += 1;
+    }
+  }
+  const minimumVisible = prefixVisible + (prefixMaximum < size ? 1 : 0);
+  const maximumVisible = prefixVisible + (size - prefixMaximum);
+  if (target < minimumVisible || target > maximumVisible) return false;
+
+  let availableMask = 0;
+  for (let digit = 1; digit <= size; digit += 1) {
+    if (!fixed.includes(digit)) availableMask |= 1 << (digit - 1);
+  }
+  let explored = 0;
+  const memo = new Map<string, SearchResult>();
+  const visit = (
+    position: number,
+    remainingMask: number,
+    tallest: number,
+    visible: number,
+  ): SearchResult => {
+    if (visible > target) return "no";
+    if (position === size) return visible === target ? "yes" : "no";
+    const positionsLeft = size - position;
+    if (
+      visible + positionsLeft < target ||
+      visible + (size - tallest) < target
+    ) {
+      return "no";
+    }
+    explored += 1;
+    if (explored > MAX_SKYSCRAPER_STATES) return "unknown";
+    const key = `${position}:${remainingMask}:${tallest}:${visible}`;
+    const cached = memo.get(key);
+    if (cached !== undefined) return cached;
+
+    const fixedValue = line[position] ?? 0;
+    if (fixedValue !== 0) {
+      const result = visit(
+        position + 1,
+        remainingMask,
+        Math.max(tallest, fixedValue),
+        visible + (fixedValue > tallest ? 1 : 0),
+      );
+      memo.set(key, result);
+      return result;
+    }
+
+    let sawUnknown = false;
+    for (let mask = remainingMask; mask !== 0; mask &= mask - 1) {
+      const bit = mask & -mask;
+      const digit = 32 - Math.clz32(bit);
+      const result = visit(
+        position + 1,
+        remainingMask & ~bit,
+        Math.max(tallest, digit),
+        visible + (digit > tallest ? 1 : 0),
+      );
+      if (result === "yes") {
+        memo.set(key, result);
+        return result;
+      }
+      if (result === "unknown") sawUnknown = true;
+    }
+    const result = sawUnknown ? "unknown" : "no";
+    memo.set(key, result);
+    return result;
+  };
+
+  return visit(0, availableMask, 0, 0) !== "no";
+}
+
+function quadrupleCanMeet(
+  constraint: Extract<VariantConstraint, { readonly type: "quadruple" }>,
+  values: readonly number[],
+): boolean {
+  const assigned = new Map<number, number>();
+  let blanks = 0;
+  for (const cell of constraint.cells) {
+    const value = values[cell] ?? 0;
+    if (value === 0) blanks += 1;
+    else assigned.set(value, (assigned.get(value) ?? 0) + 1);
+  }
+  const required = new Map<number, number>();
+  for (const digit of constraint.digits) {
+    required.set(digit, (required.get(digit) ?? 0) + 1);
+  }
+  let missing = 0;
+  for (const [digit, count] of required) {
+    missing += Math.max(0, count - (assigned.get(digit) ?? 0));
+  }
+  return missing <= blanks;
+}
+
+function maximumCanMeet(
+  cell: CellId,
+  values: readonly number[],
+  size: number,
+): boolean {
+  const maximum = values[cell] ?? 0;
+  const neighbours = orthogonalNeighbours(size, cell).map(
+    (neighbour) => values[neighbour] ?? 0,
+  );
+  if (maximum === 0) {
+    return neighbours.every((value) => value === 0 || value < size);
+  }
+  return neighbours.every((value) =>
+    value === 0 ? maximum > 1 : value < maximum,
+  );
+}
+
+function positiveConstraintIsFeasible(
   constraint: VariantConstraint,
   values: readonly number[],
   size: number,
@@ -168,9 +383,147 @@ export function constraintIsFeasible(
       }
       return true;
     }
+    case "x-sum":
+      return xSumCanMeet(
+        values,
+        outsideLineCells(size, constraint.side, constraint.index),
+        size,
+        constraint.sum,
+      );
+    case "skyscraper":
+      return skyscraperCanMeet(
+        values,
+        outsideLineCells(size, constraint.side, constraint.index),
+        size,
+        constraint.count,
+      );
+    case "quadruple":
+      return quadrupleCanMeet(constraint, values);
+    case "maximum":
+      return maximumCanMeet(constraint.cell, values, size);
   }
 }
 
+function completedCells(
+  constraint: VariantConstraint,
+  size: number,
+): readonly CellId[] | undefined {
+  switch (constraint.type) {
+    case "diagonal":
+    case "anti-knight":
+    case "anti-king":
+    case "non-consecutive":
+      return undefined;
+    case "killer-cage":
+    case "thermo":
+    case "renban":
+    case "palindrome":
+    case "quadruple":
+      return constraint.cells;
+    case "arrow":
+      return [...constraint.bulb, ...constraint.line];
+    case "kropki":
+    case "xv":
+      return [constraint.a, constraint.b];
+    case "inequality":
+      return [constraint.lesser, constraint.greater];
+    case "x-sum":
+    case "skyscraper":
+      return outsideLineCells(size, constraint.side, constraint.index);
+    case "maximum":
+      return [constraint.cell, ...orthogonalNeighbours(size, constraint.cell)];
+  }
+}
+
+/**
+ * Returns whether a false clue can still be satisfied. Unlike an ordinary
+ * feasibility check, a false clue only constrains the grid once the truth of
+ * its positive statement is fixed. Several clue families become fixed before
+ * every geometrically related cell is filled, which is important for bounded
+ * exact search on liar/Wrogn puzzles.
+ */
+function negatedConstraintIsFeasible(
+  constraint: VariantConstraint,
+  values: readonly number[],
+  size: number,
+): boolean {
+  if (constraint.type === "x-sum") {
+    const line = valuesAt(
+      values,
+      outsideLineCells(size, constraint.side, constraint.index),
+    );
+    const first = line[0] ?? 0;
+    if (first === 0) return true;
+    const prefix = line.slice(0, first);
+    if (prefix.some((value) => value === 0)) return true;
+    return prefix.reduce((sum, value) => sum + value, 0) !== constraint.sum;
+  }
+
+  if (constraint.type === "quadruple") {
+    const assigned = new Map<number, number>();
+    for (const cell of constraint.cells) {
+      const value = values[cell] ?? 0;
+      if (value !== 0) assigned.set(value, (assigned.get(value) ?? 0) + 1);
+    }
+    const required = new Map<number, number>();
+    for (const digit of constraint.digits) {
+      required.set(digit, (required.get(digit) ?? 0) + 1);
+    }
+    const positiveAlreadyTrue = [...required].every(
+      ([digit, count]) => (assigned.get(digit) ?? 0) >= count,
+    );
+    return !positiveAlreadyTrue;
+  }
+
+  if (constraint.type === "maximum") {
+    const maximum = values[constraint.cell] ?? 0;
+    if (maximum === 0) return true;
+    const neighbours = orthogonalNeighbours(size, constraint.cell).map(
+      (cell) => values[cell] ?? 0,
+    );
+    if (neighbours.some((value) => value !== 0 && value >= maximum)) {
+      return true;
+    }
+    return !(maximum === size || neighbours.every((value) => value !== 0));
+  }
+
+  if (constraint.type === "palindrome") {
+    let allPairsKnown = true;
+    for (
+      let index = 0;
+      index < Math.floor(constraint.cells.length / 2);
+      index += 1
+    ) {
+      const a = values[constraint.cells[index] ?? -1] ?? 0;
+      const b =
+        values[constraint.cells[constraint.cells.length - index - 1] ?? -1] ??
+        0;
+      if (a !== 0 && b !== 0 && a !== b) return true;
+      if (a === 0 || b === 0) allPairsKnown = false;
+    }
+    if (allPairsKnown) return false;
+  }
+
+  const relevant = completedCells(constraint, size);
+  if (
+    relevant === undefined ||
+    relevant.some((cell) => (values[cell] ?? 0) === 0)
+  ) {
+    return true;
+  }
+  return !positiveConstraintIsFeasible(constraint, values, size);
+}
+
+export function constraintIsFeasible(
+  constraint: VariantConstraint,
+  values: readonly number[],
+  size: number,
+): boolean {
+  const negated = "negated" in constraint && constraint.negated === true;
+  if (!negated) return positiveConstraintIsFeasible(constraint, values, size);
+  return negatedConstraintIsFeasible(constraint, values, size);
+}
+
 function asCompiled(
   puzzle: PuzzleDefinition | NormalizedPuzzle | CompiledPuzzle,
 ): CompiledPuzzle {
@@ -308,6 +661,7 @@ export function findConflicts(
           case "thermo":
           case "renban":
           case "palindrome":
+          case "quadruple":
             return constraint.cells;
           case "arrow":
             return [...constraint.bulb, ...constraint.line];
@@ -316,12 +670,27 @@ export function findConflicts(
             return [constraint.a, constraint.b];
           case "inequality":
             return [constraint.lesser, constraint.greater];
+          case "x-sum":
+          case "skyscraper":
+            return outsideLineCells(
+              compiled.puzzle.size,
+              constraint.side,
+              constraint.index,
+            );
+          case "maximum":
+            return [
+              constraint.cell,
+              ...orthogonalNeighbours(compiled.puzzle.size, constraint.cell),
+            ];
         }
       })();
       conflicts.push({
         kind: "constraint",
         cells,
-        message: `${constraint.type} constraint cannot be satisfied.`,
+        message:
+          "negated" in constraint && constraint.negated === true
+            ? `${constraint.type} clue is true but must be false.`
+            : `${constraint.type} constraint cannot be satisfied.`,
         constraintIndex,
       });
     }

src/domain/types.ts

@@ -29,12 +29,15 @@ export interface KillerCageConstraint {
   readonly sum: number;
   /** Killer cages normally do not repeat digits. Defaults to true. */
   readonly noRepeat?: boolean;
+  /** If true, the completed clue must be false instead of true. */
+  readonly negated?: boolean;
 }
 
 export interface ThermoConstraint {
   readonly type: "thermo";
   /** Ordered from bulb to tip. Values must increase strictly. */
   readonly cells: readonly CellId[];
+  readonly negated?: boolean;
 }
 
 export interface ArrowConstraint {
@@ -42,6 +45,7 @@ export interface ArrowConstraint {
   /** Bulb cells. Their values sum to the values on the line. */
   readonly bulb: readonly CellId[];
   readonly line: readonly CellId[];
+  readonly negated?: boolean;
 }
 
 export interface KropkiConstraint {
@@ -50,6 +54,7 @@ export interface KropkiConstraint {
   readonly b: CellId;
   /** White means consecutive; black means a 1:2 ratio. */
   readonly kind: "white" | "black";
+  readonly negated?: boolean;
 }
 
 export interface XvConstraint {
@@ -57,22 +62,64 @@ export interface XvConstraint {
   readonly a: CellId;
   readonly b: CellId;
   readonly total: 5 | 10;
+  readonly negated?: boolean;
 }
 
 export interface InequalityConstraint {
   readonly type: "inequality";
   readonly lesser: CellId;
   readonly greater: CellId;
+  readonly negated?: boolean;
 }
 
 export interface RenbanConstraint {
   readonly type: "renban";
   readonly cells: readonly CellId[];
+  readonly negated?: boolean;
 }
 
 export interface PalindromeConstraint {
   readonly type: "palindrome";
   readonly cells: readonly CellId[];
+  readonly negated?: boolean;
+}
+
+export type OutsideClueSide = "top" | "right" | "bottom" | "left";
+
+/**
+ * The first digit seen from `side` selects how many cells, including itself,
+ * must add to `sum`. `index` is the zero-based row or column on that side.
+ */
+export interface XSumConstraint {
+  readonly type: "x-sum";
+  readonly side: OutsideClueSide;
+  readonly index: number;
+  readonly sum: number;
+  readonly negated?: boolean;
+}
+
+/** Number of increasing-height records seen across a row or column. */
+export interface SkyscraperConstraint {
+  readonly type: "skyscraper";
+  readonly side: OutsideClueSide;
+  readonly index: number;
+  readonly count: number;
+  readonly negated?: boolean;
+}
+
+/** Every listed digit, including repetitions, must occur in the clue cells. */
+export interface QuadrupleConstraint {
+  readonly type: "quadruple";
+  readonly cells: readonly CellId[];
+  readonly digits: readonly CellValue[];
+  readonly negated?: boolean;
+}
+
+/** The marked cell is greater than each orthogonally adjacent cell. */
+export interface MaximumConstraint {
+  readonly type: "maximum";
+  readonly cell: CellId;
+  readonly negated?: boolean;
 }
 
 export type VariantConstraint =
@@ -87,7 +134,11 @@ export type VariantConstraint =
   | XvConstraint
   | InequalityConstraint
   | RenbanConstraint
-  | PalindromeConstraint;
+  | PalindromeConstraint
+  | XSumConstraint
+  | SkyscraperConstraint
+  | QuadrupleConstraint
+  | MaximumConstraint;
 
 export interface PuzzleDefinition {
   readonly version: 1;

src/domain/validation.ts

@@ -1,4 +1,4 @@
-import { classicRegions } from "./geometry";
+import { cellsFormQuadruple, classicRegions } from "./geometry";
 import { compilePuzzle } from "./compile";
 import { findConflicts } from "./rules";
 import {
@@ -15,6 +15,8 @@ import {
 const MAX_CONSTRAINTS = 4_096;
 const MAX_SHORT_TEXT = 256;
 const MAX_RULES_TEXT = 16_384;
+/** Keeps deliberately impossible false-clue labels finite without requiring reachability. */
+const maximumFalseClueValue = (size: number): number => size ** 4;
 const ROOT_KEYS = new Set([
   "version",
   "size",
@@ -35,16 +37,22 @@ const CONSTRAINT_KEYS: Readonly<
   "anti-knight": new Set(["type"]),
   "anti-king": new Set(["type"]),
   "non-consecutive": new Set(["type"]),
-  "killer-cage": new Set(["type", "cells", "sum", "noRepeat"]),
+  "killer-cage": new Set(["type", "cells", "sum", "noRepeat", "negated"]),
-  thermo: new Set(["type", "cells"]),
+  thermo: new Set(["type", "cells", "negated"]),
-  arrow: new Set(["type", "bulb", "line"]),
+  arrow: new Set(["type", "bulb", "line", "negated"]),
-  kropki: new Set(["type", "a", "b", "kind"]),
+  kropki: new Set(["type", "a", "b", "kind", "negated"]),
-  xv: new Set(["type", "a", "b", "total"]),
+  xv: new Set(["type", "a", "b", "total", "negated"]),
-  inequality: new Set(["type", "lesser", "greater"]),
+  inequality: new Set(["type", "lesser", "greater", "negated"]),
-  renban: new Set(["type", "cells"]),
+  renban: new Set(["type", "cells", "negated"]),
-  palindrome: new Set(["type", "cells"]),
+  palindrome: new Set(["type", "cells", "negated"]),
+  "x-sum": new Set(["type", "side", "index", "sum", "negated"]),
+  skyscraper: new Set(["type", "side", "index", "count", "negated"]),
+  quadruple: new Set(["type", "cells", "digits", "negated"]),
+  maximum: new Set(["type", "cell", "negated"]),
 };
 
+const reachableXSumCache = new Map<number, ReadonlySet<number>>();
+
 function isRecord(value: unknown): value is Record<string, unknown> {
   return typeof value === "object" && value !== null && !Array.isArray(value);
 }
@@ -108,6 +116,72 @@ function validateCells(
   return true;
 }
 
+function validateIntegerRange(
+  value: unknown,
+  path: string,
+  minimum: number,
+  maximum: number,
+  issues: ValidationIssue[],
+): value is number {
+  if (
+    !Number.isInteger(value) ||
+    (value as number) < minimum ||
+    (value as number) > maximum
+  ) {
+    add(issues, path, `must be an integer from ${minimum} to ${maximum}`);
+    return false;
+  }
+  return true;
+}
+
+function validateOutsideClue(
+  value: Record<string, unknown>,
+  path: string,
+  size: number,
+  issues: ValidationIssue[],
+): void {
+  if (
+    value.side !== "top" &&
+    value.side !== "right" &&
+    value.side !== "bottom" &&
+    value.side !== "left"
+  ) {
+    add(issues, `${path}.side`, 'must be "top", "right", "bottom" or "left"');
+  }
+  validateIntegerRange(value.index, `${path}.index`, 0, size - 1, issues);
+}
+
+function reachableXSumTotals(size: number): ReadonlySet<number> {
+  const cached = reachableXSumCache.get(size);
+  if (cached !== undefined) return cached;
+
+  const total = (size * (size + 1)) / 2;
+  const reachable = new Set<number>();
+  for (let first = 1; first <= size; first += 1) {
+    const choose = first - 1;
+    const sums = Array.from(
+      { length: choose + 1 },
+      () => new Uint8Array(total + 1),
+    );
+    sums[0]![0] = 1;
+    for (let digit = 1; digit <= size; digit += 1) {
+      if (digit === first) continue;
+      for (let count = choose; count >= 1; count -= 1) {
+        const current = sums[count]!;
+        const previous = sums[count - 1]!;
+        for (let sum = total; sum >= digit; sum -= 1) {
+          if (previous[sum - digit] !== 0) current[sum] = 1;
+        }
+      }
+    }
+    for (let sum = 0; sum <= total - first; sum += 1) {
+      if (sums[choose]![sum] !== 0) reachable.add(first + sum);
+    }
+  }
+  reachableXSumCache.set(size, reachable);
+  return reachable;
+}
+
 function validateConstraint(
   value: unknown,
   index: number,
@@ -129,6 +203,13 @@ function validateConstraint(
     if (!allowed.has(key))
       add(issues, `${path}.${key}`, "is not a recognized field");
   }
+  if (
+    allowed.has("negated") &&
+    value.negated !== undefined &&
+    typeof value.negated !== "boolean"
+  ) {
+    add(issues, `${path}.negated`, "must be a boolean");
+  }
   const cellCount = size * size;
   switch (type) {
     case "diagonal":
@@ -166,8 +247,17 @@ function validateConstraint(
           ? (length * (2 * size - length + 1)) / 2
           : length * size;
         if (
-          (value.sum as number) < minimum ||
+          value.negated === true &&
-          (value.sum as number) > maximum
+          ((value.sum as number) < 1 || (value.sum as number) > size ** 3)
+        ) {
+          add(
+            issues,
+            `${path}.sum`,
+            `must be a bounded positive integer (1 to ${size ** 3})`,
+          );
+        } else if (
+          value.negated !== true &&
+          ((value.sum as number) < minimum || (value.sum as number) > maximum)
         ) {
           add(
             issues,
@@ -242,6 +332,86 @@ function validateConstraint(
         issues,
       );
       break;
+    case "x-sum": {
+      validateOutsideClue(value, path, size, issues);
+      const sumValid = validateIntegerRange(
+        value.sum,
+        `${path}.sum`,
+        1,
+        value.negated === true
+          ? maximumFalseClueValue(size)
+          : (size * (size + 1)) / 2,
+        issues,
+      );
+      if (
+        sumValid &&
+        value.negated !== true &&
+        !reachableXSumTotals(size).has(value.sum as number)
+      ) {
+        add(issues, `${path}.sum`, "cannot be formed by a valid X-sum line");
+      }
+      break;
+    }
+    case "skyscraper":
+      validateOutsideClue(value, path, size, issues);
+      validateIntegerRange(
+        value.count,
+        `${path}.count`,
+        1,
+        value.negated === true ? maximumFalseClueValue(size) : size,
+        issues,
+      );
+      break;
+    case "quadruple": {
+      const cellsValid = validateCells(
+        value.cells,
+        `${path}.cells`,
+        cellCount,
+        1,
+        4,
+        issues,
+      );
+      if (!Array.isArray(value.digits)) {
+        add(issues, `${path}.digits`, "must be an array");
+        break;
+      }
+      if (value.digits.length < 1 || value.digits.length > 4) {
+        add(issues, `${path}.digits`, "must contain 1 to 4 digits");
+      }
+      value.digits.forEach((digit, digitIndex) => {
+        validateIntegerRange(
+          digit,
+          `${path}.digits[${digitIndex}]`,
+          1,
+          size,
+          issues,
+        );
+      });
+      if (
+        cellsValid &&
+        value.digits.length > (value.cells as readonly number[]).length
+      ) {
+        add(
+          issues,
+          `${path}.digits`,
+          "must not contain more digits than clue cells",
+        );
+      }
+      if (
+        cellsValid &&
+        !cellsFormQuadruple(size, value.cells as readonly number[])
+      ) {
+        add(
+          issues,
+          `${path}.cells`,
+          "must be the four cells surrounding one grid intersection",
+        );
+      }
+      break;
+    }
+    case "maximum":
+      validateCell(value.cell, `${path}.cell`, cellCount, issues);
+      break;
   }
 }
 
@@ -287,16 +457,28 @@ function cloneConstraint(constraint: VariantConstraint): VariantConstraint {
         ...(constraint.noRepeat === undefined
           ? {}
           : { noRepeat: constraint.noRepeat }),
+        ...(constraint.negated === undefined
+          ? {}
+          : { negated: constraint.negated }),
       };
     case "thermo":
     case "renban":
     case "palindrome":
-      return { type: constraint.type, cells: [...constraint.cells] };
+      return {
+        type: constraint.type,
+        cells: [...constraint.cells],
+        ...(constraint.negated === undefined
+          ? {}
+          : { negated: constraint.negated }),
+      };
     case "arrow":
       return {
         type: constraint.type,
         bulb: [...constraint.bulb],
         line: [...constraint.line],
+        ...(constraint.negated === undefined
+          ? {}
+          : { negated: constraint.negated }),
       };
     case "kropki":
       return {
@@ -304,6 +486,9 @@ function cloneConstraint(constraint: VariantConstraint): VariantConstraint {
         a: constraint.a,
         b: constraint.b,
         kind: constraint.kind,
+        ...(constraint.negated === undefined
+          ? {}
+          : { negated: constraint.negated }),
       };
     case "xv":
       return {
@@ -311,12 +496,55 @@ function cloneConstraint(constraint: VariantConstraint): VariantConstraint {
         a: constraint.a,
         b: constraint.b,
         total: constraint.total,
+        ...(constraint.negated === undefined
+          ? {}
+          : { negated: constraint.negated }),
       };
     case "inequality":
       return {
         type: constraint.type,
         lesser: constraint.lesser,
         greater: constraint.greater,
+        ...(constraint.negated === undefined
+          ? {}
+          : { negated: constraint.negated }),
+      };
+    case "x-sum":
+      return {
+        type: constraint.type,
+        side: constraint.side,
+        index: constraint.index,
+        sum: constraint.sum,
+        ...(constraint.negated === undefined
+          ? {}
+          : { negated: constraint.negated }),
+      };
+    case "skyscraper":
+      return {
+        type: constraint.type,
+        side: constraint.side,
+        index: constraint.index,
+        count: constraint.count,
+        ...(constraint.negated === undefined
+          ? {}
+          : { negated: constraint.negated }),
+      };
+    case "quadruple":
+      return {
+        type: constraint.type,
+        cells: [...constraint.cells],
+        digits: [...constraint.digits],
+        ...(constraint.negated === undefined
+          ? {}
+          : { negated: constraint.negated }),
+      };
+    case "maximum":
+      return {
+        type: constraint.type,
+        cell: constraint.cell,
+        ...(constraint.negated === undefined
+          ? {}
+          : { negated: constraint.negated }),
       };
   }
 }

src/formats/boundedLz.ts

@@ -0,0 +1,247 @@
+/**
+ * A size-bounded adaptation of the LZ-String decompressor (MIT).
+ *
+ * LZ-String's public decompressors only return after constructing the complete
+ * output. Importers need to stop while expanding untrusted payloads, so this
+ * implementation applies both UTF-16 character and UTF-8 byte budgets before
+ * appending every decoded dictionary entry.
+ */
+
+const BASE64_ALPHABET =
+  "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/=";
+const URI_SAFE_ALPHABET =
+  "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+-$";
+
+export class LzStringOutputLimitError extends Error {
+  readonly maxOutputBytes: number;
+
+  constructor(maxOutputBytes: number) {
+    super(
+      `The decompressed LZ-String output exceeds ${maxOutputBytes.toLocaleString()} bytes.`,
+    );
+    this.name = "LzStringOutputLimitError";
+    this.maxOutputBytes = maxOutputBytes;
+  }
+}
+
+class OutputBudget {
+  private characters = 0;
+  private bytes = 0;
+  private pendingHighSurrogate = false;
+  private readonly maximum: number;
+
+  constructor(maximum: number) {
+    this.maximum = maximum;
+  }
+
+  append(value: string): void {
+    this.characters += value.length;
+    if (this.characters > this.maximum) this.exceeded();
+
+    let index = 0;
+    if (this.pendingHighSurrogate) {
+      if (isLowSurrogate(value.charCodeAt(0))) {
+        this.bytes += 4;
+        index = 1;
+      } else {
+        this.bytes += 3;
+      }
+      this.pendingHighSurrogate = false;
+    }
+
+    while (index < value.length) {
+      const codeUnit = value.charCodeAt(index);
+      if (codeUnit <= 0x7f) {
+        this.bytes += 1;
+      } else if (codeUnit <= 0x7ff) {
+        this.bytes += 2;
+      } else if (isHighSurrogate(codeUnit)) {
+        const next = value.charCodeAt(index + 1);
+        if (isLowSurrogate(next)) {
+          this.bytes += 4;
+          index += 1;
+        } else if (index + 1 === value.length) {
+          this.pendingHighSurrogate = true;
+        } else {
+          this.bytes += 3;
+        }
+      } else {
+        // TextEncoder replaces lone low surrogates with U+FFFD (three bytes).
+        this.bytes += 3;
+      }
+      if (this.bytes > this.maximum) this.exceeded();
+      index += 1;
+    }
+  }
+
+  finish(): void {
+    if (this.pendingHighSurrogate) {
+      this.bytes += 3;
+      this.pendingHighSurrogate = false;
+    }
+    if (this.bytes > this.maximum) this.exceeded();
+  }
+
+  private exceeded(): never {
+    throw new LzStringOutputLimitError(this.maximum);
+  }
+}
+
+function isHighSurrogate(codeUnit: number): boolean {
+  return codeUnit >= 0xd800 && codeUnit <= 0xdbff;
+}
+
+function isLowSurrogate(codeUnit: number): boolean {
+  return codeUnit >= 0xdc00 && codeUnit <= 0xdfff;
+}
+
+function alphabetReader(alphabet: string, input: string) {
+  const reverse = new Map<string, number>();
+  for (let index = 0; index < alphabet.length; index += 1) {
+    reverse.set(alphabet.charAt(index), index);
+  }
+  return (index: number) => reverse.get(input.charAt(index)) ?? 0;
+}
+
+function decompressBounded(
+  input: string,
+  alphabet: string,
+  maxOutputBytes: number,
+): string | null {
+  if (input.length === 0) return null;
+  if (!Number.isSafeInteger(maxOutputBytes) || maxOutputBytes < 1) {
+    throw new RangeError("maxOutputBytes must be a positive safe integer.");
+  }
+
+  const nextValue = alphabetReader(alphabet, input);
+  const dictionary: Array<string | null | undefined> = ["", "", ""];
+  const output: string[] = [];
+  const budget = new OutputBudget(maxOutputBytes);
+  let enlargeIn = 4;
+  let dictionarySize = 4;
+  let numberOfBits = 3;
+  let dataValue = nextValue(0);
+  let dataPosition = 32;
+  let dataIndex = 1;
+
+  const readBits = (count: number) => {
+    let bits = 0;
+    let power = 1;
+    const maximumPower = 2 ** count;
+    while (power !== maximumPower) {
+      const bit = dataValue & dataPosition;
+      dataPosition >>= 1;
+      if (dataPosition === 0) {
+        dataPosition = 32;
+        dataValue = nextValue(dataIndex);
+        dataIndex += 1;
+      }
+      if (bit > 0) bits |= power;
+      power <<= 1;
+    }
+    return bits;
+  };
+
+  const firstCode = readBits(2);
+  let first: string;
+  if (firstCode === 0) first = String.fromCharCode(readBits(8));
+  else if (firstCode === 1) first = String.fromCharCode(readBits(16));
+  else if (firstCode === 2) return "";
+  else return null;
+
+  dictionary[3] = first;
+  let previous = first;
+  budget.append(first);
+  output.push(first);
+
+  while (true) {
+    if (dataIndex > input.length) return "";
+
+    let code = readBits(numberOfBits);
+    if (code === 0 || code === 1) {
+      const literal = String.fromCharCode(readBits(code === 0 ? 8 : 16));
+      dictionary[dictionarySize] = literal;
+      code = dictionarySize;
+      dictionarySize += 1;
+      enlargeIn -= 1;
+    } else if (code === 2) {
+      budget.finish();
+      return output.join("");
+    }
+
+    if (enlargeIn === 0) {
+      enlargeIn = 2 ** numberOfBits;
+      numberOfBits += 1;
+    }
+
+    const known = dictionary[code];
+    let entry: string;
+    if (known === null) {
+      throw new LzStringOutputLimitError(maxOutputBytes);
+    } else if (known !== undefined && known.length > 0) {
+      entry = known;
+    } else if (code === dictionarySize) {
+      if (previous.length >= maxOutputBytes) {
+        throw new LzStringOutputLimitError(maxOutputBytes);
+      }
+      entry = previous + previous.charAt(0);
+    } else {
+      return null;
+    }
+
+    budget.append(entry);
+    output.push(entry);
+
+    dictionary[dictionarySize] =
+      previous.length < maxOutputBytes ? previous + entry.charAt(0) : null;
+    dictionarySize += 1;
+    enlargeIn -= 1;
+    previous = entry;
+
+    if (enlargeIn === 0) {
+      enlargeIn = 2 ** numberOfBits;
+      numberOfBits += 1;
+    }
+  }
+}
+
+export function decompressFromBase64Bounded(
+  input: string,
+  maxOutputBytes: number,
+): string | null {
+  return decompressBounded(input, BASE64_ALPHABET, maxOutputBytes);
+}
+
+export function decompressFromEncodedURIComponentBounded(
+  input: string,
+  maxOutputBytes: number,
+): string | null {
+  return decompressBounded(
+    input.replaceAll(" ", "+"),
+    URI_SAFE_ALPHABET,
+    maxOutputBytes,
+  );
+}
+
+/**
+ * Decode an LZ-String payload which may use either public six-bit alphabet.
+ *
+ * Values 0–62 have identical symbols in the Base64 and URI-safe alphabets.
+ * Base64 uniquely uses `/` and `=`, while the URI-safe form uniquely uses `-`
+ * and `$`. Selecting from those markers is important: LZ-String treats an
+ * unknown symbol as zero, which can otherwise yield non-empty, subtly corrupt
+ * JSON instead of a decompression failure.
+ */
+export function decompressFromBase64OrUriComponentBounded(
+  input: string,
+  maxOutputBytes: number,
+): string | null {
+  const normalized = input.replaceAll(" ", "+");
+  const hasBase64OnlySymbol = /[/=]/u.test(normalized);
+  const hasUriOnlySymbol = /[-$]/u.test(normalized);
+  if (hasBase64OnlySymbol && hasUriOnlySymbol) return null;
+  if (hasUriOnlySymbol) {
+    return decompressFromEncodedURIComponentBounded(normalized, maxOutputBytes);
+  }
+  return decompressFromBase64Bounded(normalized, maxOutputBytes);
+}

src/formats/document.ts

@@ -1,7 +1,10 @@
+import { cellsFormQuadruple } from "../domain/geometry";
+import { normalizePortableAidMemoire } from "../state/aidMemoire";
 import {
   SUDOKU_DOCUMENT_SCHEMA,
   SUDOKU_DOCUMENT_VERSION,
   cloneConstraint,
+  type PortableAidMemoire,
   type PortableConstraint,
   type SudokuDocument,
 } from "./types";
@@ -121,6 +124,34 @@ function pair(
   return { a, b };
 }
 
+function outsideSide(value: unknown): "top" | "right" | "bottom" | "left" {
+  if (
+    value !== "top" &&
+    value !== "right" &&
+    value !== "bottom" &&
+    value !== "left"
+  ) {
+    return fail(
+      "INVALID_CONSTRAINT",
+      "An outside clue side must be top, right, bottom, or left.",
+    );
+  }
+  return value;
+}
+
+function cluePolarity(
+  value: Record<string, unknown>,
+  label: string,
+): { negated?: boolean } {
+  if (value.negated !== undefined && typeof value.negated !== "boolean") {
+    return fail(
+      "INVALID_CONSTRAINT",
+      `${label}.negated must be true or false.`,
+    );
+  }
+  return value.negated === true ? { negated: true } : {};
+}
+
 function parseConstraint(
   value: unknown,
   cellCount: number,
@@ -131,6 +162,7 @@ function parseConstraint(
       "Each constraint must be an object with a type.",
     );
   }
+  const size = Math.sqrt(cellCount);
   switch (value.type) {
     case "diagonal": {
       if (value.direction !== "main" && value.direction !== "anti") {
@@ -164,6 +196,7 @@ function parseConstraint(
         cells: cageCells,
         sum,
         ...(value.noRepeat === undefined ? {} : { noRepeat: value.noRepeat }),
+        ...cluePolarity(value, "killer-cage"),
       };
     }
     case "thermo":
@@ -172,12 +205,14 @@ function parseConstraint(
       return {
         type: value.type,
         cells: cells(value.cells, `${value.type}.cells`, cellCount, 2),
+        ...cluePolarity(value, value.type),
       };
     case "arrow":
       return {
         type: "arrow",
         bulb: cells(value.bulb, "arrow.bulb", cellCount),
         line: cells(value.line, "arrow.line", cellCount),
+        ...cluePolarity(value, "arrow"),
       };
     case "kropki": {
       const related = pair(value, cellCount);
@@ -187,7 +222,12 @@ function parseConstraint(
           "A Kropki kind must be white or black.",
         );
       }
-      return { type: "kropki", ...related, kind: value.kind };
+      return {
+        type: "kropki",
+        ...related,
+        kind: value.kind,
+        ...cluePolarity(value, "kropki"),
+      };
     }
     case "xv": {
       const related = pair(value, cellCount);
@@ -198,6 +238,7 @@ function parseConstraint(
         type: "xv",
         ...related,
         total: value.total,
+        ...cluePolarity(value, "xv"),
       };
     }
     case "inequality": {
@@ -209,8 +250,83 @@ function parseConstraint(
           "An inequality must join two different cells.",
         );
       }
-      return { type: "inequality", lesser, greater };
+      return {
+        type: "inequality",
+        lesser,
+        greater,
+        ...cluePolarity(value, "inequality"),
+      };
     }
+    case "x-sum": {
+      const polarity = cluePolarity(value, "x-sum");
+      return {
+        type: "x-sum",
+        side: outsideSide(value.side),
+        index: integer(value.index, "x-sum.index", 0, size - 1),
+        sum: integer(
+          value.sum,
+          "x-sum.sum",
+          1,
+          polarity.negated === true ? size ** 4 : (size * (size + 1)) / 2,
+        ),
+        ...polarity,
+      };
+    }
+    case "skyscraper": {
+      const polarity = cluePolarity(value, "skyscraper");
+      return {
+        type: "skyscraper",
+        side: outsideSide(value.side),
+        index: integer(value.index, "skyscraper.index", 0, size - 1),
+        count: integer(
+          value.count,
+          "skyscraper.count",
+          1,
+          polarity.negated === true ? size ** 4 : size,
+        ),
+        ...polarity,
+      };
+    }
+    case "quadruple": {
+      const quadrupleCells = cells(value.cells, "quadruple.cells", cellCount);
+      if (quadrupleCells.length > 4) {
+        return fail(
+          "INVALID_CELLS",
+          "quadruple.cells must contain at most four cells.",
+        );
+      }
+      if (
+        !Array.isArray(value.digits) ||
+        value.digits.length < 1 ||
+        value.digits.length > 4 ||
+        value.digits.length > quadrupleCells.length
+      ) {
+        return fail(
+          "INVALID_CONSTRAINT",
+          "quadruple.digits must contain one to four digits and no more digits than clue cells.",
+        );
+      }
+      if (!cellsFormQuadruple(size, quadrupleCells)) {
+        return fail(
+          "INVALID_CELLS",
+          "quadruple.cells must be the four cells surrounding one grid intersection.",
+        );
+      }
+      return {
+        type: "quadruple",
+        cells: quadrupleCells,
+        digits: value.digits.map((digit, index) =>
+          integer(digit, `quadruple.digits[${index}]`, 1, size),
+        ),
+        ...cluePolarity(value, "quadruple"),
+      };
+    }
+    case "maximum":
+      return {
+        type: "maximum",
+        cell: cell(value.cell, "maximum.cell", cellCount),
+        ...cluePolarity(value, "maximum"),
+      };
     default:
       return fail(
         "UNSUPPORTED_CONSTRAINT",
@@ -316,6 +432,19 @@ export function normalizeSudokuDocument(value: unknown): SudokuDocument {
     }
     elapsedMs = value.elapsedMs;
   }
+  let aidMemoire: PortableAidMemoire | undefined;
+  if (value.aidMemoire !== undefined) {
+    try {
+      aidMemoire = normalizePortableAidMemoire(value.aidMemoire, size);
+    } catch (error) {
+      return fail(
+        "INVALID_AID_MEMOIRE",
+        error instanceof Error
+          ? error.message
+          : "The aid-mémoire data is invalid.",
+      );
+    }
+  }
 
   if (
     !Array.isArray(value.constraints) ||
@@ -348,6 +477,7 @@ export function normalizeSudokuDocument(value: unknown): SudokuDocument {
     ...(candidates === undefined ? {} : { candidates }),
     ...(colors === undefined ? {} : { colors }),
     ...(elapsedMs === undefined ? {} : { elapsedMs }),
+    ...(aidMemoire === undefined ? {} : { aidMemoire }),
     ...(regions === undefined ? {} : { regions }),
     ...(title === undefined ? {} : { title }),
     ...(author === undefined ? {} : { author }),
@@ -416,6 +546,14 @@ export function cloneSudokuDocument(value: SudokuDocument): SudokuDocument {
     ...(normalized.colors === undefined
       ? {}
       : { colors: [...normalized.colors] }),
+    ...(normalized.aidMemoire === undefined
+      ? {}
+      : {
+          aidMemoire: normalizePortableAidMemoire(
+            normalized.aidMemoire,
+            normalized.size,
+          ),
+        }),
     ...(normalized.regions === undefined
       ? {}
       : { regions: [...normalized.regions] }),

src/formats/fpuzzles.ts

@@ -1,14 +1,16 @@
+import { compressToBase64 } from "lz-string";
+import { cellsFormQuadruple } from "../domain/geometry";
 import {
-  compressToBase64,
+  LzStringOutputLimitError,
-  decompressFromBase64,
+  decompressFromBase64OrUriComponentBounded,
-  decompressFromEncodedURIComponent,
+} from "./boundedLz";
-} from "lz-string";
 import {
   MAX_BOARD_SIZE,
   MAX_DOCUMENT_BYTES,
   MIN_BOARD_SIZE,
   SudokuFormatError,
 } from "./document";
+import { UnsupportedPuzzleConstructsError } from "./interoperability";
 import {
   SUDOKU_DOCUMENT_SCHEMA,
   SUDOKU_DOCUMENT_VERSION,
@@ -38,6 +40,10 @@ const SUPPORTED_ROOT_FIELDS = new Set([
   "ratio",
   "xv",
   "inequality",
+  "xsum",
+  "skyscraper",
+  "quadruple",
+  "maximum",
   "renban",
   "palindrome",
   "disabledlogic",
@@ -54,10 +60,8 @@ const UNSUPPORTED_RULE_FIELDS: Readonly<Record<string, string>> = {
   odd: "odd cells",
   extraregion: "extra regions",
   clone: "clone regions",
-  quadruple: "quadruples",
   betweenline: "between lines",
   minimum: "minimum cells",
-  maximum: "maximum cells",
   whispers: "whisper lines",
   regionsumline: "region-sum lines",
   entropicline: "entropic lines",
@@ -69,8 +73,6 @@ const UNSUPPORTED_RULE_FIELDS: Readonly<Record<string, string>> = {
   rowindexer: "row indexers",
   columnindexer: "column indexers",
   boxindexer: "box indexers",
-  xsum: "X-sums",
-  skyscraper: "skyscrapers",
   fogofwar: "fog of war",
   foglight: "fog lights",
   cage: "generic cages",
@@ -115,32 +117,29 @@ function present(value: unknown): boolean {
 }
 
 function assertSupportedRootFields(value: JsonRecord): void {
+  const constructs: string[] = [];
   for (const [field, raw] of Object.entries(value)) {
     const unsupported = UNSUPPORTED_RULE_FIELDS[field];
     if (unsupported !== undefined && present(raw)) {
-      return fail(
+      constructs.push(unsupported);
-        "UNSUPPORTED_FPUZZLES",
+      continue;
-        `This puzzle uses ${unsupported}, which Sudoku Tools cannot enforce yet. Import stopped rather than silently weakening the puzzle.`,
-      );
     }
     const decoration = DECORATION_FIELDS[field];
     if (decoration !== undefined && present(raw)) {
-      return fail(
+      constructs.push(decoration);
-        "UNSUPPORTED_FPUZZLES",
+      continue;
-        `This puzzle contains ${decoration}, which cannot be preserved yet. Import stopped rather than discarding them.`,
-      );
     }
     if (
       !SUPPORTED_ROOT_FIELDS.has(field) &&
       unsupported === undefined &&
       decoration === undefined
     ) {
-      return fail(
+      constructs.push(`Unknown fpuzzles field “${field}”`);
-        "UNSUPPORTED_FPUZZLES",
-        `Unknown fpuzzles field “${field}”. Import stopped so a rule or visual cannot be silently lost.`,
-      );
     }
   }
+  if (constructs.length > 0) {
+    throw new UnsupportedPuzzleConstructsError("f-puzzles", constructs);
+  }
 }
 
 function boundedJson(input: string): unknown {
@@ -190,6 +189,56 @@ export function addressFromCellIndex(index: number, size: number): string {
   return `R${Math.floor(index / size) + 1}C${(index % size) + 1}`;
 }
 
+type OutsideSide = "top" | "right" | "bottom" | "left";
+
+function outsideClueFromAddress(
+  value: unknown,
+  size: number,
+): { side: OutsideSide; index: number } {
+  if (typeof value !== "string") {
+    return fail(
+      "INVALID_CELL",
+      "An fpuzzles outside clue must use an RnCn address.",
+    );
+  }
+  const match = /^R(\d+)C(\d+)$/iu.exec(value.trim());
+  if (match === null) {
+    return fail("INVALID_CELL", `Invalid fpuzzles outside address: ${value}.`);
+  }
+  const row = Number(match[1]);
+  const column = Number(match[2]);
+  if (row === 0 && column >= 1 && column <= size)
+    return { side: "top", index: column - 1 };
+  if (row === size + 1 && column >= 1 && column <= size)
+    return { side: "bottom", index: column - 1 };
+  if (column === 0 && row >= 1 && row <= size)
+    return { side: "left", index: row - 1 };
+  if (column === size + 1 && row >= 1 && row <= size)
+    return { side: "right", index: row - 1 };
+  return fail(
+    "INVALID_CELL",
+    `Outside clue ${value} must sit immediately beyond one grid edge.`,
+  );
+}
+
+function addressFromOutsideClue(
+  side: OutsideSide,
+  index: number,
+  size: number,
+): string {
+  const position = index + 1;
+  switch (side) {
+    case "top":
+      return `R0C${position}`;
+    case "right":
+      return `R${position}C${size + 1}`;
+    case "bottom":
+      return `R${size + 1}C${position}`;
+    case "left":
+      return `R${position}C0`;
+  }
+}
+
 function fpCells(value: unknown, size: number, minimum = 1): number[] {
   if (
     !Array.isArray(value) ||
@@ -470,7 +519,62 @@ export function parseFpuzzles(value: unknown): SudokuDocument {
     const [a, b] = inequalityCells as [number, number];
     if (inequality.value === ">")
       constraints.push({ type: "inequality", lesser: b, greater: a });
-    else constraints.push({ type: "inequality", lesser: a, greater: b });
+    else if (inequality.value === "<")
+      constraints.push({ type: "inequality", lesser: a, greater: b });
+    else {
+      return fail(
+        "INVALID_FPUZZLES",
+        'inequality.value must be either ">" or "<".',
+      );
+    }
+  }
+  for (const clue of objects(value.xsum)) {
+    constraints.push({
+      type: "x-sum",
+      ...outsideClueFromAddress(clue.cell, size),
+      sum: numeric(clue.value, "xsum.value", 1, (size * (size + 1)) / 2),
+    });
+  }
+  for (const clue of objects(value.skyscraper)) {
+    constraints.push({
+      type: "skyscraper",
+      ...outsideClueFromAddress(clue.cell, size),
+      count: numeric(clue.value, "skyscraper.value", 1, size),
+    });
+  }
+  for (const clue of objects(value.quadruple)) {
+    const quadrupleCells = fpCells(clue.cells, size);
+    if (
+      quadrupleCells.length > 4 ||
+      !Array.isArray(clue.values) ||
+      clue.values.length < 1 ||
+      clue.values.length > 4 ||
+      clue.values.length > quadrupleCells.length
+    ) {
+      return fail(
+        "INVALID_FPUZZLES",
+        "A quadruple must contain one to four cells and clue digits.",
+      );
+    }
+    if (!cellsFormQuadruple(size, quadrupleCells)) {
+      return fail(
+        "INVALID_CELLS",
+        "A quadruple must use the four cells surrounding one grid intersection.",
+      );
+    }
+    constraints.push({
+      type: "quadruple",
+      cells: quadrupleCells,
+      digits: clue.values.map((digit, index) =>
+        numeric(digit, `quadruple.values[${index}]`, 1, size),
+      ),
+    });
+  }
+  for (const clue of objects(value.maximum)) {
+    constraints.push({
+      type: "maximum",
+      cell: cellIndexFromAddress(clue.cell, size),
+    });
   }
 
   const regions = readRegions(grid, size);
@@ -548,6 +652,12 @@ export function exportFpuzzles(document: SudokuDocument): JsonRecord {
   };
 
   for (const constraint of document.constraints) {
+    if ("negated" in constraint && constraint.negated === true) {
+      return fail(
+        "UNSUPPORTED_FPUZZLES",
+        "fpuzzles export cannot preserve an individually false clue. Use Sudoku Tools JSON instead.",
+      );
+    }
     switch (constraint.type) {
       case "diagonal":
         output[constraint.direction === "main" ? "diagonal+" : "diagonal-"] =
@@ -621,6 +731,39 @@ export function exportFpuzzles(document: SudokuDocument): JsonRecord {
           value: "<",
         });
         break;
+      case "x-sum":
+        append("xsum", {
+          cell: addressFromOutsideClue(
+            constraint.side,
+            numeric(constraint.index, "xsum.index", 0, size - 1),
+            size,
+          ),
+          value: String(
+            numeric(constraint.sum, "xsum.value", 1, (size * (size + 1)) / 2),
+          ),
+        });
+        break;
+      case "skyscraper":
+        append("skyscraper", {
+          cell: addressFromOutsideClue(
+            constraint.side,
+            numeric(constraint.index, "skyscraper.index", 0, size - 1),
+            size,
+          ),
+          value: String(numeric(constraint.count, "skyscraper.value", 1, size)),
+        });
+        break;
+      case "quadruple":
+        append("quadruple", {
+          cells: constraintCells(constraint.cells, size),
+          values: [...constraint.digits],
+        });
+        break;
+      case "maximum":
+        append("maximum", {
+          cell: addressFromCellIndex(constraint.cell, size),
+        });
+        break;
     }
   }
 
@@ -675,21 +818,27 @@ function decodePayload(payload: string): string {
   } catch {
     // URLSearchParams already decodes input. Keep the original if a literal % is malformed.
   }
-  const base64 = decompressFromBase64(decodedPayload.replaceAll(" ", "+"));
+  let uriEncoded: string | null;
-  const uriEncoded =
+  try {
-    base64 || decompressFromEncodedURIComponent(decodedPayload);
+    uriEncoded = decompressFromBase64OrUriComponentBounded(
+      decodedPayload,
+      MAX_DOCUMENT_BYTES,
+    );
+  } catch (error) {
+    if (error instanceof LzStringOutputLimitError) {
+      return fail(
+        "LIMIT_EXCEEDED",
+        "The decompressed fpuzzles puzzle is too large to open safely.",
+      );
+    }
+    throw error;
+  }
   if (uriEncoded === null || uriEncoded === "") {
     return fail(
       "INVALID_FPUZZLES",
       "The inline fpuzzles payload could not be decompressed.",
     );
   }
-  if (new TextEncoder().encode(uriEncoded).byteLength > MAX_DOCUMENT_BYTES) {
-    return fail(
-      "LIMIT_EXCEEDED",
-      "The decompressed fpuzzles puzzle is too large to open safely.",
-    );
-  }
   return uriEncoded;
 }
 

src/formats/import.ts

@@ -0,0 +1,189 @@
+import {
+  MAX_DOCUMENT_BYTES,
+  parseSudokuDocument,
+  SudokuFormatError,
+} from "./document";
+import {
+  importFpuzzles,
+  NetworkPuzzleIdError,
+  parseFpuzzles,
+} from "./fpuzzles";
+import {
+  type PuzzleImportResult,
+  RemotePuzzleReferenceError,
+} from "./interoperability";
+import { importPenpa, parsePenpaText } from "./penpa";
+import { parsePlainGrid } from "./grid";
+import { decodePuzzleHash } from "./share";
+import { importSudokuPad, parseSudokuPadPuzzle } from "./sudokupad";
+import type { SudokuDocument } from "./types";
+
+function isRecord(value: unknown): value is Record<string, unknown> {
+  return typeof value === "object" && value !== null && !Array.isArray(value);
+}
+
+function urlPayload(input: string): {
+  readonly kind: "fpuzzles" | "sudokupad" | "penpa" | "remote";
+  readonly value: string;
+} | null {
+  if (!/^https?:\/\//iu.test(input)) return null;
+  let url: URL;
+  try {
+    url = new URL(input);
+  } catch {
+    return { kind: "remote", value: input };
+  }
+  const host = url.hostname.toLowerCase();
+  if (url.pathname.includes("/penpa-edit/")) {
+    return { kind: "penpa", value: input };
+  }
+  if (host === "f-puzzles.com" || host === "www.f-puzzles.com") {
+    return { kind: "fpuzzles", value: input };
+  }
+  if (host === "sudokupad.app" || host.endsWith(".sudokupad.app")) {
+    let pathCandidate: string;
+    try {
+      pathCandidate = decodeURIComponent(
+        url.pathname.replace(/^\/+|\/+$/gu, ""),
+      );
+    } catch (error) {
+      throw new SudokuFormatError(
+        "INVALID_SUDOKUPAD_URL",
+        "The SudokuPad URL contains invalid escaped text.",
+        { cause: error },
+      );
+    }
+    const candidate =
+      url.searchParams.get("puzzleid") ??
+      url.searchParams.get("load") ??
+      pathCandidate;
+    if (/^(?:ctc|scl)/iu.test(candidate)) {
+      return { kind: "sudokupad", value: candidate };
+    }
+    if (/^fpuzzles/iu.test(candidate)) {
+      return { kind: "fpuzzles", value: input };
+    }
+    throw new NetworkPuzzleIdError(candidate || "unknown");
+  }
+  return { kind: "remote", value: input };
+}
+
+/**
+ * Detect and import every supported local representation. The function is
+ * asynchronous only because Penpa+ uses browser-native raw-deflate streams;
+ * no branch performs a network request.
+ */
+export async function importPuzzle(
+  input: string,
+): Promise<PuzzleImportResult<SudokuDocument>> {
+  if (input.length > MAX_DOCUMENT_BYTES) {
+    throw new SudokuFormatError(
+      "LIMIT_EXCEEDED",
+      "The pasted puzzle data is too large to open safely.",
+    );
+  }
+  const trimmed = input.trim().replace(/^\uFEFF/u, "");
+  const url = urlPayload(trimmed);
+  if (url?.kind === "remote") {
+    throw new RemotePuzzleReferenceError("The pasted URL");
+  }
+  if (url?.kind === "penpa") {
+    return {
+      document: await importPenpa(url.value),
+      format: "penpa",
+      label: "Penpa+",
+    };
+  }
+  if (url?.kind === "sudokupad") {
+    return {
+      document: importSudokuPad(url.value),
+      format: "sudokupad",
+      label: "SudokuPad/CTC",
+    };
+  }
+  if (url?.kind === "fpuzzles") {
+    return {
+      document: importFpuzzles(url.value),
+      format: "fpuzzles",
+      label: "f-puzzles",
+    };
+  }
+
+  if (trimmed.startsWith("#sudoku=") || trimmed.includes("#sudoku=")) {
+    return {
+      document: decodePuzzleHash(trimmed),
+      format: "sudoku-tools",
+      label: "Sudoku Tools share link",
+    };
+  }
+  if (/^(?:ctc|scl)/iu.test(trimmed)) {
+    return {
+      document: importSudokuPad(trimmed),
+      format: "sudokupad",
+      label: "SudokuPad/CTC",
+    };
+  }
+  if (/^penpa:/iu.test(trimmed) || /^[?#]?(?:m=[^&]+&)?p=/iu.test(trimmed)) {
+    return {
+      document: await importPenpa(trimmed),
+      format: "penpa",
+      label: "Penpa+",
+    };
+  }
+  if (/^(?:square|sudoku),[^\r\n]+[\r\n]/iu.test(trimmed)) {
+    return {
+      document: parsePenpaText(trimmed),
+      format: "penpa",
+      label: "Penpa+ text",
+    };
+  }
+  if (/^fpuzzles/iu.test(trimmed)) {
+    return {
+      document: importFpuzzles(trimmed),
+      format: "fpuzzles",
+      label: "f-puzzles",
+    };
+  }
+  if (trimmed.startsWith("{")) {
+    if (new TextEncoder().encode(trimmed).byteLength > MAX_DOCUMENT_BYTES) {
+      throw new SudokuFormatError(
+        "LIMIT_EXCEEDED",
+        "The pasted puzzle JSON is too large to open safely.",
+      );
+    }
+    let parsed: unknown;
+    try {
+      parsed = JSON.parse(trimmed) as unknown;
+    } catch (error) {
+      throw new SudokuFormatError(
+        "INVALID_JSON",
+        "The pasted puzzle data is not valid JSON.",
+        { cause: error },
+      );
+    }
+    if (isRecord(parsed) && "schema" in parsed) {
+      return {
+        document: parseSudokuDocument(trimmed),
+        format: "sudoku-tools",
+        label: "Sudoku Tools JSON",
+      };
+    }
+    if (isRecord(parsed) && "cells" in parsed && !("grid" in parsed)) {
+      return {
+        document: parseSudokuPadPuzzle(parsed),
+        format: "sudokupad",
+        label: "SudokuPad/CTC JSON",
+      };
+    }
+    return {
+      document: parseFpuzzles(parsed),
+      format: "fpuzzles",
+      label: "f-puzzles JSON",
+    };
+  }
+  return {
+    document: parsePlainGrid(trimmed),
+    format: "plain-grid",
+    label: "plain grid",
+  };
+}

src/formats/index.ts

@@ -1,5 +1,10 @@
 export * from "./document";
 export * from "./fpuzzles";
 export * from "./grid";
+export * from "./import";
+export * from "./interoperability";
+export * from "./penpa";
 export * from "./share";
+export * from "./sudokupad";
 export * from "./types";
+export * from "./visual";

src/formats/interoperability.ts

@@ -0,0 +1,37 @@
+import { SudokuFormatError } from "./document";
+
+export type PuzzleSourceFormat =
+  "sudoku-tools" | "plain-grid" | "fpuzzles" | "sudokupad" | "penpa";
+
+export interface PuzzleImportResult<T> {
+  readonly document: T;
+  readonly format: PuzzleSourceFormat;
+  readonly label: string;
+}
+
+export class UnsupportedPuzzleConstructsError extends SudokuFormatError {
+  readonly format: string;
+  readonly constructs: readonly string[];
+
+  constructor(format: string, constructs: readonly string[]) {
+    const unique = [...new Set(constructs)].slice(0, 24);
+    const remainder = Math.max(0, new Set(constructs).size - unique.length);
+    super(
+      `UNSUPPORTED_${format.toUpperCase().replaceAll(/[^A-Z0-9]+/gu, "_")}`,
+      `${format} contains unsupported constructs: ${unique.join(", ")}${remainder > 0 ? `, and ${String(remainder)} more` : ""}. Import stopped rather than silently weakening or changing the puzzle.`,
+    );
+    this.name = "UnsupportedPuzzleConstructsError";
+    this.format = format;
+    this.constructs = unique;
+  }
+}
+
+export class RemotePuzzleReferenceError extends SudokuFormatError {
+  constructor(service: string) {
+    super(
+      "REMOTE_PUZZLE_REFERENCE",
+      `${service} is a server-hosted or shortened puzzle reference. This local-only app never fetches remote puzzle IDs; paste a self-contained link or exported puzzle data instead.`,
+    );
+    this.name = "RemotePuzzleReferenceError";
+  }
+}

src/formats/penpa.ts

@@ -0,0 +1,581 @@
+import {
+  MAX_BOARD_SIZE,
+  MAX_DOCUMENT_BYTES,
+  MIN_BOARD_SIZE,
+  SudokuFormatError,
+} from "./document";
+import {
+  RemotePuzzleReferenceError,
+  UnsupportedPuzzleConstructsError,
+} from "./interoperability";
+import {
+  SUDOKU_DOCUMENT_SCHEMA,
+  SUDOKU_DOCUMENT_VERSION,
+  type PortableConstraint,
+  type SudokuDocument,
+} from "./types";
+
+export const MAX_PENPA_PAYLOAD_LENGTH = 524_288;
+
+type JsonRecord = Record<string, unknown>;
+
+/* Penpa+ applies these substitutions before raw-deflate compression. */
+const PENPA_SUBSTITUTIONS = [
+  ["z", "zZ"],
+  ['"qa"', "z9"],
+  ['"pu_q"', "zQ"],
+  ['"pu_a"', "zA"],
+  ['"grid"', "zG"],
+  ['"edit_mode"', "zM"],
+  ['"surface"', "zS"],
+  ['"line"', "zL"],
+  ['"lineE"', "zE"],
+  ['"wall"', "zW"],
+  ['"cage"', "zC"],
+  ['"number"', "zN"],
+  ['"symbol"', "zY"],
+  ['"special"', "zP"],
+  ['"board"', "zB"],
+  ['"command_redo"', "zR"],
+  ['"command_undo"', "zU"],
+  ['"command_replay"', "z8"],
+  ['"numberS"', "z1"],
+  ['"freeline"', "zF"],
+  ['"freelineE"', "z2"],
+  ['"thermo"', "zT"],
+  ['"arrows"', "z3"],
+  ['"direction"', "zD"],
+  ['"squareframe"', "z0"],
+  ['"polygon"', "z5"],
+  ['"deletelineE"', "z4"],
+  ['"killercages"', "z6"],
+  ['"nobulbthermo"', "z7"],
+  ['"__a"', "z_"],
+  ["null", "zO"],
+] as const;
+
+const LAYER_FIELDS = new Set([
+  "command_redo",
+  "command_undo",
+  "command_replay",
+  "surface",
+  "number",
+  "numberS",
+  "symbol",
+  "thermo",
+  "arrows",
+  "direction",
+  "squareframe",
+  "polygon",
+  "line",
+  "lineE",
+  "wall",
+  "cage",
+  "freeline",
+  "freelineE",
+  "deletelineE",
+  "killercages",
+  "nobulbthermo",
+]);
+
+function fail(code: string, message: string): never {
+  throw new SudokuFormatError(code, message);
+}
+
+function isRecord(value: unknown): value is JsonRecord {
+  return typeof value === "object" && value !== null && !Array.isArray(value);
+}
+
+function boundedJson(input: string, label: string): unknown {
+  if (input.length > MAX_DOCUMENT_BYTES) {
+    return fail("LIMIT_EXCEEDED", `${label} is too large to open safely.`);
+  }
+  try {
+    return JSON.parse(input) as unknown;
+  } catch (error) {
+    throw new SudokuFormatError(
+      "INVALID_PENPA",
+      `${label} is not valid JSON.`,
+      {
+        cause: error,
+      },
+    );
+  }
+}
+
+function integer(
+  value: unknown,
+  label: string,
+  minimum: number,
+  maximum: number,
+): number {
+  const parsed =
+    typeof value === "string" && value.trim() !== "" ? Number(value) : value;
+  if (
+    !Number.isInteger(parsed) ||
+    (parsed as number) < minimum ||
+    (parsed as number) > maximum
+  ) {
+    return fail(
+      "INVALID_PENPA",
+      `${label} must be an integer from ${minimum} to ${maximum}.`,
+    );
+  }
+  return parsed as number;
+}
+
+function hasContent(value: unknown): boolean {
+  if (value === undefined || value === null) return false;
+  if (Array.isArray(value)) return value.length > 0;
+  if (isRecord(value)) {
+    if (
+      Object.keys(value).length === 1 &&
+      isRecord(value.command_redo) &&
+      Array.isArray(value.command_redo.__a)
+    ) {
+      return value.command_redo.__a.length > 0;
+    }
+    return Object.keys(value).length > 0;
+  }
+  return Boolean(value);
+}
+
+function expandCenterList(value: unknown): number[] {
+  if (!Array.isArray(value) || value.length > MAX_BOARD_SIZE ** 2) {
+    return fail("LIMIT_EXCEEDED", "Penpa+ has an invalid or oversized grid.");
+  }
+  const result: number[] = [];
+  let previous = 0;
+  value.forEach((raw, index) => {
+    const delta = integer(
+      raw,
+      `centerlist[${String(index)}]`,
+      -100_000,
+      100_000,
+    );
+    const point = index === 0 ? delta : previous + delta;
+    if (point < 0) {
+      return fail(
+        "INVALID_PENPA",
+        "Penpa+ centerlist contains a negative point.",
+      );
+    }
+    result.push(point);
+    previous = point;
+  });
+  return result;
+}
+
+function restoreSubstitutions(value: string): string {
+  let restored = value;
+  for (let index = PENPA_SUBSTITUTIONS.length - 1; index >= 0; index -= 1) {
+    const substitution = PENPA_SUBSTITUTIONS[index];
+    if (substitution === undefined) continue;
+    restored = restored.split(substitution[1]).join(substitution[0]);
+  }
+  return restored;
+}
+
+function decodeNumber(value: unknown, size: number): number | undefined {
+  if (!Array.isArray(value) || value.length < 3 || value.length > 8) {
+    return undefined;
+  }
+  const rawDigit = value[0];
+  const type = String(value[2]);
+  if (["1", "2", "4", "10"].includes(type)) {
+    const parsed =
+      typeof rawDigit === "string" && /^\d+$/u.test(rawDigit)
+        ? Number(rawDigit)
+        : rawDigit;
+    return Number.isInteger(parsed) && (parsed as number) >= 1 && parsed <= size
+      ? (parsed as number)
+      : undefined;
+  }
+  if (type === "7" && Array.isArray(rawDigit) && rawDigit.length === size) {
+    const enabled = rawDigit
+      .map((flag, index) => (flag === 1 ? index + 1 : 0))
+      .filter(Boolean);
+    return enabled.length === 1 ? enabled[0] : undefined;
+  }
+  return undefined;
+}
+
+function plainMetadata(value: string | undefined, prefix: string) {
+  if (value === undefined) return undefined;
+  return value
+    .replaceAll("%2C", ",")
+    .replace(new RegExp(`^${prefix}:\\s*`, "iu"), "")
+    .slice(0, 256);
+}
+
+function rulesMetadata(value: string | undefined) {
+  if (value === undefined || value === "") return undefined;
+  return value
+    .replaceAll("%2C", ",")
+    .replaceAll("%2D", "\n")
+    .replaceAll("%2E", "&")
+    .replaceAll("%2F", "=")
+    .slice(0, 16_384);
+}
+
+function layer(value: unknown, label: string): JsonRecord {
+  if (!isRecord(value) || Object.keys(value).length > 100) {
+    return fail("INVALID_PENPA", `${label} must be a bounded object.`);
+  }
+  return value;
+}
+
+function validateLayerFields(value: JsonRecord, label: string): void {
+  const unsupported = Object.keys(value)
+    .filter((field) => !LAYER_FIELDS.has(field))
+    .map((field) => `${label} field “${field}”`);
+  if (unsupported.length > 0) {
+    throw new UnsupportedPuzzleConstructsError("Penpa+", unsupported);
+  }
+}
+
+function parseLineConstraints(
+  value: unknown,
+  field: "thermo" | "arrows",
+  pointToCell: ReadonlyMap<number, number>,
+): PortableConstraint[] {
+  if (value === undefined) return [];
+  if (!Array.isArray(value) || value.length > 5_000) {
+    return fail("LIMIT_EXCEEDED", `Penpa+ ${field} data is too large.`);
+  }
+  return value.map((raw, index) => {
+    if (
+      !Array.isArray(raw) ||
+      raw.length < 2 ||
+      raw.length > pointToCell.size
+    ) {
+      return fail(
+        "INVALID_PENPA",
+        `Penpa+ ${field}[${String(index)}] is not a bounded cell path.`,
+      );
+    }
+    const cells = raw.map((point, pointIndex) => {
+      const parsed = integer(
+        point,
+        `${field}[${String(index)}][${String(pointIndex)}]`,
+        0,
+        1_000_000,
+      );
+      const cell = pointToCell.get(parsed);
+      if (cell === undefined) {
+        return fail(
+          "UNSUPPORTED_PENPA_GEOMETRY",
+          `Penpa+ ${field} uses a point outside the rectangular Sudoku grid.`,
+        );
+      }
+      return cell;
+    });
+    if (new Set(cells).size !== cells.length) {
+      return fail("INVALID_PENPA", `Penpa+ ${field} repeats a path cell.`);
+    }
+    return field === "thermo"
+      ? ({ type: "thermo", cells } as const)
+      : ({ type: "arrow", bulb: [cells[0]!], line: cells.slice(1) } as const);
+  });
+}
+
+/** Parse the locally decompressed text stored in a Penpa+ long URL. */
+export function parsePenpaText(compressedText: string): SudokuDocument {
+  if (
+    new TextEncoder().encode(compressedText).byteLength > MAX_DOCUMENT_BYTES
+  ) {
+    return fail(
+      "LIMIT_EXCEEDED",
+      "The decompressed Penpa+ puzzle is too large to open safely.",
+    );
+  }
+  const text = restoreSubstitutions(compressedText);
+  const rows = text.split("\n");
+  if (rows.length < 7 || rows.length > 32) {
+    return fail("INVALID_PENPA", "The Penpa+ puzzle record is incomplete.");
+  }
+  const header = rows[0]?.split(",") ?? [];
+  if (header.length < 15) {
+    return fail("INVALID_PENPA", "The Penpa+ puzzle header is incomplete.");
+  }
+  const gridType = header[0]?.toLowerCase();
+  if (gridType !== "square" && gridType !== "sudoku") {
+    throw new UnsupportedPuzzleConstructsError("Penpa+", [
+      `grid type “${gridType ?? "unknown"}”`,
+    ]);
+  }
+  const nx = integer(header[1], "Penpa+ width", 1, 100);
+  const ny = integer(header[2], "Penpa+ height", 1, 100);
+  const rotation = integer(header[4] ?? 0, "Penpa+ rotation", -360, 360);
+  const reflectX = integer(header[5] ?? 1, "Penpa+ reflection", -1, 1);
+  const reflectY = integer(header[6] ?? 1, "Penpa+ reflection", -1, 1);
+  if (rotation !== 0 || reflectX !== 1 || reflectY !== 1) {
+    throw new UnsupportedPuzzleConstructsError("Penpa+", [
+      "rotated or reflected grids",
+    ]);
+  }
+  boundedJson(rows[1] ?? "", "Penpa+ spacing data");
+  const problem = layer(
+    boundedJson(rows[3] ?? "", "Penpa+ problem layer"),
+    "Penpa+ problem layer",
+  );
+  const progress = layer(
+    boundedJson(rows[4] ?? "{}", "Penpa+ answer layer"),
+    "Penpa+ answer layer",
+  );
+  validateLayerFields(problem, "problem layer");
+  validateLayerFields(progress, "answer layer");
+
+  const centerList = expandCenterList(
+    boundedJson(rows[5] ?? "", "Penpa+ centerlist"),
+  );
+  if (centerList.length === 0) {
+    return fail("INVALID_PENPA", "Penpa+ contains no active grid cells.");
+  }
+  const nx0 = nx + 4;
+  const positions = centerList.map((point) => ({
+    point,
+    row: Math.floor(point / nx0) - 2,
+    column: (point % nx0) - 2,
+  }));
+  const minimumRow = Math.min(...positions.map(({ row }) => row));
+  const maximumRow = Math.max(...positions.map(({ row }) => row));
+  const minimumColumn = Math.min(...positions.map(({ column }) => column));
+  const maximumColumn = Math.max(...positions.map(({ column }) => column));
+  const height = maximumRow - minimumRow + 1;
+  const width = maximumColumn - minimumColumn + 1;
+  if (
+    width !== height ||
+    width < MIN_BOARD_SIZE ||
+    width > MAX_BOARD_SIZE ||
+    positions.length !== width * height ||
+    width > nx ||
+    height > ny
+  ) {
+    throw new UnsupportedPuzzleConstructsError("Penpa+", [
+      "masked, non-square or unsupported-size Sudoku grids",
+    ]);
+  }
+  const pointToCell = new Map<number, number>();
+  for (const position of positions) {
+    const row = position.row - minimumRow;
+    const column = position.column - minimumColumn;
+    const cell = row * width + column;
+    if (
+      pointToCell.has(position.point) ||
+      [...pointToCell.values()].includes(cell)
+    ) {
+      return fail(
+        "INVALID_PENPA",
+        "Penpa+ centerlist contains duplicate cells.",
+      );
+    }
+    pointToCell.set(position.point, cell);
+  }
+
+  const unsupported: string[] = [];
+  const supportedFields = new Set(["number", "thermo", "arrows"]);
+  for (const [field, raw] of Object.entries(problem)) {
+    if (
+      !supportedFields.has(field) &&
+      !field.startsWith("command_") &&
+      hasContent(raw)
+    ) {
+      unsupported.push(`problem ${field}`);
+    }
+  }
+  for (const [field, raw] of Object.entries(progress)) {
+    if (
+      field !== "number" &&
+      !field.startsWith("command_") &&
+      hasContent(raw)
+    ) {
+      unsupported.push(`answer ${field}`);
+    }
+  }
+  if (unsupported.length > 0) {
+    throw new UnsupportedPuzzleConstructsError("Penpa+", unsupported);
+  }
+
+  const givens = Array<number>(width * width).fill(0);
+  const values = Array<number>(width * width).fill(0);
+  const parseNumbers = (
+    raw: unknown,
+    target: number[],
+    requireGivenStyle: boolean,
+    label: string,
+  ) => {
+    if (raw === undefined) return;
+    if (!isRecord(raw) || Object.keys(raw).length > width * width * 4) {
+      return fail("LIMIT_EXCEEDED", `Penpa+ ${label} numbers are too large.`);
+    }
+    const unsupportedNumbers: string[] = [];
+    for (const [pointText, entry] of Object.entries(raw)) {
+      const point = integer(pointText, `${label} point`, 0, 1_000_000);
+      const cell = pointToCell.get(point);
+      const digit = decodeNumber(entry, width);
+      const style = Array.isArray(entry) ? entry[1] : undefined;
+      if (
+        cell === undefined ||
+        digit === undefined ||
+        (requireGivenStyle && style !== 1)
+      ) {
+        unsupportedNumbers.push(
+          `${label} number or style at point ${pointText}`,
+        );
+        continue;
+      }
+      target[cell] = digit;
+    }
+    if (unsupportedNumbers.length > 0) {
+      throw new UnsupportedPuzzleConstructsError("Penpa+", unsupportedNumbers);
+    }
+  };
+  parseNumbers(problem.number, givens, true, "problem");
+  values.splice(0, values.length, ...givens);
+  parseNumbers(progress.number, values, false, "answer");
+  for (const [cell, given] of givens.entries()) {
+    if (given !== 0) values[cell] = given;
+  }
+
+  const constraints = [
+    ...parseLineConstraints(problem.thermo, "thermo", pointToCell),
+    ...parseLineConstraints(problem.arrows, "arrows", pointToCell),
+  ];
+  const title = plainMetadata(header[15], "Title");
+  const author = plainMetadata(header[16], "Author");
+  const rules = rulesMetadata(header[18]);
+  return {
+    schema: SUDOKU_DOCUMENT_SCHEMA,
+    version: SUDOKU_DOCUMENT_VERSION,
+    size: width,
+    givens,
+    values,
+    constraints,
+    ...(title === undefined || title === "" ? {} : { title }),
+    ...(author === undefined || author === "" ? {} : { author }),
+    ...(rules === undefined ? {} : { rules: [rules] }),
+  };
+}
+
+function extractPenpaPayload(input: string): string {
+  const trimmed = input.trim();
+  if (trimmed.startsWith("penpa:")) return trimmed.slice("penpa:".length);
+  let params: URLSearchParams;
+  if (/^https?:\/\//iu.test(trimmed)) {
+    let url: URL;
+    try {
+      url = new URL(trimmed);
+    } catch (error) {
+      throw new SudokuFormatError("INVALID_PENPA_URL", "Invalid Penpa+ URL.", {
+        cause: error,
+      });
+    }
+    if (!url.pathname.includes("/penpa-edit/")) {
+      throw new RemotePuzzleReferenceError("The pasted URL");
+    }
+    params = new URLSearchParams(
+      url.hash.length > 1 ? url.hash.slice(1) : url.search.slice(1),
+    );
+  } else {
+    params = new URLSearchParams(trimmed.replace(/^[?#]/u, ""));
+  }
+  const payload = params.get("p");
+  if (payload === null || payload.startsWith("http")) {
+    throw new RemotePuzzleReferenceError("The Penpa+ link");
+  }
+  return payload;
+}
+
+function base64Bytes(payload: string): Uint8Array {
+  const normalized = payload.replaceAll(" ", "+");
+  if (
+    normalized.length === 0 ||
+    normalized.length > MAX_PENPA_PAYLOAD_LENGTH ||
+    !/^[A-Za-z0-9+/]*={0,2}$/u.test(normalized)
+  ) {
+    return fail("INVALID_PENPA", "The Penpa+ payload is invalid or too large.");
+  }
+  let binary: string;
+  try {
+    binary = atob(normalized);
+  } catch (error) {
+    throw new SudokuFormatError(
+      "INVALID_PENPA",
+      "The Penpa+ payload is not valid base64.",
+      { cause: error },
+    );
+  }
+  return Uint8Array.from(binary, (character) => character.charCodeAt(0));
+}
+
+async function inflateRaw(bytes: Uint8Array): Promise<string> {
+  if (typeof DecompressionStream === "undefined") {
+    return fail(
+      "UNSUPPORTED_BROWSER",
+      "This browser cannot decompress Penpa+ data locally.",
+    );
+  }
+  let stream: ReadableStream<Uint8Array>;
+  try {
+    const input = new ArrayBuffer(bytes.byteLength);
+    new Uint8Array(input).set(bytes);
+    const body = new Response(input).body;
+    if (body === null) {
+      return fail("INVALID_PENPA", "The Penpa+ payload stream is empty.");
+    }
+    stream = body.pipeThrough(new DecompressionStream("deflate-raw"));
+  } catch (error) {
+    throw new SudokuFormatError(
+      "INVALID_PENPA",
+      "The Penpa+ raw-deflate stream could not be opened.",
+      { cause: error },
+    );
+  }
+  const reader = stream.getReader();
+  const chunks: Uint8Array[] = [];
+  let total = 0;
+  try {
+    while (true) {
+      const chunk = await reader.read();
+      if (chunk.done) break;
+      total += chunk.value.byteLength;
+      if (total > MAX_DOCUMENT_BYTES) {
+        await reader.cancel();
+        return fail(
+          "LIMIT_EXCEEDED",
+          "The decompressed Penpa+ puzzle is too large to open safely.",
+        );
+      }
+      chunks.push(chunk.value);
+    }
+  } catch (error) {
+    throw new SudokuFormatError(
+      "INVALID_PENPA",
+      "The Penpa+ payload could not be decompressed.",
+      { cause: error },
+    );
+  }
+  const output = new Uint8Array(total);
+  let offset = 0;
+  for (const chunk of chunks) {
+    output.set(chunk, offset);
+    offset += chunk.byteLength;
+  }
+  try {
+    return new TextDecoder("utf-8", { fatal: true }).decode(output);
+  } catch (error) {
+    throw new SudokuFormatError(
+      "INVALID_PENPA",
+      "The decompressed Penpa+ payload is not valid UTF-8 text.",
+      { cause: error },
+    );
+  }
+}
+
+/** Import a self-contained Penpa+ long URL without making a network request. */
+export async function importPenpa(input: string): Promise<SudokuDocument> {
+  return parsePenpaText(
+    await inflateRaw(base64Bytes(extractPenpaPayload(input))),
+  );
+}

src/formats/share.ts

@@ -1,7 +1,8 @@
+import { compressToEncodedURIComponent } from "lz-string";
 import {
-  compressToEncodedURIComponent,
+  LzStringOutputLimitError,
-  decompressFromEncodedURIComponent,
+  decompressFromEncodedURIComponentBounded,
-} from "lz-string";
+} from "./boundedLz";
 import {
   MAX_DOCUMENT_BYTES,
   SudokuFormatError,
@@ -49,18 +50,27 @@ export function decodePuzzleHash(hashOrUrl: string): SudokuDocument {
     );
   }
   const compressed = hash.slice(PUZZLE_HASH_PREFIX.length);
-  const json = decompressFromEncodedURIComponent(compressed);
+  let json: string | null;
+  try {
+    json = decompressFromEncodedURIComponentBounded(
+      compressed,
+      MAX_DOCUMENT_BYTES,
+    );
+  } catch (error) {
+    if (error instanceof LzStringOutputLimitError) {
+      throw new SudokuFormatError(
+        "LIMIT_EXCEEDED",
+        "The decompressed puzzle is too large to open safely.",
+        { cause: error },
+      );
+    }
+    throw error;
+  }
   if (json === null || json === "") {
     throw new SudokuFormatError(
       "INVALID_SHARE",
       "The share payload could not be decompressed.",
     );
   }
-  if (new TextEncoder().encode(json).byteLength > MAX_DOCUMENT_BYTES) {
-    throw new SudokuFormatError(
-      "LIMIT_EXCEEDED",
-      "The decompressed puzzle is too large to open safely.",
-    );
-  }
   return parseSudokuDocument(json);
 }

src/formats/sudokupad.ts

@@ -0,0 +1,489 @@
+import {
+  LzStringOutputLimitError,
+  decompressFromBase64OrUriComponentBounded,
+} from "./boundedLz";
+import {
+  MAX_BOARD_SIZE,
+  MAX_DOCUMENT_BYTES,
+  MIN_BOARD_SIZE,
+  SudokuFormatError,
+} from "./document";
+import { UnsupportedPuzzleConstructsError } from "./interoperability";
+import {
+  SUDOKU_DOCUMENT_SCHEMA,
+  SUDOKU_DOCUMENT_VERSION,
+  type PortableConstraint,
+  type SudokuDocument,
+} from "./types";
+
+export const MAX_SUDOKUPAD_PAYLOAD_LENGTH = 262_144;
+
+type JsonRecord = Record<string, unknown>;
+
+const ROOT_FIELDS = new Set([
+  "id",
+  "cellSize",
+  "cells",
+  "settings",
+  "metadata",
+  "metaData",
+  "global",
+  "regions",
+  "lines",
+  "underlays",
+  "overlays",
+  "arrows",
+  "cages",
+  "title",
+  "author",
+  "rules",
+  "solution",
+]);
+
+const CELL_FIELDS = new Set(["value", "given", "pencilMarks", "centremarks"]);
+
+function fail(code: string, message: string): never {
+  throw new SudokuFormatError(code, message);
+}
+
+function isRecord(value: unknown): value is JsonRecord {
+  return typeof value === "object" && value !== null && !Array.isArray(value);
+}
+
+function present(value: unknown): boolean {
+  if (value === undefined || value === null || value === false) return false;
+  if (Array.isArray(value)) return value.length > 0;
+  if (isRecord(value)) return Object.keys(value).length > 0;
+  if (typeof value === "string") return value.trim().length > 0;
+  return true;
+}
+
+function boundedText(value: unknown, label: string, maximum = 16_384) {
+  if (value === undefined || value === null || value === "") return undefined;
+  if (typeof value !== "string" || value.length > maximum) {
+    return fail(
+      "INVALID_SUDOKUPAD",
+      `${label} must be text of at most ${maximum} characters.`,
+    );
+  }
+  return value;
+}
+
+function integer(
+  value: unknown,
+  label: string,
+  minimum: number,
+  maximum: number,
+): number {
+  const parsed =
+    typeof value === "string" && value.trim() !== "" ? Number(value) : value;
+  if (
+    !Number.isInteger(parsed) ||
+    (parsed as number) < minimum ||
+    (parsed as number) > maximum
+  ) {
+    return fail(
+      "INVALID_SUDOKUPAD",
+      `${label} must be an integer from ${minimum} to ${maximum}.`,
+    );
+  }
+  return parsed as number;
+}
+
+function coordinate(value: unknown, size: number, label: string): number {
+  if (
+    !Array.isArray(value) ||
+    value.length !== 2 ||
+    !Number.isInteger(value[0]) ||
+    !Number.isInteger(value[1])
+  ) {
+    return fail(
+      "INVALID_SUDOKUPAD",
+      `${label} must be a zero-based [row, column] cell.`,
+    );
+  }
+  const row = integer(value[0], `${label}[0]`, 0, size - 1);
+  const column = integer(value[1], `${label}[1]`, 0, size - 1);
+  return row * size + column;
+}
+
+function digitList(value: unknown, size: number, label: string): number[] {
+  if (!Array.isArray(value) || value.length > size) {
+    return fail("INVALID_SUDOKUPAD", `${label} must be a bounded digit array.`);
+  }
+  return [
+    ...new Set(
+      value.map((digit, index) =>
+        integer(digit, `${label}[${String(index)}]`, 1, size),
+      ),
+    ),
+  ].sort((left, right) => left - right);
+}
+
+function metadataFrom(value: JsonRecord): JsonRecord {
+  const metadata = value.metadata ?? value.metaData;
+  if (metadata === undefined) return {};
+  if (!isRecord(metadata)) {
+    return fail("INVALID_SUDOKUPAD", "SudokuPad metadata must be an object.");
+  }
+  if (Object.keys(metadata).length > 100) {
+    return fail("LIMIT_EXCEEDED", "SudokuPad metadata has too many fields.");
+  }
+  return metadata;
+}
+
+function metaText(
+  root: JsonRecord,
+  metadata: JsonRecord,
+  key: "title" | "author" | "rules" | "solution",
+): string | undefined {
+  const value = root[key] ?? metadata[key];
+  if (Array.isArray(value)) {
+    if (!value.every((entry) => typeof entry === "string")) {
+      return fail("INVALID_SUDOKUPAD", `${key} metadata must be text.`);
+    }
+    return value.join(key === "rules" ? "\n" : " ").slice(0, 16_384);
+  }
+  return boundedText(value, `SudokuPad ${key}`);
+}
+
+function solutionDigits(value: string | undefined, size: number) {
+  if (value === undefined) return undefined;
+  const tokens = value.includes(",") ? value.split(",") : [...value];
+  if (tokens.length !== size * size) {
+    return fail(
+      "INVALID_SUDOKUPAD",
+      `SudokuPad solution must contain exactly ${size * size} digits.`,
+    );
+  }
+  return tokens.map((digit, index) =>
+    integer(digit, `solution[${String(index)}]`, 1, size),
+  );
+}
+
+function parseRegions(value: unknown, size: number): number[] | undefined {
+  if (value === undefined) return undefined;
+  if (!Array.isArray(value) || value.length !== size) {
+    return fail(
+      "INVALID_SUDOKUPAD",
+      `SudokuPad regions must contain exactly ${size} regions.`,
+    );
+  }
+  const regions = Array<number>(size * size).fill(-1);
+  value.forEach((rawRegion, regionIndex) => {
+    if (!Array.isArray(rawRegion) || rawRegion.length !== size) {
+      return fail(
+        "INVALID_SUDOKUPAD",
+        `SudokuPad region ${String(regionIndex + 1)} must contain ${size} cells.`,
+      );
+    }
+    rawRegion.forEach((cell, cellIndex) => {
+      const index = coordinate(
+        cell,
+        size,
+        `regions[${String(regionIndex)}][${String(cellIndex)}]`,
+      );
+      if (regions[index] !== -1) {
+        return fail(
+          "INVALID_SUDOKUPAD",
+          "SudokuPad regions contain a duplicate cell.",
+        );
+      }
+      regions[index] = regionIndex;
+    });
+  });
+  if (regions.some((region) => region === -1)) {
+    return fail(
+      "INVALID_SUDOKUPAD",
+      "SudokuPad regions do not cover every grid cell.",
+    );
+  }
+  return regions;
+}
+
+function parseCages(
+  value: unknown,
+  size: number,
+  metadata: JsonRecord,
+): PortableConstraint[] {
+  if (value === undefined) return [];
+  if (!Array.isArray(value) || value.length > 5_000) {
+    return fail("LIMIT_EXCEEDED", "SudokuPad cages must be a bounded array.");
+  }
+  const constraints: PortableConstraint[] = [];
+  const unsupported: string[] = [];
+  for (const [index, raw] of value.entries()) {
+    if (!isRecord(raw)) {
+      return fail(
+        "INVALID_SUDOKUPAD",
+        `cages[${String(index)}] must be an object.`,
+      );
+    }
+    const cells = raw.cells;
+    if (!Array.isArray(cells) || cells.length === 0) {
+      const rawValue = boundedText(raw.value, `cages[${String(index)}].value`);
+      const match = /^([^: ]+):\s*([\s\S]+)$/u.exec(rawValue ?? "");
+      if (match !== null && metadata[match[1]!] === undefined) {
+        metadata[match[1]!] = match[2]!;
+      } else if (rawValue !== undefined) {
+        unsupported.push("cell-free cage annotations");
+      }
+      continue;
+    }
+    if (cells.length > size * size) {
+      return fail(
+        "LIMIT_EXCEEDED",
+        "A SudokuPad cage contains too many cells.",
+      );
+    }
+    const cageCells = cells.map((cell, cellIndex) =>
+      coordinate(
+        cell,
+        size,
+        `cages[${String(index)}].cells[${String(cellIndex)}]`,
+      ),
+    );
+    if (new Set(cageCells).size !== cageCells.length) {
+      return fail(
+        "INVALID_SUDOKUPAD",
+        `cages[${String(index)}] contains a duplicate cell.`,
+      );
+    }
+    if (raw.hidden === true) {
+      unsupported.push("hidden or masked cells");
+      continue;
+    }
+    const sumValue = raw.sum ?? raw.value;
+    if (sumValue === undefined || sumValue === "") {
+      unsupported.push("cages without numeric sums");
+      continue;
+    }
+    const sum = integer(sumValue, `cages[${String(index)}].sum`, 1, size ** 3);
+    constraints.push({
+      type: "killer-cage",
+      cells: cageCells,
+      sum,
+      noRepeat: raw.unique !== false,
+    });
+  }
+  if (unsupported.length > 0) {
+    throw new UnsupportedPuzzleConstructsError("SudokuPad/CTC", unsupported);
+  }
+  return constraints;
+}
+
+/** Parse raw, already-decoded SudokuPad/CTC (often called SCL) JSON. */
+export function parseSudokuPadPuzzle(value: unknown): SudokuDocument {
+  if (!isRecord(value)) {
+    return fail("INVALID_SUDOKUPAD", "The SudokuPad puzzle must be an object.");
+  }
+  const unsupported: string[] = [];
+  for (const field of Object.keys(value)) {
+    if (!ROOT_FIELDS.has(field))
+      unsupported.push(`unknown root field “${field}”`);
+  }
+  for (const field of ["lines", "underlays", "overlays", "arrows"] as const) {
+    if (present(value[field])) unsupported.push(`visual ${field}`);
+  }
+  if (present(value.global)) unsupported.push("custom global rules");
+  if (isRecord(value.settings)) {
+    for (const key of Object.keys(value.settings)) {
+      if (key !== "conflictchecker") unsupported.push(`setting “${key}”`);
+    }
+  } else if (value.settings !== undefined) {
+    return fail("INVALID_SUDOKUPAD", "SudokuPad settings must be an object.");
+  }
+  if (unsupported.length > 0) {
+    throw new UnsupportedPuzzleConstructsError("SudokuPad/CTC", unsupported);
+  }
+
+  if (!Array.isArray(value.cells)) {
+    return fail("INVALID_SUDOKUPAD", "SudokuPad cells must be a square array.");
+  }
+  const size = integer(
+    value.cells.length,
+    "SudokuPad grid size",
+    MIN_BOARD_SIZE,
+    MAX_BOARD_SIZE,
+  );
+  if (!value.cells.every((row) => Array.isArray(row) && row.length === size)) {
+    return fail(
+      "INVALID_SUDOKUPAD",
+      "SudokuPad cells must form a square grid.",
+    );
+  }
+
+  const givens: number[] = [];
+  const values: number[] = [];
+  const cornerMarks: number[][] = [];
+  const centerMarks: number[][] = [];
+  for (const [rowIndex, rawRow] of value.cells.entries()) {
+    for (const [columnIndex, rawCell] of (rawRow as unknown[]).entries()) {
+      if (!isRecord(rawCell)) {
+        return fail(
+          "INVALID_SUDOKUPAD",
+          `cells[${String(rowIndex)}][${String(columnIndex)}] must be an object.`,
+        );
+      }
+      const unknown = Object.keys(rawCell).filter(
+        (field) => !CELL_FIELDS.has(field),
+      );
+      if (unknown.length > 0) {
+        throw new UnsupportedPuzzleConstructsError(
+          "SudokuPad/CTC",
+          unknown.map((field) => `cell field “${field}”`),
+        );
+      }
+      const digit =
+        rawCell.value === undefined || rawCell.value === ""
+          ? 0
+          : integer(
+              rawCell.value,
+              `cells[${String(rowIndex)}][${String(columnIndex)}].value`,
+              1,
+              size,
+            );
+      const isGiven = digit !== 0 && rawCell.given !== false;
+      givens.push(isGiven ? digit : 0);
+      values.push(digit);
+      cornerMarks.push(
+        digitList(
+          rawCell.pencilMarks ?? [],
+          size,
+          `cells[${String(rowIndex)}][${String(columnIndex)}].pencilMarks`,
+        ),
+      );
+      centerMarks.push(
+        digitList(
+          rawCell.centremarks ?? [],
+          size,
+          `cells[${String(rowIndex)}][${String(columnIndex)}].centremarks`,
+        ),
+      );
+    }
+  }
+
+  const metadata = metadataFrom(value);
+  const constraints = parseCages(value.cages, size, metadata);
+  if (metadata.antiknight === true || metadata.antiknight === "true") {
+    constraints.push({ type: "anti-knight" });
+  }
+  if (metadata.antiking === true || metadata.antiking === "true") {
+    constraints.push({ type: "anti-king" });
+  }
+  if (metadata.nonconsecutive === true || metadata.nonconsecutive === "true") {
+    constraints.push({ type: "non-consecutive" });
+  }
+  const knownMetadata = new Set([
+    "title",
+    "author",
+    "rules",
+    "solution",
+    "antiknight",
+    "antiking",
+    "nonconsecutive",
+  ]);
+  const unknownMetadata = Object.keys(metadata).filter(
+    (key) => !knownMetadata.has(key),
+  );
+  if (unknownMetadata.length > 0) {
+    throw new UnsupportedPuzzleConstructsError(
+      "SudokuPad/CTC",
+      unknownMetadata.map((key) => `metadata “${key}”`),
+    );
+  }
+
+  const title = metaText(value, metadata, "title");
+  const author = metaText(value, metadata, "author");
+  const rules = metaText(value, metadata, "rules");
+  const solution = solutionDigits(metaText(value, metadata, "solution"), size);
+  const regions = parseRegions(value.regions, size);
+  const id = boundedText(value.id, "SudokuPad id", 256);
+  return {
+    schema: SUDOKU_DOCUMENT_SCHEMA,
+    version: SUDOKU_DOCUMENT_VERSION,
+    size,
+    givens,
+    values,
+    cornerMarks,
+    centerMarks,
+    constraints,
+    ...(regions === undefined ? {} : { regions }),
+    ...(title === undefined ? {} : { title: title.slice(0, 256) }),
+    ...(author === undefined ? {} : { author: author.slice(0, 256) }),
+    ...(rules === undefined ? {} : { rules: [rules.slice(0, 16_384)] }),
+    ...(solution === undefined ? {} : { solution }),
+    ...(id === undefined ? {} : { id }),
+  };
+}
+
+function boundedJson(input: string): unknown {
+  if (new TextEncoder().encode(input).byteLength > MAX_DOCUMENT_BYTES) {
+    return fail(
+      "LIMIT_EXCEEDED",
+      "The decoded SudokuPad puzzle is too large to open safely.",
+    );
+  }
+  try {
+    return JSON.parse(input) as unknown;
+  } catch (error) {
+    throw new SudokuFormatError(
+      "INVALID_SUDOKUPAD",
+      "The SudokuPad payload does not contain valid JSON.",
+      { cause: error },
+    );
+  }
+}
+
+function decodePayload(payload: string): string {
+  if (payload.length === 0 || payload.length > MAX_SUDOKUPAD_PAYLOAD_LENGTH) {
+    return fail(
+      "LIMIT_EXCEEDED",
+      "The inline SudokuPad payload is empty or too large.",
+    );
+  }
+  let decoded = payload;
+  try {
+    decoded = decodeURIComponent(payload);
+  } catch {
+    // A malformed literal percent will fail decompression below.
+  }
+  let text: string | null;
+  try {
+    text = decompressFromBase64OrUriComponentBounded(
+      decoded,
+      MAX_DOCUMENT_BYTES,
+    );
+  } catch (error) {
+    if (error instanceof LzStringOutputLimitError) {
+      return fail(
+        "LIMIT_EXCEEDED",
+        "The decoded SudokuPad puzzle is too large to open safely.",
+      );
+    }
+    throw error;
+  }
+  if (text === null || text === "") {
+    return fail(
+      "INVALID_SUDOKUPAD",
+      "The inline SudokuPad payload could not be decompressed.",
+    );
+  }
+  return text;
+}
+
+/** Import raw SCL/CTC JSON or a self-contained `ctc…`/`scl…` payload. */
+export function importSudokuPad(input: string): SudokuDocument {
+  const trimmed = input.trim();
+  if (trimmed.startsWith("{")) {
+    return parseSudokuPadPuzzle(boundedJson(trimmed));
+  }
+  const payload = trimmed.replace(/^(?:ctc|scl)/iu, "");
+  if (payload === trimmed) {
+    return fail(
+      "INVALID_SUDOKUPAD",
+      "Expected raw SudokuPad JSON or a self-contained ctc/scl payload.",
+    );
+  }
+  return parseSudokuPadPuzzle(boundedJson(decodePayload(payload)));
+}

src/formats/types.ts

@@ -1,45 +1,84 @@
+import type { PortableAidMemoire } from "../state/aidMemoire";
+
+export type {
+  PortableAidMemoire,
+  PortableAidMemoireCell,
+} from "../state/aidMemoire";
+
 export const SUDOKU_DOCUMENT_SCHEMA =
   "de.add-ideas.sudoku-tools.puzzle" as const;
 export const SUDOKU_DOCUMENT_VERSION = 1 as const;
 
 export type CellIndex = number;
+export type OutsideSide = "top" | "right" | "bottom" | "left";
+export interface CluePolarity {
+  /** When true, the completed clue must be false rather than true. */
+  readonly negated?: boolean;
+}
 
 export type PortableConstraint =
   | { readonly type: "diagonal"; readonly direction: "main" | "anti" }
   | { readonly type: "anti-knight" }
   | { readonly type: "anti-king" }
   | { readonly type: "non-consecutive" }
-  | {
+  | ({
       readonly type: "killer-cage";
       readonly cells: readonly CellIndex[];
       readonly sum: number;
       readonly noRepeat?: boolean;
-    }
+    } & CluePolarity)
-  | { readonly type: "thermo"; readonly cells: readonly CellIndex[] }
+  | ({
-  | {
+      readonly type: "thermo";
+      readonly cells: readonly CellIndex[];
+    } & CluePolarity)
+  | ({
       readonly type: "arrow";
       readonly bulb: readonly CellIndex[];
       readonly line: readonly CellIndex[];
-    }
+    } & CluePolarity)
-  | {
+  | ({
       readonly type: "kropki";
       readonly a: CellIndex;
       readonly b: CellIndex;
       readonly kind: "white" | "black";
-    }
+    } & CluePolarity)
-  | {
+  | ({
       readonly type: "xv";
       readonly a: CellIndex;
       readonly b: CellIndex;
       readonly total: 5 | 10;
-    }
+    } & CluePolarity)
-  | {
+  | ({
       readonly type: "inequality";
       readonly lesser: CellIndex;
       readonly greater: CellIndex;
-    }
+    } & CluePolarity)
-  | { readonly type: "renban"; readonly cells: readonly CellIndex[] }
+  | ({
-  | { readonly type: "palindrome"; readonly cells: readonly CellIndex[] };
+      readonly type: "x-sum";
+      readonly side: OutsideSide;
+      readonly index: number;
+      readonly sum: number;
+    } & CluePolarity)
+  | ({
+      readonly type: "skyscraper";
+      readonly side: OutsideSide;
+      readonly index: number;
+      readonly count: number;
+    } & CluePolarity)
+  | ({
+      readonly type: "quadruple";
+      readonly cells: readonly CellIndex[];
+      readonly digits: readonly number[];
+    } & CluePolarity)
+  | ({ readonly type: "maximum"; readonly cell: CellIndex } & CluePolarity)
+  | ({
+      readonly type: "renban";
+      readonly cells: readonly CellIndex[];
+    } & CluePolarity)
+  | ({
+      readonly type: "palindrome";
+      readonly cells: readonly CellIndex[];
+    } & CluePolarity);
 
 /**
  * Stable, versioned interchange format owned by Sudoku Tools. Cell indices are
@@ -57,6 +96,8 @@ export interface SudokuDocument {
   readonly candidates?: readonly (readonly number[])[];
   readonly colors?: readonly number[];
   readonly elapsedMs?: number;
+  /** Optional, non-constraining scratch cells used while solving. */
+  readonly aidMemoire?: PortableAidMemoire;
   readonly solution?: readonly number[];
   readonly regions?: readonly number[];
   readonly constraints: readonly PortableConstraint[];
@@ -136,6 +177,12 @@ export function cloneConstraint(
     case "renban":
     case "palindrome":
       return { ...constraint, cells: [...constraint.cells] };
+    case "quadruple":
+      return {
+        ...constraint,
+        cells: [...constraint.cells],
+        digits: [...constraint.digits],
+      };
     case "arrow":
       return {
         ...constraint,

src/formats/visual.ts

@@ -0,0 +1,669 @@
+import { normalizePuzzle } from "../domain/validation";
+import type {
+  NormalizedPuzzle,
+  OutsideClueSide,
+  VariantConstraint,
+} from "../domain/types";
+import { symbolFor } from "../state/session";
+import { normalizeSudokuDocument, SudokuFormatError } from "./document";
+import { toDomainPuzzle, type SudokuDocument } from "./types";
+
+export interface VisualExportOptions {
+  readonly includeProgress?: boolean;
+  readonly includeNotes?: boolean;
+  readonly rasterScale?: number;
+}
+
+export const MAX_VISUAL_EXPORT_DIMENSION = 4_096;
+export const MAX_VISUAL_EXPORT_BYTES = 5_242_880;
+
+const CELL_SIZE = 72;
+const OUTSIDE_MARGIN = 58;
+const BOARD_MARGIN = 20;
+const HEADER_HEIGHT = 74;
+
+function escapeXml(value: unknown): string {
+  const unicode = new TextDecoder().decode(
+    new TextEncoder().encode(String(value)),
+  );
+  const xmlCharacters = [...unicode]
+    .map((character) => {
+      const codePoint = character.codePointAt(0)!;
+      return codePoint === 0x09 ||
+        codePoint === 0x0a ||
+        codePoint === 0x0d ||
+        (codePoint >= 0x20 && codePoint <= 0xd7ff) ||
+        (codePoint >= 0xe000 && codePoint <= 0xfffd) ||
+        (codePoint >= 0x1_0000 && codePoint <= 0x10_ffff)
+        ? character
+        : "�";
+    })
+    .join("");
+  return xmlCharacters
+    .replaceAll("&", "&amp;")
+    .replaceAll("<", "&lt;")
+    .replaceAll(">", "&gt;")
+    .replaceAll('"', "&quot;")
+    .replaceAll("'", "&apos;");
+}
+
+function number(value: number): string {
+  return Number(value.toFixed(3)).toString();
+}
+
+interface BoardOrigin {
+  readonly x: number;
+  readonly y: number;
+}
+
+function point(size: number, cell: number, origin: BoardOrigin) {
+  return {
+    x: origin.x + ((cell % size) + 0.5) * CELL_SIZE,
+    y: origin.y + (Math.floor(cell / size) + 0.5) * CELL_SIZE,
+  };
+}
+
+function linePoints(
+  size: number,
+  cells: readonly number[],
+  origin: BoardOrigin,
+) {
+  return cells
+    .map((cell) => {
+      const position = point(size, cell, origin);
+      return `${number(position.x)},${number(position.y)}`;
+    })
+    .join(" ");
+}
+
+function pathBoundary(
+  size: number,
+  cells: ReadonlySet<number>,
+  origin: BoardOrigin,
+  inset: number,
+): string {
+  const commands: string[] = [];
+  for (const cell of cells) {
+    const row = Math.floor(cell / size);
+    const column = cell % size;
+    const x0 = origin.x + column * CELL_SIZE + inset;
+    const x1 = origin.x + (column + 1) * CELL_SIZE - inset;
+    const y0 = origin.y + row * CELL_SIZE + inset;
+    const y1 = origin.y + (row + 1) * CELL_SIZE - inset;
+    if (row === 0 || !cells.has(cell - size))
+      commands.push(`M${number(x0)} ${number(y0)}H${number(x1)}`);
+    if (row === size - 1 || !cells.has(cell + size))
+      commands.push(`M${number(x0)} ${number(y1)}H${number(x1)}`);
+    if (column === 0 || !cells.has(cell - 1))
+      commands.push(`M${number(x0)} ${number(y0)}V${number(y1)}`);
+    if (column === size - 1 || !cells.has(cell + 1))
+      commands.push(`M${number(x1)} ${number(y0)}V${number(y1)}`);
+  }
+  return commands.join(" ");
+}
+
+function outsidePoint(
+  size: number,
+  side: OutsideClueSide,
+  index: number,
+  origin: BoardOrigin,
+) {
+  const board = size * CELL_SIZE;
+  switch (side) {
+    case "top":
+      return {
+        x: origin.x + (index + 0.5) * CELL_SIZE,
+        y: origin.y - OUTSIDE_MARGIN * 0.52,
+      };
+    case "right":
+      return {
+        x: origin.x + board + OUTSIDE_MARGIN * 0.52,
+        y: origin.y + (index + 0.5) * CELL_SIZE,
+      };
+    case "bottom":
+      return {
+        x: origin.x + (index + 0.5) * CELL_SIZE,
+        y: origin.y + board + OUTSIDE_MARGIN * 0.52,
+      };
+    case "left":
+      return {
+        x: origin.x - OUTSIDE_MARGIN * 0.52,
+        y: origin.y + (index + 0.5) * CELL_SIZE,
+      };
+  }
+}
+
+function globalRuleLabels(puzzle: NormalizedPuzzle): string[] {
+  const labels: string[] = [];
+  if (puzzle.constraints.some(({ type }) => type === "anti-knight"))
+    labels.push("Anti-knight");
+  if (puzzle.constraints.some(({ type }) => type === "anti-king"))
+    labels.push("Anti-king");
+  if (puzzle.constraints.some(({ type }) => type === "non-consecutive"))
+    labels.push("Non-consecutive");
+  return labels;
+}
+
+function renderConstraint(
+  constraint: VariantConstraint,
+  index: number,
+  puzzle: NormalizedPuzzle,
+  origin: BoardOrigin,
+): string {
+  const { size } = puzzle;
+  const negated = "negated" in constraint && constraint.negated === true;
+  const polarity = negated ? " negated" : "";
+  const marker = negated ? "≠" : "";
+  if (
+    constraint.type === "anti-knight" ||
+    constraint.type === "anti-king" ||
+    constraint.type === "non-consecutive"
+  ) {
+    return "";
+  }
+  if (constraint.type === "diagonal") {
+    const startX =
+      origin.x + (constraint.direction === "main" ? 0 : size * CELL_SIZE);
+    const endX =
+      origin.x + (constraint.direction === "main" ? size * CELL_SIZE : 0);
+    return `<line class="constraint diagonal" x1="${number(startX)}" y1="${number(origin.y)}" x2="${number(endX)}" y2="${number(origin.y + size * CELL_SIZE)}"/>`;
+  }
+  if (constraint.type === "killer-cage") {
+    const first = Math.min(...constraint.cells);
+    const label = point(size, first, origin);
+    return `<g class="constraint cage${polarity}" data-constraint="${index}"><path d="${pathBoundary(size, new Set(constraint.cells), origin, 7)}"/><text class="cage-label" x="${number(label.x - CELL_SIZE * 0.34)}" y="${number(label.y - CELL_SIZE * 0.27)}">${marker}${String(constraint.sum)}</text></g>`;
+  }
+  if (constraint.type === "thermo") {
+    const bulb = point(size, constraint.cells[0]!, origin);
+    return `<g class="constraint thermo${polarity}" data-constraint="${index}"><polyline points="${linePoints(size, constraint.cells, origin)}"/><circle cx="${number(bulb.x)}" cy="${number(bulb.y)}" r="${number(CELL_SIZE * 0.3)}"/>${negated ? `<text class="false-marker" x="${number(bulb.x)}" y="${number(bulb.y)}">≠</text>` : ""}</g>`;
+  }
+  if (constraint.type === "arrow") {
+    const bulbPoints = constraint.bulb.map((cell) => point(size, cell, origin));
+    const bulb = bulbPoints[0]!;
+    const path = [constraint.bulb.at(-1)!, ...constraint.line];
+    const tip = point(size, constraint.line.at(-1)!, origin);
+    const minimumX = Math.min(...bulbPoints.map(({ x }) => x));
+    const maximumX = Math.max(...bulbPoints.map(({ x }) => x));
+    const minimumY = Math.min(...bulbPoints.map(({ y }) => y));
+    const maximumY = Math.max(...bulbPoints.map(({ y }) => y));
+    return `<g class="constraint arrow${polarity}" data-constraint="${index}"><polyline points="${linePoints(size, path, origin)}"/><rect x="${number(minimumX - CELL_SIZE * 0.3)}" y="${number(minimumY - CELL_SIZE * 0.3)}" width="${number(maximumX - minimumX + CELL_SIZE * 0.6)}" height="${number(maximumY - minimumY + CELL_SIZE * 0.6)}" rx="${number(CELL_SIZE * 0.3)}"/><circle class="arrow-tip" cx="${number(tip.x)}" cy="${number(tip.y)}" r="${number(CELL_SIZE * 0.075)}"/>${negated ? `<text class="false-marker" x="${number(bulb.x)}" y="${number(bulb.y)}">≠</text>` : ""}</g>`;
+  }
+  if (constraint.type === "renban" || constraint.type === "palindrome") {
+    return `<g class="constraint ${constraint.type}${polarity}" data-constraint="${index}"><polyline points="${linePoints(size, constraint.cells, origin)}"/>${
+      constraint.type === "palindrome"
+        ? constraint.cells
+            .map((cell) => {
+              const center = point(size, cell, origin);
+              return `<circle cx="${number(center.x)}" cy="${number(center.y)}" r="${number(CELL_SIZE * 0.13)}"/>`;
+            })
+            .join("")
+        : ""
+    }</g>`;
+  }
+  if (constraint.type === "maximum") {
+    const center = point(size, constraint.cell, origin);
+    const offset = CELL_SIZE * 0.28;
+    const inner = CELL_SIZE * 0.14;
+    return `<g class="constraint maximum${polarity}" data-constraint="${index}"><circle cx="${number(center.x)}" cy="${number(center.y)}" r="${number(CELL_SIZE * 0.18)}"/><path d="M${number(center.x - inner)} ${number(center.y - inner)}L${number(center.x)} ${number(center.y - offset)}L${number(center.x + inner)} ${number(center.y - inner)}M${number(center.x - inner)} ${number(center.y + inner)}L${number(center.x)} ${number(center.y + offset)}L${number(center.x + inner)} ${number(center.y + inner)}M${number(center.x - inner)} ${number(center.y - inner)}L${number(center.x - offset)} ${number(center.y)}L${number(center.x - inner)} ${number(center.y + inner)}M${number(center.x + inner)} ${number(center.y - inner)}L${number(center.x + offset)} ${number(center.y)}L${number(center.x + inner)} ${number(center.y + inner)}"/></g>`;
+  }
+  if (constraint.type === "quadruple") {
+    const positions = constraint.cells.map((cell) => point(size, cell, origin));
+    const center = {
+      x:
+        positions.reduce((sum, position) => sum + position.x, 0) /
+        positions.length,
+      y:
+        positions.reduce((sum, position) => sum + position.y, 0) /
+        positions.length,
+    };
+    return `<g class="constraint quadruple${polarity}" data-constraint="${index}"><circle cx="${number(center.x)}" cy="${number(center.y)}" r="${number(CELL_SIZE * 0.29)}"/><text x="${number(center.x)}" y="${number(center.y)}">${marker}${escapeXml(constraint.digits.map((digit) => symbolFor(digit, size)).join(""))}</text></g>`;
+  }
+  if (constraint.type === "x-sum" || constraint.type === "skyscraper") {
+    const position = outsidePoint(
+      size,
+      constraint.side,
+      constraint.index,
+      origin,
+    );
+    const value =
+      constraint.type === "x-sum" ? constraint.sum : constraint.count;
+    const companionIndex = puzzle.constraints.findIndex(
+      (candidate) =>
+        candidate.type !== constraint.type &&
+        (candidate.type === "x-sum" || candidate.type === "skyscraper") &&
+        candidate.side === constraint.side &&
+        candidate.index === constraint.index &&
+        (candidate.type === "x-sum" ? candidate.sum : candidate.count) ===
+          value &&
+        ("negated" in candidate && candidate.negated === true) === negated,
+    );
+    const combined = companionIndex >= 0;
+    if (combined && companionIndex < index) return "";
+    if (combined) {
+      return `<g class="constraint outside combined${polarity}" data-constraint="${index}"><rect x="${number(position.x - 25)}" y="${number(position.y - 23)}" width="50" height="46" rx="8"/><text class="outside-kinds" x="${number(position.x)}" y="${number(position.y - 8)}">Σ · ▥</text><text class="outside-value" x="${number(position.x)}" y="${number(position.y + 10)}">${marker}${String(value)}</text></g>`;
+    }
+    return `<g class="constraint outside ${constraint.type}${polarity}" data-constraint="${index}"><rect x="${number(position.x - 25)}" y="${number(position.y - 18)}" width="50" height="36" rx="8"/><text x="${number(position.x)}" y="${number(position.y)}">${constraint.type === "x-sum" ? "Σ" : "▥"}${marker}${String(value)}</text></g>`;
+  }
+  const a = point(
+    size,
+    constraint.type === "inequality" ? constraint.lesser : constraint.a,
+    origin,
+  );
+  const b = point(
+    size,
+    constraint.type === "inequality" ? constraint.greater : constraint.b,
+    origin,
+  );
+  const middle = { x: (a.x + b.x) / 2, y: (a.y + b.y) / 2 };
+  if (constraint.type === "kropki") {
+    return `<g class="constraint kropki ${constraint.kind}${polarity}" data-constraint="${index}"><circle cx="${number(middle.x)}" cy="${number(middle.y)}" r="${number(CELL_SIZE * 0.11)}"/>${negated ? `<text class="pair-false-marker" x="${number(middle.x)}" y="${number(middle.y)}">×</text>` : ""}</g>`;
+  }
+  if (constraint.type === "xv") {
+    return `<g class="constraint xv total-${String(constraint.total)}${polarity}" data-constraint="${index}"><circle cx="${number(middle.x)}" cy="${number(middle.y)}" r="${number(CELL_SIZE * 0.19)}"/><text x="${number(middle.x)}" y="${number(middle.y)}">${marker}${String(constraint.total)}</text></g>`;
+  }
+  const dx = a.x - b.x;
+  const dy = a.y - b.y;
+  const length = Math.hypot(dx, dy) || 1;
+  const ux = dx / length;
+  const uy = dy / length;
+  const perpendicular = { x: -uy, y: ux };
+  const tip = {
+    x: middle.x + ux * CELL_SIZE * 0.15,
+    y: middle.y + uy * CELL_SIZE * 0.15,
+  };
+  const back = {
+    x: middle.x - ux * CELL_SIZE * 0.15,
+    y: middle.y - uy * CELL_SIZE * 0.15,
+  };
+  return `<g class="constraint inequality${polarity}" data-constraint="${index}"><polyline points="${number(back.x + perpendicular.x * CELL_SIZE * 0.14)},${number(back.y + perpendicular.y * CELL_SIZE * 0.14)} ${number(tip.x)},${number(tip.y)} ${number(back.x - perpendicular.x * CELL_SIZE * 0.14)},${number(back.y - perpendicular.y * CELL_SIZE * 0.14)}"/><circle class="inequality-tip" cx="${number(tip.x)}" cy="${number(tip.y)}" r="${number(CELL_SIZE * 0.035)}"/></g>`;
+}
+
+function renderRegionBoundaries(puzzle: NormalizedPuzzle, origin: BoardOrigin) {
+  const { size, regions } = puzzle;
+  const lines: string[] = [];
+  const board = size * CELL_SIZE;
+  lines.push(
+    `<rect x="${origin.x}" y="${origin.y}" width="${board}" height="${board}"/>`,
+  );
+  for (let row = 0; row < size; row += 1) {
+    for (let column = 0; column < size; column += 1) {
+      const cell = row * size + column;
+      if (column < size - 1 && regions[cell] !== regions[cell + 1]) {
+        const x = origin.x + (column + 1) * CELL_SIZE;
+        const y = origin.y + row * CELL_SIZE;
+        lines.push(
+          `<line x1="${x}" y1="${y}" x2="${x}" y2="${y + CELL_SIZE}"/>`,
+        );
+      }
+      if (row < size - 1 && regions[cell] !== regions[cell + size]) {
+        const x = origin.x + column * CELL_SIZE;
+        const y = origin.y + (row + 1) * CELL_SIZE;
+        lines.push(
+          `<line x1="${x}" y1="${y}" x2="${x + CELL_SIZE}" y2="${y}"/>`,
+        );
+      }
+    }
+  }
+  return `<g class="region-boundaries">${lines.join("")}</g>`;
+}
+
+const COLOR_FILLS = [
+  "transparent",
+  "#fff2a8",
+  "#ffd0c7",
+  "#ccefd8",
+  "#cde6ff",
+  "#e3d4ff",
+  "#ffe0b7",
+  "#cdeeed",
+  "#f3d0e6",
+];
+
+/** Render a standalone, print-friendly SVG without external resources. */
+export function renderPuzzleSvg(
+  document: SudokuDocument,
+  options: VisualExportOptions = {},
+): string {
+  const normalizedDocument = normalizeSudokuDocument(document);
+  const puzzle = normalizePuzzle(toDomainPuzzle(normalizedDocument));
+  const includeProgress = options.includeProgress ?? true;
+  const includeNotes = options.includeNotes ?? includeProgress;
+  const hasOutside = puzzle.constraints.some(
+    ({ type }) => type === "x-sum" || type === "skyscraper",
+  );
+  const sideMargin = hasOutside ? OUTSIDE_MARGIN : BOARD_MARGIN;
+  const boardSize = puzzle.size * CELL_SIZE;
+  const width = boardSize + sideMargin * 2;
+  const height = HEADER_HEIGHT + boardSize + sideMargin * 2;
+  const origin: BoardOrigin = {
+    x: sideMargin,
+    y: sideMargin + HEADER_HEIGHT,
+  };
+  const title = (normalizedDocument.title ?? "Sudoku").slice(0, 256);
+  const byline = normalizedDocument.author
+    ? `by ${normalizedDocument.author.slice(0, 256)}`
+    : "Sudoku Tools";
+  const globals = globalRuleLabels(puzzle);
+  const values = includeProgress
+    ? (normalizedDocument.values ?? puzzle.givens)
+    : puzzle.givens;
+  const cornerMarks = includeNotes
+    ? (normalizedDocument.cornerMarks ?? [])
+    : [];
+  const centerMarks = includeNotes
+    ? (normalizedDocument.centerMarks ?? normalizedDocument.candidates ?? [])
+    : [];
+  const colors = includeProgress ? (normalizedDocument.colors ?? []) : [];
+  const cellCount = puzzle.size * puzzle.size;
+  if (
+    values.length !== cellCount ||
+    (normalizedDocument.colors !== undefined &&
+      normalizedDocument.colors.length !== cellCount)
+  ) {
+    throw new SudokuFormatError(
+      "INVALID_VISUAL_EXPORT",
+      "Puzzle progress does not match the grid size.",
+    );
+  }
+
+  const backgrounds = Array.from({ length: cellCount }, (_, cell) => {
+    const color = colors[cell] ?? 0;
+    const fill = COLOR_FILLS[color] ?? "transparent";
+    if (fill === "transparent") return "";
+    const row = Math.floor(cell / puzzle.size);
+    const column = cell % puzzle.size;
+    return `<rect class="cell-color" x="${origin.x + column * CELL_SIZE}" y="${origin.y + row * CELL_SIZE}" width="${CELL_SIZE}" height="${CELL_SIZE}" fill="${fill}"/>`;
+  }).join("");
+
+  const gridLines = Array.from({ length: puzzle.size - 1 }, (_, index) => {
+    const offset = (index + 1) * CELL_SIZE;
+    return `<path d="M${origin.x + offset} ${origin.y}V${origin.y + boardSize}M${origin.x} ${origin.y + offset}H${origin.x + boardSize}"/>`;
+  }).join("");
+  const constraints = puzzle.constraints
+    .map((constraint, index) =>
+      renderConstraint(constraint, index, puzzle, origin),
+    )
+    .join("");
+  const digits = Array.from({ length: cellCount }, (_, cell) => {
+    const value = puzzle.givens[cell] || values[cell] || 0;
+    const center = point(puzzle.size, cell, origin);
+    if (value !== 0) {
+      if (!Number.isInteger(value) || value < 1 || value > puzzle.size) {
+        throw new SudokuFormatError(
+          "INVALID_VISUAL_EXPORT",
+          `Cell ${String(cell + 1)} contains an out-of-range value.`,
+        );
+      }
+      return `<text class="cell-value ${puzzle.givens[cell] ? "given" : "progress"}" x="${number(center.x)}" y="${number(center.y)}">${escapeXml(symbolFor(value, puzzle.size))}</text>`;
+    }
+    const corner = cornerMarks[cell] ?? [];
+    const centerNotes = centerMarks[cell] ?? [];
+    const cornerText = corner
+      .slice(0, puzzle.size)
+      .map((digit, noteIndex) => {
+        const columns = Math.ceil(Math.sqrt(puzzle.size));
+        const x =
+          center.x -
+          CELL_SIZE * 0.39 +
+          ((noteIndex % columns) * (CELL_SIZE * 0.78)) /
+            Math.max(1, columns - 1);
+        const y =
+          center.y -
+          CELL_SIZE * 0.34 +
+          Math.floor(noteIndex / columns) * CELL_SIZE * 0.19;
+        return `<text class="corner-note" x="${number(x)}" y="${number(y)}">${escapeXml(symbolFor(digit, puzzle.size))}</text>`;
+      })
+      .join("");
+    const centerText = centerNotes.length
+      ? `<text class="center-note" x="${number(center.x)}" y="${number(center.y)}">${escapeXml(centerNotes.map((digit) => symbolFor(digit, puzzle.size)).join(""))}</text>`
+      : "";
+    return cornerText + centerText;
+  }).join("");
+
+  const svg = `<?xml version="1.0" encoding="UTF-8"?>
+<svg xmlns="http://www.w3.org/2000/svg" width="${width}" height="${height}" viewBox="0 0 ${width} ${height}" role="img" aria-labelledby="title description">
+  <title id="title">${escapeXml(title)}</title>
+  <desc id="description">${escapeXml(`${String(puzzle.size)} by ${String(puzzle.size)} Sudoku${includeProgress ? " with current progress" : ""}`)}</desc>
+  <style>
+    .background{fill:#fff}.heading{fill:#172033;font-family:system-ui,sans-serif}.title{font-size:28px;font-weight:750}.byline,.global-rules{fill:#5d6678;font-size:14px}.grid-lines{fill:none;stroke:#a5acb8;stroke-width:1}.region-boundaries{fill:none;stroke:#172033;stroke-width:3;stroke-linecap:square}.constraint{fill:none;stroke:#596273;stroke-width:6;stroke-linecap:round;stroke-linejoin:round}.constraint text{dominant-baseline:central;text-anchor:middle;fill:#172033;stroke:none;font-family:system-ui,sans-serif;font-weight:700}.constraint.negated{stroke:#c63f52;stroke-dasharray:10 7}.constraint.negated text{fill:#a5283b}.diagonal{stroke:#4da3d6;stroke-width:3}.cage{stroke-width:2.2;stroke-dasharray:6 5}.cage-label{font-size:14px;text-anchor:start!important}.thermo{stroke:#c3c7ce;stroke-width:20}.thermo circle{fill:#c3c7ce;stroke:none}.thermo.negated{stroke-width:13}.false-marker{font-size:22px}.arrow{stroke:#929aa7;stroke-width:5}.arrow rect{fill:#fff;stroke:#929aa7}.arrow-tip{fill:#929aa7;stroke:none}.renban{stroke:#b55b8c;stroke-width:14;opacity:.72}.palindrome{stroke:#9ba1ad;stroke-width:13}.palindrome circle{fill:#d8dbe1;stroke:none}.maximum circle{fill:#eef0f4;stroke:#596273;stroke-width:2}.maximum path{stroke-width:3}.quadruple circle{fill:#fff;stroke:#596273;stroke-width:2}.quadruple text{font-size:15px}.outside rect{fill:#fff;stroke:#788191;stroke-width:1.5}.outside text{font-size:17px}.outside .outside-kinds{font-size:12px}.outside .outside-value{font-size:16px}.kropki circle{stroke:#172033;stroke-width:2}.kropki.white circle{fill:#fff}.kropki.black circle{fill:#172033}.pair-false-marker{fill:#c63f52!important;font-size:14px}.xv circle{fill:#fff;stroke:#fff}.xv text{font-size:18px}.inequality{stroke:#172033;stroke-width:4}.inequality-tip{fill:#172033;stroke:none}.cell-value,.corner-note,.center-note{dominant-baseline:central;text-anchor:middle;font-family:system-ui,sans-serif}.cell-value{fill:#273c75;font-size:${number(CELL_SIZE * 0.58)}px}.cell-value.given{fill:#111827;font-weight:800}.cell-value.progress{font-weight:600}.corner-note{fill:#596273;font-size:${number(CELL_SIZE * 0.15)}px}.center-note{fill:#596273;font-size:${number(CELL_SIZE * 0.2)}px;letter-spacing:1px}
+  </style>
+  <rect class="background" width="100%" height="100%"/>
+  <g class="heading"><text class="title" x="${origin.x}" y="34">${escapeXml(title)}</text><text class="byline" x="${origin.x}" y="57">${escapeXml(byline)}</text>${globals.length > 0 ? `<text class="global-rules" x="${width - sideMargin}" y="57" text-anchor="end">${escapeXml(globals.join(" · "))}</text>` : ""}</g>
+  <g>${backgrounds}<g class="grid-lines">${gridLines}</g>${constraints}${renderRegionBoundaries(puzzle, origin)}${digits}</g>
+</svg>`;
+  if (new TextEncoder().encode(svg).byteLength > MAX_VISUAL_EXPORT_BYTES) {
+    throw new SudokuFormatError(
+      "LIMIT_EXCEEDED",
+      "The rendered SVG is too large to export safely.",
+    );
+  }
+  return svg;
+}
+
+function svgDimensions(svg: string): { width: number; height: number } {
+  const match = /<svg[^>]+width="(\d+)"[^>]+height="(\d+)"/u.exec(svg);
+  if (match === null) {
+    throw new SudokuFormatError(
+      "INVALID_VISUAL_EXPORT",
+      "The generated SVG has no dimensions.",
+    );
+  }
+  return { width: Number(match[1]), height: Number(match[2]) };
+}
+
+async function loadSvgImage(svg: string): Promise<CanvasImageSource> {
+  const blob = new Blob([svg], { type: "image/svg+xml;charset=utf-8" });
+  if (typeof createImageBitmap === "function") {
+    try {
+      return await createImageBitmap(blob);
+    } catch {
+      // Safari and some hardened browsers cannot decode SVG through ImageBitmap.
+    }
+  }
+  const url = URL.createObjectURL(blob);
+  try {
+    return await new Promise<HTMLImageElement>((resolve, reject) => {
+      const image = new Image();
+      image.onload = () => resolve(image);
+      image.onerror = () =>
+        reject(new Error("The SVG image could not be decoded."));
+      image.src = url;
+    });
+  } finally {
+    URL.revokeObjectURL(url);
+  }
+}
+
+async function rasterizeSvg(
+  svg: string,
+  scale: number,
+): Promise<HTMLCanvasElement> {
+  if (!Number.isFinite(scale) || scale < 0.5 || scale > 4) {
+    throw new RangeError("rasterScale must be from 0.5 to 4.");
+  }
+  const dimensions = svgDimensions(svg);
+  const boundedScale = Math.min(
+    scale,
+    MAX_VISUAL_EXPORT_DIMENSION / Math.max(dimensions.width, dimensions.height),
+  );
+  const canvas = document.createElement("canvas");
+  canvas.width = Math.max(1, Math.round(dimensions.width * boundedScale));
+  canvas.height = Math.max(1, Math.round(dimensions.height * boundedScale));
+  const context = canvas.getContext("2d");
+  if (context === null) {
+    throw new SudokuFormatError(
+      "UNSUPPORTED_BROWSER",
+      "This browser cannot create a canvas for visual export.",
+    );
+  }
+  context.fillStyle = "#ffffff";
+  context.fillRect(0, 0, canvas.width, canvas.height);
+  const image = await loadSvgImage(svg);
+  context.drawImage(image, 0, 0, canvas.width, canvas.height);
+  if ("close" in image && typeof image.close === "function") image.close();
+  return canvas;
+}
+
+function canvasBlob(
+  canvas: HTMLCanvasElement,
+  type: "image/png" | "image/jpeg",
+  quality?: number,
+): Promise<Blob> {
+  return new Promise((resolve, reject) => {
+    canvas.toBlob(
+      (blob) =>
+        blob === null
+          ? reject(new Error(`The browser could not encode ${type}.`))
+          : resolve(blob),
+      type,
+      quality,
+    );
+  });
+}
+
+export async function renderPuzzlePng(
+  document: SudokuDocument,
+  options: VisualExportOptions = {},
+): Promise<Blob> {
+  const canvas = await rasterizeSvg(
+    renderPuzzleSvg(document, options),
+    options.rasterScale ?? 2,
+  );
+  const blob = await canvasBlob(canvas, "image/png");
+  if (blob.size > MAX_VISUAL_EXPORT_BYTES) {
+    throw new SudokuFormatError(
+      "LIMIT_EXCEEDED",
+      "The rendered PNG is too large to export safely.",
+    );
+  }
+  return blob;
+}
+
+function ascii(value: string): Uint8Array {
+  return new TextEncoder().encode(value);
+}
+
+function concatenate(parts: readonly Uint8Array[]): Uint8Array {
+  const length = parts.reduce((sum, part) => sum + part.byteLength, 0);
+  const output = new Uint8Array(length);
+  let offset = 0;
+  for (const part of parts) {
+    output.set(part, offset);
+    offset += part.byteLength;
+  }
+  return output;
+}
+
+/** Build a single-page PDF around browser-generated JPEG bytes. */
+export function buildJpegPdf(
+  jpeg: Uint8Array,
+  imageWidth: number,
+  imageHeight: number,
+): Uint8Array {
+  if (
+    jpeg.byteLength < 4 ||
+    jpeg.byteLength > MAX_VISUAL_EXPORT_BYTES ||
+    jpeg[0] !== 0xff ||
+    jpeg[1] !== 0xd8 ||
+    jpeg.at(-2) !== 0xff ||
+    jpeg.at(-1) !== 0xd9
+  ) {
+    throw new SudokuFormatError(
+      "INVALID_VISUAL_EXPORT",
+      "The PDF renderer did not receive a bounded JPEG image.",
+    );
+  }
+  if (
+    !Number.isInteger(imageWidth) ||
+    !Number.isInteger(imageHeight) ||
+    imageWidth < 1 ||
+    imageHeight < 1 ||
+    imageWidth > MAX_VISUAL_EXPORT_DIMENSION ||
+    imageHeight > MAX_VISUAL_EXPORT_DIMENSION
+  ) {
+    throw new SudokuFormatError(
+      "INVALID_VISUAL_EXPORT",
+      "The PDF image dimensions are invalid.",
+    );
+  }
+  const pageWidth = 595;
+  const pageHeight = 842;
+  const maximumWidth = pageWidth - 64;
+  const maximumHeight = pageHeight - 64;
+  const scale = Math.min(
+    maximumWidth / imageWidth,
+    maximumHeight / imageHeight,
+  );
+  const drawWidth = imageWidth * scale;
+  const drawHeight = imageHeight * scale;
+  const x = (pageWidth - drawWidth) / 2;
+  const y = (pageHeight - drawHeight) / 2;
+  const content = `q\n${number(drawWidth)} 0 0 ${number(drawHeight)} ${number(x)} ${number(y)} cm\n/Im0 Do\nQ\n`;
+  const objects: Uint8Array[] = [
+    ascii("<< /Type /Catalog /Pages 2 0 R >>"),
+    ascii("<< /Type /Pages /Kids [3 0 R] /Count 1 >>"),
+    ascii(
+      `<< /Type /Page /Parent 2 0 R /MediaBox [0 0 ${pageWidth} ${pageHeight}] /Resources << /XObject << /Im0 4 0 R >> >> /Contents 5 0 R >>`,
+    ),
+    concatenate([
+      ascii(
+        `<< /Type /XObject /Subtype /Image /Width ${String(imageWidth)} /Height ${String(imageHeight)} /ColorSpace /DeviceRGB /BitsPerComponent 8 /Filter /DCTDecode /Length ${String(jpeg.byteLength)} >>\nstream\n`,
+      ),
+      jpeg,
+      ascii("\nendstream"),
+    ]),
+    ascii(
+      `<< /Length ${String(ascii(content).byteLength)} >>\nstream\n${content}endstream`,
+    ),
+  ];
+  const parts: Uint8Array[] = [
+    new Uint8Array([
+      ...ascii("%PDF-1.4\n%"),
+      0xe2,
+      0xe3,
+      0xcf,
+      0xd3,
+      ...ascii("\n"),
+    ]),
+  ];
+  const offsets = [0];
+  let byteOffset = parts[0]!.byteLength;
+  objects.forEach((object, index) => {
+    offsets.push(byteOffset);
+    const wrapped = concatenate([
+      ascii(`${String(index + 1)} 0 obj\n`),
+      object,
+      ascii("\nendobj\n"),
+    ]);
+    parts.push(wrapped);
+    byteOffset += wrapped.byteLength;
+  });
+  const xrefOffset = byteOffset;
+  const xref = [
+    `xref\n0 ${String(objects.length + 1)}\n`,
+    "0000000000 65535 f \n",
+    ...offsets
+      .slice(1)
+      .map((offset) => `${String(offset).padStart(10, "0")} 00000 n \n`),
+    `trailer\n<< /Size ${String(objects.length + 1)} /Root 1 0 R >>\nstartxref\n${String(xrefOffset)}\n%%EOF\n`,
+  ].join("");
+  parts.push(ascii(xref));
+  return concatenate(parts);
+}
+
+export async function renderPuzzlePdf(
+  document: SudokuDocument,
+  options: VisualExportOptions = {},
+): Promise<Blob> {
+  const canvas = await rasterizeSvg(
+    renderPuzzleSvg(document, options),
+    options.rasterScale ?? 2,
+  );
+  const jpeg = new Uint8Array(
+    await (await canvasBlob(canvas, "image/jpeg", 0.94)).arrayBuffer(),
+  );
+  const pdf = buildJpegPdf(jpeg, canvas.width, canvas.height);
+  const buffer = new ArrayBuffer(pdf.byteLength);
+  new Uint8Array(buffer).set(pdf);
+  return new Blob([buffer], { type: "application/pdf" });
+}

src/helpers/candidates.ts

@@ -0,0 +1,379 @@
+import {
+  compilePuzzle,
+  type CompiledPuzzle,
+  type NormalizedPuzzle,
+  type SudokuUnit,
+  type UnitKind,
+} from "../domain";
+
+export interface CandidateNode {
+  readonly cell: number;
+  readonly value: number;
+}
+
+export type CandidateLinkKind = "strong" | "weak";
+
+export interface CandidateLinkContext {
+  readonly kind: "cell" | "house";
+  readonly label: string;
+  readonly unitKind?: UnitKind;
+  readonly unitIndex?: number;
+}
+
+/**
+ * A graph edge between two candidates. Strong edges mean that at least one
+ * endpoint must be true; weak edges mean that both endpoints cannot be true.
+ * A strong Sudoku link is also weak, but is rendered once as the more useful
+ * strong relationship.
+ */
+export interface CandidateLink {
+  readonly id: string;
+  readonly kind: CandidateLinkKind;
+  readonly a: CandidateNode;
+  readonly b: CandidateNode;
+  readonly contexts: readonly CandidateLinkContext[];
+}
+
+export interface CandidatePosition {
+  readonly value: number;
+  readonly cells: readonly number[];
+  readonly linkKind: CandidateLinkKind | "none";
+}
+
+export interface HouseCandidateInspection {
+  readonly unitIndex: number;
+  readonly kind: UnitKind;
+  readonly index: number;
+  readonly label: string;
+  readonly cells: readonly number[];
+  readonly missingValues: readonly number[];
+  readonly positions: readonly CandidatePosition[];
+}
+
+export interface CellCandidateInspection {
+  readonly cell: number;
+  readonly values: readonly number[];
+  readonly houseLabels: readonly string[];
+}
+
+export interface CandidateOverlay {
+  readonly activeValues: readonly number[];
+  readonly candidateCells: readonly number[];
+  readonly links: readonly CandidateLink[];
+}
+
+export interface CandidateLinkOptions {
+  /** Only derive house links from these compiled unit indices. */
+  readonly unitIndices?: readonly number[];
+  /** Only retain links whose two endpoints use one of these values. */
+  readonly values?: readonly number[];
+  /** Cells from which same-cell links are derived. Defaults to every cell. */
+  readonly cellIndices?: readonly number[];
+  readonly includeCellLinks?: boolean;
+}
+
+function nodeKey(node: CandidateNode): string {
+  return `${String(node.cell)}:${String(node.value)}`;
+}
+
+function orderedNodes(
+  first: CandidateNode,
+  second: CandidateNode,
+): readonly [CandidateNode, CandidateNode] {
+  return nodeKey(first) < nodeKey(second) ? [first, second] : [second, first];
+}
+
+function linkKey(a: CandidateNode, b: CandidateNode): string {
+  const [first, second] = orderedNodes(a, b);
+  return `${nodeKey(first)}-${nodeKey(second)}`;
+}
+
+function addLink(
+  links: Map<
+    string,
+    {
+      kind: CandidateLinkKind;
+      a: CandidateNode;
+      b: CandidateNode;
+      contexts: CandidateLinkContext[];
+    }
+  >,
+  kind: CandidateLinkKind,
+  first: CandidateNode,
+  second: CandidateNode,
+  context: CandidateLinkContext,
+): void {
+  const [a, b] = orderedNodes(first, second);
+  const key = linkKey(a, b);
+  const existing = links.get(key);
+  if (existing === undefined) {
+    links.set(key, { kind, a, b, contexts: [context] });
+    return;
+  }
+  if (kind === "strong") existing.kind = "strong";
+  if (!existing.contexts.some(({ label }) => label === context.label)) {
+    existing.contexts.push(context);
+  }
+}
+
+function candidateValues(mask: number, size: number): number[] {
+  const result: number[] = [];
+  for (let value = 1; value <= size; value += 1) {
+    if ((mask & (1 << (value - 1))) !== 0) result.push(value);
+  }
+  return result;
+}
+
+export function candidateValuesFromMask(mask: number, size: number): number[] {
+  if (!Number.isInteger(size) || size < 1 || size > 30) return [];
+  return candidateValues(Number.isInteger(mask) ? mask : 0, size);
+}
+
+export function houseLabel(unit: Pick<SudokuUnit, "kind" | "index">): string {
+  switch (unit.kind) {
+    case "row":
+      return `Row ${String(unit.index + 1)}`;
+    case "column":
+      return `Column ${String(unit.index + 1)}`;
+    case "region":
+      return `Region ${String(unit.index + 1)}`;
+    case "diagonal":
+      return unit.index === 0 ? "Main diagonal" : "Anti-diagonal";
+  }
+}
+
+/** All houses touching at least one of the supplied cells, in compile order. */
+export function candidateUnitIndicesForCells(
+  puzzle: NormalizedPuzzle,
+  cells: readonly number[],
+): number[] {
+  const compiled = compilePuzzle(puzzle);
+  const indices = new Set<number>();
+  for (const cell of cells) {
+    for (const unitIndex of compiled.unitsByCell[cell] ?? []) {
+      indices.add(unitIndex);
+    }
+  }
+  return [...indices].sort((a, b) => a - b);
+}
+
+export function inspectCandidateCells(
+  puzzle: NormalizedPuzzle,
+  candidateMasks: readonly number[],
+  cells: readonly number[],
+): CellCandidateInspection[] {
+  const compiled = compilePuzzle(puzzle);
+  return [...new Set(cells)]
+    .filter(
+      (cell) => Number.isInteger(cell) && cell >= 0 && cell < puzzle.size ** 2,
+    )
+    .sort((a, b) => a - b)
+    .map((cell) => ({
+      cell,
+      values: candidateValues(candidateMasks[cell] ?? 0, puzzle.size),
+      houseLabels: (compiled.unitsByCell[cell] ?? []).map((unitIndex) =>
+        houseLabel(compiled.units[unitIndex]!),
+      ),
+    }));
+}
+
+export function inspectCandidateHouse(
+  puzzle: NormalizedPuzzle,
+  values: readonly number[],
+  candidateMasks: readonly number[],
+  unitIndex: number,
+): HouseCandidateInspection | undefined {
+  const compiled = compilePuzzle(puzzle);
+  return inspectCandidateHouseWithCompiled(
+    compiled,
+    values,
+    candidateMasks,
+    unitIndex,
+  );
+}
+
+function inspectCandidateHouseWithCompiled(
+  compiled: CompiledPuzzle,
+  values: readonly number[],
+  candidateMasks: readonly number[],
+  unitIndex: number,
+): HouseCandidateInspection | undefined {
+  const { puzzle } = compiled;
+  const unit = compiled.units[unitIndex];
+  if (unit === undefined) return undefined;
+  const placed = new Set(
+    unit.cells
+      .map((cell) => values[cell] ?? 0)
+      .filter((value) => value >= 1 && value <= puzzle.size),
+  );
+  const missingValues = Array.from(
+    { length: puzzle.size },
+    (_, index) => index + 1,
+  ).filter((value) => !placed.has(value));
+  const positions = missingValues.map((value) => {
+    const cells = unit.cells.filter(
+      (cell) =>
+        (values[cell] ?? 0) === 0 &&
+        ((candidateMasks[cell] ?? 0) & (1 << (value - 1))) !== 0,
+    );
+    return {
+      value,
+      cells,
+      linkKind:
+        cells.length === 2
+          ? ("strong" as const)
+          : cells.length > 2
+            ? ("weak" as const)
+            : ("none" as const),
+    };
+  });
+  return {
+    unitIndex,
+    kind: unit.kind,
+    index: unit.index,
+    label: houseLabel(unit),
+    cells: unit.cells,
+    missingValues,
+    positions,
+  };
+}
+
+export function inspectCandidateHouses(
+  puzzle: NormalizedPuzzle,
+  values: readonly number[],
+  candidateMasks: readonly number[],
+  unitIndices?: readonly number[],
+): HouseCandidateInspection[] {
+  const compiled = compilePuzzle(puzzle);
+  const indices = unitIndices ?? compiled.units.map((_, index) => index);
+  return [...new Set(indices)]
+    .map((unitIndex) =>
+      inspectCandidateHouseWithCompiled(
+        compiled,
+        values,
+        candidateMasks,
+        unitIndex,
+      ),
+    )
+    .filter((inspection): inspection is HouseCandidateInspection =>
+      Boolean(inspection),
+    );
+}
+
+/**
+ * Derive the standard candidate-link graph from houses and cells.
+ *
+ * - two positions for a digit in a house form a strong link;
+ * - three or more positions form pairwise weak links;
+ * - two candidates in one cell form a strong link;
+ * - three or more candidates in one cell form pairwise weak links.
+ */
+export function deriveCandidateLinks(
+  puzzle: NormalizedPuzzle,
+  candidateMasks: readonly number[],
+  options: CandidateLinkOptions = {},
+): CandidateLink[] {
+  const compiled = compilePuzzle(puzzle);
+  const activeValues =
+    options.values === undefined
+      ? undefined
+      : new Set(
+          options.values.filter(
+            (value) =>
+              Number.isInteger(value) && value >= 1 && value <= puzzle.size,
+          ),
+        );
+  const links = new Map<
+    string,
+    {
+      kind: CandidateLinkKind;
+      a: CandidateNode;
+      b: CandidateNode;
+      contexts: CandidateLinkContext[];
+    }
+  >();
+  const unitIndices =
+    options.unitIndices ?? compiled.units.map((_, index) => index);
+
+  for (const unitIndex of new Set(unitIndices)) {
+    const unit = compiled.units[unitIndex];
+    if (unit === undefined) continue;
+    for (let value = 1; value <= puzzle.size; value += 1) {
+      if (activeValues !== undefined && !activeValues.has(value)) continue;
+      const nodes = unit.cells
+        .filter(
+          (cell) => ((candidateMasks[cell] ?? 0) & (1 << (value - 1))) !== 0,
+        )
+        .map((cell) => ({ cell, value }));
+      if (nodes.length < 2) continue;
+      const kind: CandidateLinkKind = nodes.length === 2 ? "strong" : "weak";
+      for (let a = 0; a < nodes.length; a += 1) {
+        for (let b = a + 1; b < nodes.length; b += 1) {
+          addLink(links, kind, nodes[a]!, nodes[b]!, {
+            kind: "house",
+            label: houseLabel(unit),
+            unitKind: unit.kind,
+            unitIndex,
+          });
+        }
+      }
+    }
+  }
+
+  if (options.includeCellLinks !== false) {
+    const cellIndices =
+      options.cellIndices ??
+      Array.from({ length: puzzle.size ** 2 }, (_, cell) => cell);
+    for (const cell of new Set(cellIndices)) {
+      if (!Number.isInteger(cell) || cell < 0 || cell >= puzzle.size ** 2)
+        continue;
+      const allValues = candidateValues(candidateMasks[cell] ?? 0, puzzle.size);
+      if (allValues.length < 2) continue;
+      const kind: CandidateLinkKind =
+        allValues.length === 2 ? "strong" : "weak";
+      const visibleValues =
+        activeValues === undefined
+          ? allValues
+          : allValues.filter((value) => activeValues.has(value));
+      for (let a = 0; a < visibleValues.length; a += 1) {
+        for (let b = a + 1; b < visibleValues.length; b += 1) {
+          addLink(
+            links,
+            kind,
+            { cell, value: visibleValues[a]! },
+            { cell, value: visibleValues[b]! },
+            { kind: "cell", label: `Cell ${cellLabel(cell, puzzle.size)}` },
+          );
+        }
+      }
+    }
+  }
+
+  return [...links.entries()]
+    .map(([id, link]) => ({ id, ...link }))
+    .sort((a, b) => {
+      if (a.kind !== b.kind) return a.kind === "strong" ? -1 : 1;
+      return a.id.localeCompare(b.id, undefined, { numeric: true });
+    });
+}
+
+export function candidateCellsForValues(
+  candidateMasks: readonly number[],
+  values: readonly number[],
+): number[] {
+  const combinedMask = values.reduce(
+    (mask, value) =>
+      Number.isInteger(value) && value >= 1 && value <= 30
+        ? mask | (1 << (value - 1))
+        : mask,
+    0,
+  );
+  if (combinedMask === 0) return [];
+  return candidateMasks.flatMap((mask, cell) =>
+    (mask & combinedMask) !== 0 ? [cell] : [],
+  );
+}
+
+export function cellLabel(cell: number, size: number): string {
+  return `r${String(Math.floor(cell / size) + 1)}c${String((cell % size) + 1)}`;
+}

src/helpers/index.ts

@@ -1,3 +1,5 @@
+export * from "./candidates";
 export * from "./killer";
 export * from "./relations";
 export * from "./residual";
+export * from "./sumLab";

src/helpers/sumLab.ts

@@ -0,0 +1,373 @@
+export const MAX_SUM_LAB_DIGIT = 25;
+export const MAX_SUM_LAB_COMBINATIONS = 10_000;
+export const MAX_SUM_LAB_ASSIGNMENTS = 50_000;
+export const MAX_SUM_LAB_SEARCH_NODES = 500_000;
+
+export interface SumLabOptions {
+  /** Number of cells whose values add up to the target. */
+  readonly cellCount: number;
+  readonly target: number;
+  readonly minimumDigit?: number;
+  readonly maximumDigit?: number;
+  readonly allowRepeats?: boolean;
+  /** Every listed digit must occur at least once. */
+  readonly requiredDigits?: readonly number[];
+  readonly excludedDigits?: readonly number[];
+  /** One bit mask per cell, with digit 1 represented by the least-significant bit. */
+  readonly candidateMasks?: readonly number[];
+  /** Canonical keys returned by `sumCombinationKey`. */
+  readonly eliminatedKeys?: ReadonlySet<string> | readonly string[];
+  readonly maxCombinations?: number;
+  readonly maxAssignments?: number;
+  readonly maxSearchNodes?: number;
+}
+
+export interface SumLabCombination {
+  readonly key: string;
+  /** Sorted digits. Repeated values are retained. */
+  readonly digits: readonly number[];
+  readonly eliminated: boolean;
+  /** Number of candidate-compatible cell orderings retained by this analysis. */
+  readonly assignmentCount: number;
+}
+
+export interface SumLabAnalysis {
+  /** All candidate-compatible combinations, including manually eliminated ones. */
+  readonly combinations: readonly SumLabCombination[];
+  readonly activeCombinations: readonly SumLabCombination[];
+  readonly eliminatedCombinations: readonly SumLabCombination[];
+  /** Candidate-compatible cell-ordered assignments for active combinations. */
+  readonly assignments: readonly (readonly number[])[];
+  readonly possibleDigits: readonly number[];
+  /** Digits present in every active combination. */
+  readonly necessaryDigits: readonly number[];
+  readonly possibleByCell: readonly (readonly number[])[];
+  readonly exploredNodes: number;
+  readonly truncated: boolean;
+  readonly truncationReason?: "combinations" | "assignments" | "search";
+}
+
+function boundedInteger(
+  value: number,
+  label: string,
+  minimum: number,
+  maximum: number,
+): number {
+  if (!Number.isInteger(value) || value < minimum || value > maximum) {
+    throw new RangeError(
+      `${label} must be an integer from ${minimum} to ${maximum}.`,
+    );
+  }
+  return value;
+}
+
+function uniqueSortedDigits(
+  values: readonly number[],
+  label: string,
+  minimumDigit: number,
+  maximumDigit: number,
+): number[] {
+  const result = [...new Set(values)];
+  for (const value of result) {
+    if (
+      !Number.isInteger(value) ||
+      value < minimumDigit ||
+      value > maximumDigit
+    ) {
+      throw new RangeError(
+        `${label} must only contain integers from ${minimumDigit} to ${maximumDigit}.`,
+      );
+    }
+  }
+  return result.sort((left, right) => left - right);
+}
+
+function intersect(
+  left: ReadonlySet<number>,
+  right: ReadonlySet<number>,
+): Set<number> {
+  return new Set([...left].filter((value) => right.has(value)));
+}
+
+function emptyAnalysis(cellCount: number): SumLabAnalysis {
+  return {
+    combinations: [],
+    activeCombinations: [],
+    eliminatedCombinations: [],
+    assignments: [],
+    possibleDigits: [],
+    necessaryDigits: [],
+    possibleByCell: Array.from({ length: cellCount }, () => []),
+    exploredNodes: 0,
+    truncated: false,
+  };
+}
+
+/**
+ * Stable identifier for a sorted sum combination. It is intentionally human
+ * readable so callers can safely retain eliminations while rendering results.
+ */
+export function sumCombinationKey(digits: readonly number[]): string {
+  return digits.join(",");
+}
+
+function digitIsInMask(mask: number, digit: number): boolean {
+  return (mask & (2 ** (digit - 1))) !== 0;
+}
+
+/**
+ * Enumerate generalized Sudoku sums without permutations. Results are ordered
+ * lexicographically and bounded by independent combination, assignment and
+ * search-node limits. Candidate masks are only used when a positional cell
+ * selection was supplied.
+ */
+export function analyzeSumLab(options: SumLabOptions): SumLabAnalysis {
+  const minimumDigit = boundedInteger(
+    options.minimumDigit ?? 1,
+    "minimumDigit",
+    1,
+    MAX_SUM_LAB_DIGIT,
+  );
+  const maximumDigit = boundedInteger(
+    options.maximumDigit ?? 9,
+    "maximumDigit",
+    minimumDigit,
+    MAX_SUM_LAB_DIGIT,
+  );
+  const cellCount = boundedInteger(options.cellCount, "cellCount", 1, 25);
+  const target = boundedInteger(
+    options.target,
+    "target",
+    0,
+    maximumDigit * cellCount,
+  );
+  const maxCombinations = boundedInteger(
+    options.maxCombinations ?? 5_000,
+    "maxCombinations",
+    1,
+    MAX_SUM_LAB_COMBINATIONS,
+  );
+  const maxAssignments = boundedInteger(
+    options.maxAssignments ?? 20_000,
+    "maxAssignments",
+    1,
+    MAX_SUM_LAB_ASSIGNMENTS,
+  );
+  const maxSearchNodes = boundedInteger(
+    options.maxSearchNodes ?? 200_000,
+    "maxSearchNodes",
+    1,
+    MAX_SUM_LAB_SEARCH_NODES,
+  );
+  const required = uniqueSortedDigits(
+    options.requiredDigits ?? [],
+    "requiredDigits",
+    minimumDigit,
+    maximumDigit,
+  );
+  const excluded = new Set(
+    uniqueSortedDigits(
+      options.excludedDigits ?? [],
+      "excludedDigits",
+      minimumDigit,
+      maximumDigit,
+    ),
+  );
+  const digits = Array.from(
+    { length: maximumDigit - minimumDigit + 1 },
+    (_, index) => minimumDigit + index,
+  ).filter((digit) => !excluded.has(digit));
+  const allowRepeats = options.allowRepeats ?? false;
+  const eliminatedKeys = new Set(options.eliminatedKeys ?? []);
+
+  if (
+    digits.length === 0 ||
+    required.some((digit) => excluded.has(digit)) ||
+    required.length > cellCount ||
+    (!allowRepeats && cellCount > digits.length)
+  ) {
+    return emptyAnalysis(cellCount);
+  }
+
+  let candidateMasks: readonly number[] | undefined;
+  if (options.candidateMasks !== undefined) {
+    if (options.candidateMasks.length !== cellCount) {
+      throw new RangeError(
+        `candidateMasks must contain exactly ${cellCount} cell entries.`,
+      );
+    }
+    for (const mask of options.candidateMasks) {
+      if (!Number.isSafeInteger(mask) || mask < 0) {
+        throw new RangeError("candidate masks must be non-negative integers.");
+      }
+    }
+    candidateMasks = options.candidateMasks;
+  }
+
+  const rawCombinations: {
+    digits: number[];
+    assignments: number[][];
+  }[] = [];
+  let exploredNodes = 0;
+  let retainedAssignments = 0;
+  let truncationReason: SumLabAnalysis["truncationReason"];
+
+  const assignmentsFor = (combination: readonly number[]): number[][] => {
+    if (candidateMasks === undefined) return [[...combination]];
+    const result: number[][] = [];
+    const remaining = new Map<number, number>();
+    for (const digit of combination) {
+      remaining.set(digit, (remaining.get(digit) ?? 0) + 1);
+    }
+    const assignment = Array<number>(cellCount).fill(0);
+
+    const visit = (position: number): void => {
+      if (truncationReason !== undefined) return;
+      exploredNodes += 1;
+      if (exploredNodes > maxSearchNodes) {
+        truncationReason = "search";
+        return;
+      }
+      if (position === cellCount) {
+        if (retainedAssignments + result.length >= maxAssignments) {
+          truncationReason = "assignments";
+          return;
+        }
+        result.push([...assignment]);
+        return;
+      }
+      const mask = candidateMasks[position] ?? 0;
+      for (const digit of [...remaining.keys()].sort(
+        (left, right) => left - right,
+      )) {
+        const count = remaining.get(digit) ?? 0;
+        if (count === 0 || !digitIsInMask(mask, digit)) continue;
+        assignment[position] = digit;
+        remaining.set(digit, count - 1);
+        visit(position + 1);
+        remaining.set(digit, count);
+        if (truncationReason !== undefined) return;
+      }
+    };
+    visit(0);
+    return result;
+  };
+
+  const current: number[] = [];
+  const enumerate = (
+    startIndex: number,
+    remainingCells: number,
+    remainingSum: number,
+  ): void => {
+    if (truncationReason !== undefined) return;
+    exploredNodes += 1;
+    if (exploredNodes > maxSearchNodes) {
+      truncationReason = "search";
+      return;
+    }
+    if (remainingCells === 0) {
+      if (
+        remainingSum !== 0 ||
+        !required.every((digit) => current.includes(digit))
+      ) {
+        return;
+      }
+      const assignments = assignmentsFor(current);
+      if (assignments.length === 0) return;
+      if (rawCombinations.length >= maxCombinations) {
+        truncationReason = "combinations";
+        return;
+      }
+      rawCombinations.push({ digits: [...current], assignments });
+      retainedAssignments += assignments.length;
+      return;
+    }
+    if (startIndex >= digits.length) return;
+
+    if (allowRepeats) {
+      const minimum = (digits[startIndex] ?? 0) * remainingCells;
+      const maximum = (digits.at(-1) ?? 0) * remainingCells;
+      if (remainingSum < minimum || remainingSum > maximum) return;
+    } else {
+      if (digits.length - startIndex < remainingCells) return;
+      let minimum = 0;
+      let maximum = 0;
+      for (let offset = 0; offset < remainingCells; offset += 1) {
+        minimum += digits[startIndex + offset] ?? 0;
+        maximum += digits[digits.length - 1 - offset] ?? 0;
+      }
+      if (remainingSum < minimum || remainingSum > maximum) return;
+    }
+
+    for (let index = startIndex; index < digits.length; index += 1) {
+      const digit = digits[index];
+      if (digit === undefined || digit > remainingSum) break;
+      current.push(digit);
+      enumerate(
+        allowRepeats ? index : index + 1,
+        remainingCells - 1,
+        remainingSum - digit,
+      );
+      current.pop();
+      if (truncationReason !== undefined) return;
+    }
+  };
+  enumerate(0, cellCount, target);
+
+  const combinations: SumLabCombination[] = [];
+  const activeCombinations: SumLabCombination[] = [];
+  const eliminatedCombinations: SumLabCombination[] = [];
+  const assignments: number[][] = [];
+  const possibleByCell = Array.from(
+    { length: cellCount },
+    () => new Set<number>(),
+  );
+  const possibleDigits = new Set<number>();
+  let necessaryDigits: Set<number> | undefined;
+
+  for (const raw of rawCombinations) {
+    const key = sumCombinationKey(raw.digits);
+    const eliminated = eliminatedKeys.has(key);
+    const combination: SumLabCombination = {
+      key,
+      digits: raw.digits,
+      eliminated,
+      assignmentCount: raw.assignments.length,
+    };
+    combinations.push(combination);
+    if (eliminated) {
+      eliminatedCombinations.push(combination);
+      continue;
+    }
+    activeCombinations.push(combination);
+    const digitSet = new Set(raw.digits);
+    necessaryDigits =
+      necessaryDigits === undefined
+        ? digitSet
+        : intersect(necessaryDigits, digitSet);
+    for (const digit of raw.digits) possibleDigits.add(digit);
+    for (const assignment of raw.assignments) {
+      assignments.push(assignment);
+      for (const [position, digit] of assignment.entries()) {
+        possibleByCell[position]?.add(digit);
+      }
+    }
+  }
+
+  return {
+    combinations,
+    activeCombinations,
+    eliminatedCombinations,
+    assignments,
+    possibleDigits: [...possibleDigits].sort((left, right) => left - right),
+    necessaryDigits: [...(necessaryDigits ?? [])].sort(
+      (left, right) => left - right,
+    ),
+    possibleByCell: possibleByCell.map((entry) =>
+      [...entry].sort((left, right) => left - right),
+    ),
+    exploredNodes,
+    truncated: truncationReason !== undefined,
+    ...(truncationReason === undefined ? {} : { truncationReason }),
+  };
+}

src/solver/exact.ts

@@ -111,6 +111,13 @@ export function solveExact(
     "timeoutMs",
   );
   const compiled = compilePuzzle(normalized);
+  const preferredSolution =
+    normalized.solution !== undefined &&
+    board.every(
+      (value, cell) => value === 0 || value === normalized.solution?.[cell],
+    )
+      ? normalized.solution
+      : undefined;
   const random: RandomSource | undefined =
     options.seed === undefined ? undefined : seededRandom(options.seed);
   const solutions: number[][] = [];
@@ -157,6 +164,15 @@ export function solveExact(
     const chosen = selection[0];
     let choices = selection[1];
     if (random !== undefined) choices = shuffled(choices, random);
+    else {
+      const preferred = preferredSolution?.[chosen];
+      if (preferred !== undefined && choices.includes(preferred)) {
+        choices = [
+          preferred,
+          ...choices.filter((value) => value !== preferred),
+        ];
+      }
+    }
     for (const value of choices) {
       board[chosen] = value;
       search();

src/solver/logical.ts

@@ -553,7 +553,8 @@ function findXyzWing(state: LogicalState): LogicalStep | undefined {
 function findKillerReduction(state: LogicalState): LogicalStep | undefined {
   const size = state.compiled.puzzle.size;
   for (const constraint of state.compiled.puzzle.constraints) {
-    if (constraint.type !== "killer-cage") continue;
+    if (constraint.type !== "killer-cage" || constraint.negated === true)
+      continue;
     const empty = constraint.cells.filter((cell) => state.values[cell] === 0);
     if (empty.length === 0) continue;
     const assigned = constraint.cells

src/solver/variantGenerator.ts

@@ -12,6 +12,7 @@ import {
   type DifficultyOptions,
 } from "./difficulty";
 import { solveExact } from "./exact";
+import type { LogicalTechnique } from "./logical";
 import {
   generateClassic,
   minimizePuzzle,
@@ -104,6 +105,27 @@ export type GeneratorVariant = (typeof GENERATOR_VARIANTS)[number]["id"];
 export type GenerationDifficultyTarget =
   "beginner" | "easy" | "medium" | "hard" | "expert";
 
+/** Human-style techniques which can be requested as generation evidence. */
+export const PRACTICE_TECHNIQUES = [
+  "naked-single",
+  "hidden-single",
+  "naked-pair",
+  "hidden-pair",
+  "pointing",
+  "claiming",
+  "naked-triple",
+  "hidden-triple",
+  "naked-quad",
+  "hidden-quad",
+  "x-wing",
+  "xy-wing",
+  "xyz-wing",
+  "swordfish",
+  "killer-cage",
+] as const satisfies readonly LogicalTechnique[];
+
+export type PracticeTechnique = (typeof PRACTICE_TECHNIQUES)[number];
+
 export interface GenerateVariantOptions {
   readonly variant?: GeneratorVariant;
   readonly size?: number;
@@ -120,6 +142,10 @@ export interface GenerateVariantOptions {
   readonly solveMaxNodes?: number;
   readonly solveTimeoutMs?: number;
   readonly difficulty?: DifficultyOptions;
+  /** Require the independently rated logical path to use this technique. */
+  readonly requiredTechnique?: PracticeTechnique;
+  /** Bounded deterministic attempts used to find the requested technique. */
+  readonly maxTechniqueAttempts?: number;
 }
 
 export interface GeneratedVariantPuzzle {
@@ -128,6 +154,8 @@ export interface GeneratedVariantPuzzle {
   readonly variant: GeneratorVariant;
   readonly seed: string | number;
   readonly generatedConstraintCount: number;
+  readonly generationAttempts: number;
+  readonly requestedTechnique?: PracticeTechnique;
 }
 
 const DEFAULT_CONSTRAINT_COUNTS: Readonly<
@@ -557,7 +585,7 @@ function fullSolution(
  * Worker: every exact search has explicit node/time caps and worker termination
  * can cancel the complete operation.
  */
-export function generateVariant(
+function generateVariantAttempt(
   options: GenerateVariantOptions = {},
 ): GeneratedVariantPuzzle {
   const variant = options.variant ?? "classic";
@@ -676,5 +704,61 @@ export function generateVariant(
     variant,
     seed,
     generatedConstraintCount: constraints.length,
+    generationAttempts: 1,
   };
 }
+
+/**
+ * Generates one uniquely checked puzzle, or deterministically mines several
+ * candidates until the requested human technique appears in the logical path.
+ */
+export function generateVariant(
+  options: GenerateVariantOptions = {},
+): GeneratedVariantPuzzle {
+  const requiredTechnique = options.requiredTechnique;
+  if (
+    requiredTechnique !== undefined &&
+    !(PRACTICE_TECHNIQUES as readonly string[]).includes(requiredTechnique)
+  ) {
+    throw new RangeError(
+      `Unsupported practice technique: ${String(requiredTechnique)}.`,
+    );
+  }
+  if (requiredTechnique === "killer-cage" && options.variant !== "killer") {
+    throw new RangeError(
+      "Killer-cage practice requires the Killer generator variant.",
+    );
+  }
+
+  const maxAttempts = boundedInteger(
+    options.maxTechniqueAttempts,
+    requiredTechnique === undefined ? 1 : 10,
+    1,
+    32,
+    "maxTechniqueAttempts",
+  );
+  const baseSeed = options.seed ?? "sudoku-tools";
+  for (let attempt = 0; attempt < maxAttempts; attempt += 1) {
+    const seed =
+      attempt === 0
+        ? baseSeed
+        : `${String(baseSeed)}:practice:${String(requiredTechnique)}:${String(attempt + 1)}`;
+    const generated = generateVariantAttempt({ ...options, seed });
+    if (
+      requiredTechnique === undefined ||
+      (generated.difficulty.techniqueCounts[requiredTechnique] ?? 0) > 0
+    ) {
+      return {
+        ...generated,
+        generationAttempts: attempt + 1,
+        ...(requiredTechnique === undefined
+          ? {}
+          : { requestedTechnique: requiredTechnique }),
+      };
+    }
+  }
+
+  throw new Error(
+    `No uniquely checked puzzle using ${requiredTechnique?.replaceAll("-", " ")} was found in ${String(maxAttempts)} deterministic attempts. Try a different seed, difficulty profile, or a larger attempt limit.`,
+  );
+}

src/state/aidMemoire.ts

@@ -0,0 +1,404 @@
+import { maskValues, symbolFor, type EntryMode } from "./session";
+
+export const AID_MEMOIRE_VERSION = 1 as const;
+export const MAX_AID_MEMOIRE_CELLS = 36;
+export const MAX_AID_MEMOIRE_COLUMNS = 36;
+export const MAX_AID_MEMOIRE_LABEL_LENGTH = 40;
+
+export interface AidMemoireCell {
+  readonly label: string;
+  readonly value: number;
+  readonly cornerMarks: number;
+  readonly centerMarks: number;
+  readonly color: number;
+}
+
+export interface AidMemoireState {
+  readonly version: typeof AID_MEMOIRE_VERSION;
+  readonly enabled: boolean;
+  readonly columns: number;
+  readonly cells: readonly AidMemoireCell[];
+}
+
+export interface PortableAidMemoireCell {
+  readonly label: string;
+  readonly value: number;
+  readonly cornerMarks: readonly number[];
+  readonly centerMarks: readonly number[];
+  readonly color: number;
+}
+
+export interface PortableAidMemoire {
+  readonly version: typeof AID_MEMOIRE_VERSION;
+  readonly enabled: boolean;
+  readonly columns: number;
+  readonly cells: readonly PortableAidMemoireCell[];
+}
+
+function integer(
+  value: unknown,
+  label: string,
+  minimum: number,
+  maximum: number,
+): number {
+  if (
+    !Number.isInteger(value) ||
+    (value as number) < minimum ||
+    (value as number) > maximum
+  ) {
+    throw new TypeError(
+      `${label} must be an integer from ${String(minimum)} to ${String(maximum)}.`,
+    );
+  }
+  return value as number;
+}
+
+function defaultLabel(index: number): string {
+  return String(index + 1);
+}
+
+function emptyCell(index: number): AidMemoireCell {
+  return {
+    label: defaultLabel(index),
+    value: 0,
+    cornerMarks: 0,
+    centerMarks: 0,
+    color: 0,
+  };
+}
+
+function cloneCell(cell: AidMemoireCell): AidMemoireCell {
+  return { ...cell };
+}
+
+function normalizedCount(size: number, count?: number): number {
+  const requested = Number.isFinite(count)
+    ? Math.trunc(count as number)
+    : Math.min(size, 16);
+  return Math.max(1, Math.min(MAX_AID_MEMOIRE_CELLS, requested));
+}
+
+export function createAidMemoire(
+  size: number,
+  options: {
+    readonly enabled?: boolean;
+    readonly cellCount?: number;
+    readonly columns?: number;
+  } = {},
+): AidMemoireState {
+  const count = normalizedCount(size, options.cellCount);
+  const columns = Math.max(
+    1,
+    Math.min(MAX_AID_MEMOIRE_COLUMNS, count, options.columns ?? count),
+  );
+  return {
+    version: AID_MEMOIRE_VERSION,
+    enabled: options.enabled ?? false,
+    columns,
+    cells: Array.from({ length: count }, (_, index) => emptyCell(index)),
+  };
+}
+
+export function cloneAidMemoire(state: AidMemoireState): AidMemoireState {
+  return { ...state, cells: state.cells.map(cloneCell) };
+}
+
+export function setAidMemoireEnabled(
+  state: AidMemoireState,
+  enabled: boolean,
+): AidMemoireState {
+  return { ...state, enabled };
+}
+
+export function configureAidMemoire(
+  state: AidMemoireState,
+  size: number,
+  cellCount: number,
+  columns: number,
+): AidMemoireState {
+  const count = normalizedCount(size, cellCount);
+  const nextColumns = Math.max(
+    1,
+    Math.min(MAX_AID_MEMOIRE_COLUMNS, count, Math.trunc(columns) || 1),
+  );
+  return {
+    ...state,
+    columns: nextColumns,
+    cells: Array.from({ length: count }, (_, index) =>
+      state.cells[index] ? cloneCell(state.cells[index]) : emptyCell(index),
+    ),
+  };
+}
+
+export function compactAidMemoireColumns(cellCount: number): number {
+  const count = Number.isFinite(cellCount)
+    ? Math.max(1, Math.min(MAX_AID_MEMOIRE_CELLS, Math.trunc(cellCount)))
+    : 1;
+  return Math.ceil(Math.sqrt(count));
+}
+
+export function labelAidMemoireCell(
+  state: AidMemoireState,
+  cell: number,
+  label: string,
+): AidMemoireState {
+  if (cell < 0 || cell >= state.cells.length) return state;
+  const cells = state.cells.map(cloneCell);
+  cells[cell] = {
+    ...cells[cell]!,
+    label: label.slice(0, MAX_AID_MEMOIRE_LABEL_LENGTH),
+  };
+  return { ...state, cells };
+}
+
+function toggleMask(mask: number, value: number): number {
+  const bit = 1 << (value - 1);
+  return mask & bit ? mask & ~bit : mask | bit;
+}
+
+export function enterAidMemoireCell(
+  state: AidMemoireState,
+  cell: number,
+  mode: EntryMode,
+  value: number,
+  size: number,
+): AidMemoireState {
+  if (cell < 0 || cell >= state.cells.length) return state;
+  if (!Number.isInteger(value)) return state;
+  if (mode !== "color" && (value < 1 || value > size)) return state;
+  if (mode === "color" && (value < 1 || value > 8)) return state;
+  const cells = state.cells.map(cloneCell);
+  const current = cells[cell]!;
+  if (mode === "value") {
+    cells[cell] = {
+      ...current,
+      value: current.value === value ? 0 : value,
+      cornerMarks: 0,
+      centerMarks: 0,
+    };
+  } else if (mode === "corner") {
+    if (current.value !== 0) return state;
+    cells[cell] = {
+      ...current,
+      cornerMarks: toggleMask(current.cornerMarks, value),
+    };
+  } else if (mode === "center") {
+    if (current.value !== 0) return state;
+    cells[cell] = {
+      ...current,
+      centerMarks: toggleMask(current.centerMarks, value),
+    };
+  } else {
+    cells[cell] = {
+      ...current,
+      color: current.color === value ? 0 : value,
+    };
+  }
+  return { ...state, cells };
+}
+
+export function eraseAidMemoireCell(
+  state: AidMemoireState,
+  cell: number,
+  mode: EntryMode,
+): AidMemoireState {
+  if (cell < 0 || cell >= state.cells.length) return state;
+  const cells = state.cells.map(cloneCell);
+  const current = cells[cell]!;
+  cells[cell] = {
+    ...current,
+    ...(mode === "value" ? { value: 0 } : {}),
+    ...(mode === "corner" ? { cornerMarks: 0 } : {}),
+    ...(mode === "center" ? { centerMarks: 0 } : {}),
+    ...(mode === "color" ? { color: 0 } : {}),
+  };
+  return { ...state, cells };
+}
+
+export function clearAidMemoireEntries(
+  state: AidMemoireState,
+): AidMemoireState {
+  return {
+    ...state,
+    cells: state.cells.map((cell) => ({
+      ...cell,
+      value: 0,
+      cornerMarks: 0,
+      centerMarks: 0,
+      color: 0,
+    })),
+  };
+}
+
+export function resetAidMemoire(
+  state: AidMemoireState,
+  size: number,
+): AidMemoireState {
+  return createAidMemoire(size, { enabled: state.enabled });
+}
+
+export function aidMemoireCellDescription(
+  cell: AidMemoireCell,
+  index: number,
+  size: number,
+): string {
+  const parts = [
+    `Aid-mémoire cell ${String(index + 1)}`,
+    cell.label ? `label ${cell.label}` : "unlabelled",
+  ];
+  if (cell.value) parts.push(`value ${symbolFor(cell.value, size)}`);
+  else parts.push("empty");
+  const corner = maskValues(cell.cornerMarks, size);
+  const center = maskValues(cell.centerMarks, size);
+  if (corner.length) {
+    parts.push(
+      `corner marks ${corner.map((value) => symbolFor(value, size)).join(", ")}`,
+    );
+  }
+  if (center.length) {
+    parts.push(
+      `centre marks ${center.map((value) => symbolFor(value, size)).join(", ")}`,
+    );
+  }
+  if (cell.color) parts.push(`colour ${String(cell.color)}`);
+  return parts.join(", ");
+}
+
+function portableMarks(value: unknown, label: string, size: number): number[] {
+  if (value === undefined) return [];
+  if (!Array.isArray(value) || value.length > size) {
+    throw new TypeError(
+      `${label} must contain at most ${String(size)} digits.`,
+    );
+  }
+  const values = value.map((entry, index) =>
+    integer(entry, `${label}[${String(index)}]`, 1, size),
+  );
+  return [...new Set(values)].sort((a, b) => a - b);
+}
+
+export function normalizePortableAidMemoire(
+  value: unknown,
+  size: number,
+): PortableAidMemoire {
+  if (typeof value !== "object" || value === null || Array.isArray(value)) {
+    throw new TypeError("aidMemoire must be an object.");
+  }
+  const record = value as Record<string, unknown>;
+  if (record.version !== AID_MEMOIRE_VERSION) {
+    throw new TypeError("aidMemoire has an unsupported version.");
+  }
+  if (typeof record.enabled !== "boolean") {
+    throw new TypeError("aidMemoire.enabled must be true or false.");
+  }
+  if (
+    !Array.isArray(record.cells) ||
+    record.cells.length < 1 ||
+    record.cells.length > MAX_AID_MEMOIRE_CELLS
+  ) {
+    throw new TypeError(
+      `aidMemoire.cells must contain 1 to ${String(MAX_AID_MEMOIRE_CELLS)} entries.`,
+    );
+  }
+  const columns = integer(
+    record.columns,
+    "aidMemoire.columns",
+    1,
+    Math.min(MAX_AID_MEMOIRE_COLUMNS, record.cells.length),
+  );
+  const cells = record.cells.map((rawCell, index): PortableAidMemoireCell => {
+    if (
+      typeof rawCell !== "object" ||
+      rawCell === null ||
+      Array.isArray(rawCell)
+    ) {
+      throw new TypeError(
+        `aidMemoire.cells[${String(index)}] must be an object.`,
+      );
+    }
+    const cell = rawCell as Record<string, unknown>;
+    if (
+      cell.label !== undefined &&
+      (typeof cell.label !== "string" ||
+        cell.label.length > MAX_AID_MEMOIRE_LABEL_LENGTH)
+    ) {
+      throw new TypeError(
+        `aidMemoire.cells[${String(index)}].label is invalid.`,
+      );
+    }
+    return {
+      label: (cell.label as string | undefined) ?? defaultLabel(index),
+      value: integer(
+        cell.value ?? 0,
+        `aidMemoire.cells[${String(index)}].value`,
+        0,
+        size,
+      ),
+      cornerMarks: portableMarks(
+        cell.cornerMarks,
+        `aidMemoire.cells[${String(index)}].cornerMarks`,
+        size,
+      ),
+      centerMarks: portableMarks(
+        cell.centerMarks,
+        `aidMemoire.cells[${String(index)}].centerMarks`,
+        size,
+      ),
+      color: integer(
+        cell.color ?? 0,
+        `aidMemoire.cells[${String(index)}].color`,
+        0,
+        8,
+      ),
+    };
+  });
+  return {
+    version: AID_MEMOIRE_VERSION,
+    enabled: record.enabled,
+    columns,
+    cells,
+  };
+}
+
+export function aidMemoireToPortable(
+  state: AidMemoireState,
+  size: number,
+): PortableAidMemoire {
+  return normalizePortableAidMemoire(
+    {
+      version: AID_MEMOIRE_VERSION,
+      enabled: state.enabled,
+      columns: state.columns,
+      cells: state.cells.map((cell) => ({
+        label: cell.label,
+        value: cell.value,
+        cornerMarks: maskValues(cell.cornerMarks, size),
+        centerMarks: maskValues(cell.centerMarks, size),
+        color: cell.color,
+      })),
+    },
+    size,
+  );
+}
+
+export function aidMemoireFromPortable(
+  value: unknown,
+  size: number,
+): AidMemoireState {
+  if (value === undefined) return createAidMemoire(size);
+  const portable = normalizePortableAidMemoire(value, size);
+  const mask = (values: readonly number[]) =>
+    values.reduce((result, digit) => result | (1 << (digit - 1)), 0);
+  return {
+    version: AID_MEMOIRE_VERSION,
+    enabled: portable.enabled,
+    columns: portable.columns,
+    cells: portable.cells.map((cell) => ({
+      label: cell.label,
+      value: cell.value,
+      cornerMarks: mask(cell.cornerMarks),
+      centerMarks: mask(cell.centerMarks),
+      color: cell.color,
+    })),
+  };
+}

src/state/gridNavigation.ts

@@ -0,0 +1,54 @@
+export type GridNavigationKey =
+  | "ArrowUp"
+  | "ArrowDown"
+  | "ArrowLeft"
+  | "ArrowRight"
+  | "Home"
+  | "End"
+  | "PageUp"
+  | "PageDown";
+
+/**
+ * Resolve WAI-ARIA grid navigation without wrapping at an edge. Home/End move
+ * within a row; Ctrl/Command+Home/End move to the first/last cell. Page keys
+ * retain the column while moving to the first/last row.
+ */
+export function navigateGridCell(
+  activeCell: number,
+  size: number,
+  key: string,
+  command = false,
+): number | null {
+  if (!Number.isInteger(size) || size < 1 || size > 64) {
+    throw new RangeError("size must be an integer from 1 to 64");
+  }
+  if (
+    !Number.isInteger(activeCell) ||
+    activeCell < 0 ||
+    activeCell >= size * size
+  ) {
+    throw new RangeError("activeCell is outside the grid");
+  }
+  const row = Math.floor(activeCell / size);
+  const column = activeCell % size;
+  switch (key as GridNavigationKey) {
+    case "ArrowUp":
+      return Math.max(0, row - 1) * size + column;
+    case "ArrowDown":
+      return Math.min(size - 1, row + 1) * size + column;
+    case "ArrowLeft":
+      return row * size + Math.max(0, column - 1);
+    case "ArrowRight":
+      return row * size + Math.min(size - 1, column + 1);
+    case "Home":
+      return command ? 0 : row * size;
+    case "End":
+      return command ? size * size - 1 : row * size + size - 1;
+    case "PageUp":
+      return column;
+    case "PageDown":
+      return (size - 1) * size + column;
+    default:
+      return null;
+  }
+}

src/state/playHistory.ts

@@ -0,0 +1,352 @@
+import {
+  snapshotSession,
+  type PlaySession,
+  type PlaySnapshot,
+} from "./session";
+import {
+  cloneAidMemoire,
+  createAidMemoire,
+  type AidMemoireState,
+} from "./aidMemoire";
+
+export type HypothesisStatus = "active" | "kept" | "discarded";
+
+export interface GameplayState extends PlaySnapshot {
+  readonly elapsedSeconds: number;
+  readonly aidMemoire?: AidMemoireState;
+}
+
+export interface GameplayMoment {
+  readonly id: string;
+  readonly sequence: number;
+  readonly branchId: string;
+  readonly label: string;
+  readonly state: GameplayState;
+}
+
+export interface HypothesisBranch {
+  readonly id: string;
+  readonly name: string;
+  readonly parentBranchId: string;
+  readonly baseMomentId: string;
+  readonly baseState: GameplayState;
+  readonly status: HypothesisStatus;
+}
+
+export interface NamedSavepoint {
+  readonly id: string;
+  readonly name: string;
+  readonly momentId: string;
+  readonly branchId: string;
+  readonly state: GameplayState;
+}
+
+export interface GameplayHistory {
+  readonly moments: readonly GameplayMoment[];
+  readonly branches: readonly HypothesisBranch[];
+  readonly savepoints: readonly NamedSavepoint[];
+  readonly activeBranchId: string;
+  readonly currentMomentId: string;
+  readonly nextSequence: number;
+}
+
+export interface HistoryTransition {
+  readonly history: GameplayHistory;
+  readonly state: GameplayState;
+}
+
+export const MAIN_BRANCH_ID = "main";
+export const MAX_GAMEPLAY_MOMENTS = 500;
+
+function cloneState(state: GameplayState): GameplayState {
+  return {
+    values: [...state.values],
+    cornerMarks: [...state.cornerMarks],
+    centerMarks: [...state.centerMarks],
+    colors: [...state.colors],
+    elapsedSeconds: state.elapsedSeconds,
+    ...(state.aidMemoire === undefined
+      ? {}
+      : { aidMemoire: cloneAidMemoire(state.aidMemoire) }),
+  };
+}
+
+function requireName(value: string, kind: string): string {
+  const name = value.trim();
+  if (!name) throw new Error(`${kind} name cannot be empty.`);
+  return name.slice(0, 80);
+}
+
+function appendMoment(
+  history: GameplayHistory,
+  state: GameplayState,
+  label: string,
+  branchId = history.activeBranchId,
+): GameplayHistory {
+  const sequence = history.nextSequence;
+  const moment: GameplayMoment = {
+    id: `moment-${String(sequence)}`,
+    sequence,
+    branchId,
+    label,
+    state: cloneState(state),
+  };
+  return {
+    ...history,
+    moments: [...history.moments, moment].slice(-MAX_GAMEPLAY_MOMENTS),
+    activeBranchId: branchId,
+    currentMomentId: moment.id,
+    nextSequence: sequence + 1,
+  };
+}
+
+export function captureGameplayState(
+  session: PlaySession,
+  aidMemoire?: AidMemoireState,
+): GameplayState {
+  return {
+    ...snapshotSession(session),
+    elapsedSeconds: session.elapsedSeconds,
+    ...(aidMemoire === undefined
+      ? {}
+      : { aidMemoire: cloneAidMemoire(aidMemoire) }),
+  };
+}
+
+export function sessionFromGameplayState(
+  state: GameplayState,
+  paused = false,
+): PlaySession {
+  return {
+    values: [...state.values],
+    cornerMarks: [...state.cornerMarks],
+    centerMarks: [...state.centerMarks],
+    colors: [...state.colors],
+    elapsedSeconds: state.elapsedSeconds,
+    paused,
+  };
+}
+
+export function aidMemoireFromGameplayState(
+  state: GameplayState,
+  size: number,
+): AidMemoireState {
+  return state.aidMemoire === undefined
+    ? createAidMemoire(size)
+    : cloneAidMemoire(state.aidMemoire);
+}
+
+export function createGameplayHistory(
+  session: PlaySession,
+  aidMemoire?: AidMemoireState,
+): GameplayHistory {
+  const initial: GameplayMoment = {
+    id: "moment-0",
+    sequence: 0,
+    branchId: MAIN_BRANCH_ID,
+    label: "Puzzle opened",
+    state: captureGameplayState(session, aidMemoire),
+  };
+  return {
+    moments: [initial],
+    branches: [],
+    savepoints: [],
+    activeBranchId: MAIN_BRANCH_ID,
+    currentMomentId: initial.id,
+    nextSequence: 1,
+  };
+}
+
+export function recordGameplayMoment(
+  history: GameplayHistory,
+  session: PlaySession,
+  label: string,
+  aidMemoire?: AidMemoireState,
+): GameplayHistory {
+  const trimmedLabel = label.trim() || "Grid updated";
+  return appendMoment(
+    history,
+    captureGameplayState(session, aidMemoire),
+    trimmedLabel,
+  );
+}
+
+export function gameplayMoment(
+  history: GameplayHistory,
+  momentId: string,
+): GameplayMoment | undefined {
+  return history.moments.find((moment) => moment.id === momentId);
+}
+
+export function activeHypothesis(
+  history: GameplayHistory,
+): HypothesisBranch | undefined {
+  return history.branches.find(
+    (branch) =>
+      branch.id === history.activeBranchId && branch.status === "active",
+  );
+}
+
+export function beginHypothesis(
+  history: GameplayHistory,
+  session: PlaySession,
+  nameValue: string,
+  fromMomentId = history.currentMomentId,
+  aidMemoire?: AidMemoireState,
+): HistoryTransition {
+  if (activeHypothesis(history) !== undefined) {
+    throw new Error("Finish the active hypothesis before starting another.");
+  }
+  const name = requireName(nameValue, "Hypothesis");
+  const source = gameplayMoment(history, fromMomentId);
+  if (source === undefined)
+    throw new Error("The replay moment is unavailable.");
+
+  const baseState =
+    fromMomentId === history.currentMomentId
+      ? captureGameplayState(session, aidMemoire)
+      : cloneState(source.state);
+  const sequence = history.nextSequence;
+  const branchId = `branch-${String(sequence)}`;
+  const branch: HypothesisBranch = {
+    id: branchId,
+    name,
+    parentBranchId: history.activeBranchId,
+    baseMomentId: source.id,
+    baseState: cloneState(baseState),
+    status: "active",
+  };
+  const withBranch: GameplayHistory = {
+    ...history,
+    branches: [...history.branches, branch],
+    activeBranchId: branchId,
+    currentMomentId: source.id,
+  };
+  return {
+    history: appendMoment(
+      withBranch,
+      baseState,
+      `Started hypothesis “${name}”`,
+      branchId,
+    ),
+    state: cloneState(baseState),
+  };
+}
+
+export function finishHypothesis(
+  history: GameplayHistory,
+  session: PlaySession,
+  decision: "keep" | "discard",
+  aidMemoire?: AidMemoireState,
+): HistoryTransition {
+  const branch = activeHypothesis(history);
+  if (branch === undefined) throw new Error("No hypothesis is active.");
+  const state =
+    decision === "keep"
+      ? captureGameplayState(session, aidMemoire)
+      : cloneState(branch.baseState);
+  const status: HypothesisStatus = decision === "keep" ? "kept" : "discarded";
+  const updated: GameplayHistory = {
+    ...history,
+    branches: history.branches.map((candidate) =>
+      candidate.id === branch.id ? { ...candidate, status } : candidate,
+    ),
+    activeBranchId: branch.parentBranchId,
+    currentMomentId: branch.baseMomentId,
+  };
+  const verb = decision === "keep" ? "Kept" : "Discarded";
+  return {
+    history: appendMoment(
+      updated,
+      state,
+      `${verb} hypothesis “${branch.name}”`,
+      branch.parentBranchId,
+    ),
+    state: cloneState(state),
+  };
+}
+
+export function createSavepoint(
+  history: GameplayHistory,
+  session: PlaySession,
+  nameValue: string,
+  aidMemoire?: AidMemoireState,
+): GameplayHistory {
+  const name = requireName(nameValue, "Savepoint");
+  const state = captureGameplayState(session, aidMemoire);
+  const withMoment = appendMoment(history, state, `Saved “${name}”`);
+  const savepoint: NamedSavepoint = {
+    id: `savepoint-${String(withMoment.nextSequence)}`,
+    name,
+    momentId: withMoment.currentMomentId,
+    branchId: withMoment.activeBranchId,
+    state: cloneState(state),
+  };
+  return {
+    ...withMoment,
+    savepoints: [...withMoment.savepoints, savepoint],
+  };
+}
+
+export function deleteSavepoint(
+  history: GameplayHistory,
+  savepointId: string,
+): GameplayHistory {
+  return {
+    ...history,
+    savepoints: history.savepoints.filter(
+      (savepoint) => savepoint.id !== savepointId,
+    ),
+  };
+}
+
+export function restoreSavepoint(
+  history: GameplayHistory,
+  savepointId: string,
+): HistoryTransition {
+  const savepoint = history.savepoints.find(
+    (candidate) => candidate.id === savepointId,
+  );
+  if (savepoint === undefined) throw new Error("The savepoint is unavailable.");
+  const state = cloneState(savepoint.state);
+  return {
+    history: appendMoment(history, state, `Restored “${savepoint.name}”`),
+    state,
+  };
+}
+
+export function describeGameplayChange(
+  before: PlaySession,
+  after: PlaySession,
+  size: number,
+): string {
+  const changedValues: number[] = [];
+  const changedNotes: number[] = [];
+  const changedColors: number[] = [];
+  for (let cell = 0; cell < after.values.length; cell += 1) {
+    if (before.values[cell] !== after.values[cell]) changedValues.push(cell);
+    if (
+      before.cornerMarks[cell] !== after.cornerMarks[cell] ||
+      before.centerMarks[cell] !== after.centerMarks[cell]
+    ) {
+      changedNotes.push(cell);
+    }
+    if (before.colors[cell] !== after.colors[cell]) changedColors.push(cell);
+  }
+  const cells = new Set([...changedValues, ...changedNotes, ...changedColors]);
+  if (cells.size !== 1) {
+    return cells.size === 0
+      ? "Grid updated"
+      : `Updated ${String(cells.size)} cells`;
+  }
+  const cell = [...cells][0]!;
+  const label = `r${String(Math.floor(cell / size) + 1)}c${String((cell % size) + 1)}`;
+  if (changedValues.length) {
+    const value = after.values[cell] ?? 0;
+    return value === 0
+      ? `Cleared ${label}`
+      : `Set ${label} to ${String(value)}`;
+  }
+  if (changedNotes.length) return `Changed notes in ${label}`;
+  return `Changed colour in ${label}`;
+}

src/storage/record.ts

@@ -4,6 +4,10 @@ import {
   cloneSudokuDocument,
   normalizeSudokuDocument,
 } from "../formats";
+import {
+  normalizePortableAidMemoire,
+  type PortableAidMemoire,
+} from "../state/aidMemoire";
 import {
   PROJECT_RECORD_SCHEMA,
   PROJECT_RECORD_VERSION,
@@ -126,6 +130,19 @@ function progress(value: unknown, size: number): SudokuProgress | undefined {
   if (value.completed !== undefined && typeof value.completed !== "boolean") {
     return storageError("INVALID_PROJECT", "completed must be true or false.");
   }
+  let aidMemoire: PortableAidMemoire | undefined;
+  if (value.aidMemoire !== undefined) {
+    try {
+      aidMemoire = normalizePortableAidMemoire(value.aidMemoire, size);
+    } catch (error) {
+      return storageError(
+        "INVALID_PROJECT",
+        error instanceof Error
+          ? error.message
+          : "Progress aid-mémoire data is invalid.",
+      );
+    }
+  }
   return {
     version: 1,
     values,
@@ -137,6 +154,7 @@ function progress(value: unknown, size: number): SudokuProgress | undefined {
       ? {}
       : { elapsedMs: value.elapsedMs as number }),
     ...(value.completed === undefined ? {} : { completed: value.completed }),
+    ...(aidMemoire === undefined ? {} : { aidMemoire }),
   };
 }
 
@@ -274,6 +292,14 @@ export function cloneProjectRecord(
                     ...entry,
                   ]),
                 }),
+            ...(normalized.progress.aidMemoire === undefined
+              ? {}
+              : {
+                  aidMemoire: normalizePortableAidMemoire(
+                    normalized.progress.aidMemoire,
+                    normalized.puzzle.size,
+                  ),
+                }),
           },
         }),
   };

src/storage/types.ts

@@ -1,4 +1,4 @@
-import type { SudokuDocument } from "../formats";
+import type { PortableAidMemoire, SudokuDocument } from "../formats";
 
 export const PROJECT_RECORD_SCHEMA =
   "de.add-ideas.sudoku-tools.project" as const;
@@ -14,6 +14,7 @@ export interface SudokuProgress {
   readonly candidates?: readonly (readonly number[])[];
   readonly elapsedMs?: number;
   readonly completed?: boolean;
+  readonly aidMemoire?: PortableAidMemoire;
 }
 
 export interface SudokuProjectRecord {

src/styles.css

@@ -644,6 +644,17 @@ body:has(.toolbox-shell[data-toolbox-theme="dark"]) .fatal-error {
   filter: saturate(0.6);
 }
 
+.board-surface.is-replay {
+  border-color: color-mix(
+    in srgb,
+    var(--toolbox-accent) 58%,
+    var(--toolbox-border)
+  );
+  box-shadow:
+    var(--toolbox-shadow),
+    0 0 0 3px color-mix(in srgb, var(--toolbox-accent) 12%, transparent);
+}
+
 .digit-completion {
   width: min(100%, 43rem);
   display: grid;
@@ -738,6 +749,205 @@ body:has(.toolbox-shell[data-toolbox-theme="dark"]) .fatal-error {
     color-mix(in srgb, var(--toolbox-accent) 22%, transparent);
 }
 
+/* Optional aid-mémoire scratch cells */
+
+.aid-memoire {
+  width: min(100%, 45rem);
+  display: grid;
+  gap: 0.7rem;
+  margin-inline: auto;
+  padding: clamp(0.72rem, 1.5vw, 0.95rem);
+  border: 1px solid var(--toolbox-border);
+  border-radius: 0.78rem;
+  background: color-mix(
+    in srgb,
+    var(--toolbox-accent-soft) 22%,
+    var(--toolbox-surface)
+  );
+}
+
+.aid-memoire__heading h2 {
+  margin-top: 0.15rem;
+  font-size: 1.05rem;
+}
+
+.aid-memoire__heading p.muted {
+  max-width: 58ch;
+  margin-top: 0.28rem;
+  font-size: 0.76rem;
+}
+
+.aid-memoire__scroller {
+  max-width: 100%;
+  overflow: auto;
+  padding: 0.18rem;
+  overscroll-behavior-inline: contain;
+  scrollbar-color: var(--toolbox-border) transparent;
+}
+
+.aid-memoire__grid {
+  width: max-content;
+  min-width: min(100%, calc(var(--aid-columns) * 3.25rem));
+  display: grid;
+  grid-template-columns: repeat(var(--aid-columns), minmax(3rem, 1fr));
+  overflow: hidden;
+  border: 1.5px solid var(--sudoku-line-strong);
+  border-radius: 0.42rem;
+  background: var(--sudoku-line);
+  container-type: inline-size;
+}
+
+.aid-memoire__row {
+  display: contents;
+}
+
+.aid-memoire__cell {
+  --cell-fill: var(--toolbox-surface);
+  position: relative;
+  width: auto;
+  min-width: 3rem !important;
+  min-height: 3.35rem !important;
+  overflow: hidden;
+  padding: 0 !important;
+  border: 0.5px solid var(--sudoku-line) !important;
+  border-radius: 0 !important;
+  outline-offset: -3px !important;
+  background: var(--cell-fill) !important;
+  box-shadow: none !important;
+  color: var(--toolbox-accent) !important;
+  font-variant-numeric: tabular-nums;
+}
+
+.aid-memoire__cell[class*="has-color-"] {
+  --cell-fill: color-mix(
+    in srgb,
+    var(--sudoku-mark-color) 24%,
+    var(--toolbox-surface)
+  );
+}
+
+.aid-memoire__cell.is-selected {
+  background: color-mix(
+    in srgb,
+    var(--toolbox-accent) 20%,
+    var(--cell-fill)
+  ) !important;
+}
+
+.aid-memoire__cell.is-selected::after,
+.aid-memoire__cell:focus-visible::after {
+  position: absolute;
+  z-index: 6;
+  inset: 2px;
+  border: 2px solid var(--toolbox-accent);
+  border-radius: 2px;
+  content: "";
+  pointer-events: none;
+}
+
+.aid-memoire__cell:focus-visible {
+  outline: none !important;
+}
+
+.aid-memoire__cell:focus-visible::after {
+  border-color: var(--toolbox-focus);
+}
+
+.aid-memoire__label,
+.aid-memoire__value,
+.aid-memoire__corner,
+.aid-memoire__centre {
+  position: absolute;
+  z-index: 4;
+  pointer-events: none;
+}
+
+.aid-memoire__label {
+  top: 0.17rem;
+  left: 0.23rem;
+  max-width: calc(100% - 0.46rem);
+  overflow: hidden;
+  color: var(--toolbox-muted);
+  font-size: 0.52rem;
+  font-weight: 760;
+  letter-spacing: 0.02em;
+  line-height: 1;
+  text-overflow: ellipsis;
+  white-space: nowrap;
+}
+
+.aid-memoire__value {
+  inset: 0;
+  display: grid;
+  place-items: center;
+  padding-top: 0.34rem;
+  font-size: 1.38rem;
+  font-weight: 680;
+}
+
+.aid-memoire__corner {
+  top: 0.92rem;
+  right: 0.22rem;
+  left: 0.22rem;
+  overflow: hidden;
+  color: color-mix(in srgb, var(--toolbox-text) 77%, var(--toolbox-muted));
+  font-size: 0.54rem;
+  font-weight: 720;
+  line-height: 1;
+  text-align: left;
+  text-overflow: ellipsis;
+  white-space: nowrap;
+}
+
+.aid-memoire__centre {
+  right: 0.2rem;
+  bottom: 0.36rem;
+  left: 0.2rem;
+  overflow: hidden;
+  color: color-mix(in srgb, var(--toolbox-text) 72%, var(--toolbox-muted));
+  font-size: 0.62rem;
+  font-weight: 680;
+  letter-spacing: 0.04em;
+  line-height: 1;
+  text-align: center;
+  text-overflow: ellipsis;
+  white-space: nowrap;
+}
+
+.aid-memoire__modes {
+  grid-template-columns: repeat(4, minmax(0, 1fr));
+}
+
+.aid-memoire__selected {
+  display: grid;
+  grid-template-columns: minmax(10rem, 0.55fr) minmax(13rem, 1fr);
+  align-items: end;
+  gap: 0.65rem;
+}
+
+.aid-memoire__selected .muted {
+  padding-bottom: 0.2rem;
+  font-size: 0.73rem;
+}
+
+.aid-memoire__settings {
+  border-top: 1px solid var(--toolbox-border);
+  padding-top: 0.58rem;
+}
+
+.aid-memoire__settings summary {
+  color: var(--toolbox-muted);
+  font-size: 0.76rem;
+  font-weight: 700;
+  cursor: pointer;
+}
+
+.aid-memoire__settings-body {
+  display: grid;
+  gap: 0.65rem;
+  padding-top: 0.7rem;
+}
+
 .side-panel {
   padding: clamp(0.85rem, 1.7vw, 1.2rem);
 }
@@ -896,6 +1106,162 @@ body:has(.toolbox-shell[data-toolbox-theme="dark"]) .fatal-error {
   display: flex;
 }
 
+.history-dialog-grid {
+  display: grid;
+  grid-template-columns: minmax(17rem, 0.72fr) minmax(22rem, 1.28fr);
+  align-items: start;
+  gap: 1rem;
+}
+
+.history-section h3 {
+  margin-top: 0.18rem;
+  font-size: 1rem;
+}
+
+.history-name-form {
+  display: grid;
+  grid-template-columns: minmax(0, 1fr) auto;
+  align-items: end;
+  gap: 0.55rem;
+}
+
+.history-name-form label {
+  min-width: 0;
+}
+
+.hypothesis-active {
+  display: grid;
+  gap: 0.7rem;
+  padding: 0.72rem;
+  border: 1px solid
+    color-mix(in srgb, var(--toolbox-accent) 38%, var(--toolbox-border));
+  border-radius: 0.62rem;
+  background: color-mix(
+    in srgb,
+    var(--toolbox-accent-soft) 58%,
+    var(--toolbox-surface)
+  );
+}
+
+.hypothesis-active > div:first-child,
+.savepoint-list li > div:first-child {
+  display: grid;
+  gap: 0.16rem;
+}
+
+.hypothesis-active span,
+.savepoint-list span,
+.history-step-copy > span {
+  color: var(--toolbox-muted);
+  font-size: 0.73rem;
+}
+
+.branch-list,
+.savepoint-list,
+.history-list {
+  margin: 0;
+  padding: 0;
+  list-style: none;
+}
+
+.branch-list,
+.savepoint-list {
+  display: grid;
+  gap: 0.35rem;
+}
+
+.branch-list li,
+.savepoint-list li {
+  min-width: 0;
+  display: flex;
+  align-items: center;
+  justify-content: space-between;
+  gap: 0.55rem;
+  padding: 0.5rem 0.58rem;
+  border: 1px solid var(--toolbox-border);
+  border-radius: 0.55rem;
+  background: var(--toolbox-surface);
+}
+
+.branch-status {
+  padding: 0.18rem 0.4rem;
+  border-radius: 999px;
+  background: var(--toolbox-surface-soft);
+  color: var(--toolbox-muted);
+  font-size: 0.65rem;
+  font-weight: 760;
+  text-transform: capitalize;
+}
+
+.branch-status--active,
+.branch-status--kept {
+  background: var(--toolbox-accent-soft);
+  color: var(--toolbox-accent);
+}
+
+.branch-status--discarded {
+  color: var(--toolbox-danger);
+}
+
+.history-replay {
+  max-height: min(67vh, 46rem);
+  overflow: hidden;
+}
+
+.history-replay-controls {
+  flex-wrap: nowrap;
+}
+
+.history-list {
+  min-height: 8rem;
+  display: grid;
+  gap: 0.35rem;
+  overflow: auto;
+  overscroll-behavior: contain;
+  scrollbar-gutter: stable;
+}
+
+.history-list button {
+  width: 100%;
+  display: grid;
+  grid-template-columns: 2.2rem minmax(0, 1fr);
+  align-items: center;
+  gap: 0.55rem;
+  padding: 0.48rem 0.58rem;
+  border-color: var(--toolbox-border);
+  border-radius: 0.58rem;
+  background: var(--toolbox-surface);
+  color: var(--toolbox-text);
+  text-align: left;
+}
+
+.history-list button.is-current {
+  border-color: var(--toolbox-accent);
+  background: var(--toolbox-accent-soft);
+}
+
+.history-step-number {
+  color: var(--toolbox-accent);
+  font-family:
+    ui-monospace, SFMono-Regular, Consolas, "Liberation Mono", monospace;
+  font-size: 0.72rem;
+  font-weight: 760;
+  text-align: center;
+}
+
+.history-step-copy {
+  min-width: 0;
+  display: grid;
+  gap: 0.1rem;
+}
+
+.history-step-copy strong,
+.history-step-copy span {
+  overflow: hidden;
+  text-overflow: ellipsis;
+  white-space: nowrap;
+}
+
 .generator-form {
   background: color-mix(
     in srgb,
@@ -1011,11 +1377,16 @@ body:has(.toolbox-shell[data-toolbox-theme="dark"]) .fatal-error {
   -webkit-user-select: none;
 }
 
+.sudoku-board-frame.has-outside-clues {
+  --board-pad: clamp(1.75rem, 4.8vw, 2.55rem);
+  width: min(100%, 48rem);
+}
+
 .sudoku-board {
   position: relative;
   width: 100%;
   display: grid;
-  grid-template-columns: repeat(var(--sudoku-size), minmax(0, 1fr));
+  grid-template-columns: minmax(0, 1fr);
   grid-template-rows: repeat(var(--sudoku-size), minmax(0, 1fr));
   aspect-ratio: 1;
   overflow: hidden;
@@ -1026,6 +1397,12 @@ body:has(.toolbox-shell[data-toolbox-theme="dark"]) .fatal-error {
   touch-action: none;
 }
 
+.sudoku-row {
+  min-height: 0;
+  display: grid;
+  grid-template-columns: repeat(var(--sudoku-size), minmax(0, 1fr));
+}
+
 .sudoku-cell {
   --cell-fill: var(--toolbox-surface);
   position: relative;
@@ -1067,6 +1444,14 @@ body:has(.toolbox-shell[data-toolbox-theme="dark"]) .fatal-error {
   ) !important;
 }
 
+.sudoku-cell.is-candidate-highlighted {
+  background: color-mix(
+    in srgb,
+    var(--toolbox-focus) 18%,
+    var(--cell-fill)
+  ) !important;
+}
+
 .sudoku-cell.is-selected {
   background: color-mix(
     in srgb,
@@ -1189,7 +1574,51 @@ body:has(.toolbox-shell[data-toolbox-theme="dark"]) .fatal-error {
   shape-rendering: geometricPrecision;
 }
 
-.constraint-layer :where(path, polyline, line, circle) {
+.candidate-link-layer {
+  position: absolute;
+  z-index: 7;
+  top: var(--board-pad);
+  left: var(--board-pad);
+  width: calc(100% - var(--board-pad) - var(--board-pad));
+  height: calc(100% - var(--board-pad) - var(--board-pad));
+  overflow: hidden;
+  pointer-events: none;
+  shape-rendering: geometricPrecision;
+}
+
+.candidate-overlay-link {
+  vector-effect: non-scaling-stroke;
+  stroke-linecap: round;
+}
+
+.candidate-overlay-link--strong {
+  stroke: color-mix(in srgb, var(--toolbox-accent) 88%, var(--toolbox-text));
+  stroke-width: clamp(2.4px, 0.38cqi, 4px);
+}
+
+.candidate-overlay-link--weak {
+  stroke: color-mix(in srgb, var(--sudoku-warning) 82%, var(--toolbox-text));
+  stroke-dasharray: 4 3.5;
+  stroke-width: clamp(1.5px, 0.25cqi, 2.6px);
+}
+
+.candidate-overlay-node circle {
+  vector-effect: non-scaling-stroke;
+  fill: color-mix(in srgb, var(--toolbox-surface) 90%, var(--toolbox-accent));
+  stroke: color-mix(in srgb, var(--toolbox-accent) 82%, var(--toolbox-text));
+  stroke-width: clamp(1.2px, 0.19cqi, 2px);
+}
+
+.candidate-overlay-node text {
+  dominant-baseline: central;
+  fill: var(--toolbox-text);
+  font-family: var(--toolbox-font);
+  font-size: 0.13px;
+  font-weight: 850;
+  text-anchor: middle;
+}
+
+.constraint-layer :where(path, polyline, line, circle, rect) {
   vector-effect: non-scaling-stroke;
 }
 
@@ -1328,6 +1757,102 @@ body:has(.toolbox-shell[data-toolbox-theme="dark"]) .fatal-error {
   stroke-width: clamp(0.8px, 0.12cqi, 1.2px);
 }
 
+.constraint-maximum circle {
+  fill: color-mix(in srgb, var(--toolbox-muted) 38%, var(--toolbox-surface));
+  stroke: color-mix(in srgb, var(--toolbox-text) 62%, var(--toolbox-muted));
+  stroke-width: clamp(1.2px, 0.2cqi, 2px);
+}
+
+.constraint-maximum path {
+  fill: none;
+  stroke: color-mix(in srgb, var(--toolbox-text) 84%, var(--toolbox-accent));
+  stroke-linejoin: round;
+  stroke-width: clamp(1.4px, 0.23cqi, 2.3px);
+}
+
+.constraint-quadruple circle {
+  fill: color-mix(in srgb, var(--toolbox-surface) 94%, var(--toolbox-accent));
+  stroke: color-mix(in srgb, var(--toolbox-text) 80%, var(--toolbox-muted));
+  stroke-width: clamp(1.2px, 0.2cqi, 2px);
+}
+
+.constraint-quadruple text,
+.constraint-outside text {
+  dominant-baseline: central;
+  fill: var(--toolbox-text);
+  font-family: var(--toolbox-font);
+  font-weight: 820;
+  text-anchor: middle;
+}
+
+.constraint-quadruple text {
+  font-size: 0.145px;
+  letter-spacing: -0.018px;
+}
+
+.constraint-outside rect {
+  fill: color-mix(in srgb, var(--toolbox-surface) 90%, var(--toolbox-accent));
+  stroke: color-mix(in srgb, var(--toolbox-border) 74%, var(--toolbox-text));
+  stroke-width: clamp(1px, 0.16cqi, 1.7px);
+}
+
+.constraint-outside text {
+  font-size: 0.22px;
+}
+
+.constraint-outside .outside-clue-kinds {
+  font-size: 0.115px;
+  font-weight: 760;
+  letter-spacing: 0.018px;
+}
+
+.constraint-outside .outside-clue-value {
+  font-size: 0.205px;
+}
+
+.constraint-skyscraper rect {
+  fill: color-mix(in srgb, var(--sudoku-info) 10%, var(--toolbox-surface));
+}
+
+.constraint-layer .is-negated :where(path, polyline, line, circle, rect),
+.constraint-layer :where(path, polyline, line, circle, rect).is-negated {
+  stroke: var(--toolbox-danger) !important;
+  stroke-dasharray: 4 2.5;
+}
+
+.constraint-layer .is-negated text {
+  fill: var(--toolbox-danger) !important;
+}
+
+.constraint-thermo.is-negated polyline {
+  stroke-dasharray: 14px 12px;
+  stroke-linecap: butt;
+}
+
+.constraint-false-mark {
+  dominant-baseline: central;
+  fill: var(--toolbox-danger);
+  font-family: var(--toolbox-font);
+  font-size: 0.22px;
+  font-weight: 900;
+  paint-order: stroke;
+  stroke: var(--toolbox-surface);
+  stroke-width: 0.055px;
+  text-anchor: middle;
+}
+
+.constraint-layer circle.is-negated {
+  fill: color-mix(
+    in srgb,
+    var(--toolbox-danger) 18%,
+    var(--toolbox-surface)
+  ) !important;
+}
+
+.constraint-layer .constraint-kropki--black.is-negated {
+  fill: color-mix(in srgb, var(--toolbox-danger) 52%, black) !important;
+}
+
 /* Number and colour entry */
 
 .number-pad {
@@ -1454,8 +1979,32 @@ body:has(.toolbox-shell[data-toolbox-theme="dark"]) .fatal-error {
   overflow-wrap: anywhere;
 }
 
+.constraint-actions,
+.constraint-batch-actions {
+  display: flex;
+  align-items: center;
+  justify-content: flex-end;
+  flex-wrap: wrap;
+  gap: 0.3rem;
+}
+
+.constraint-actions {
+  flex: 0 0 auto;
+}
+
+.constraint-batch-actions .text-button,
+.constraint-actions .text-button {
+  min-height: 1.9rem;
+  padding: 0.24rem 0.42rem;
+  font-size: 0.7rem;
+}
+
+.outside-clue-fields {
+  grid-template-columns: repeat(auto-fit, minmax(8rem, 1fr));
+}
+
 .subtabs {
-  grid-template-columns: repeat(3, minmax(0, 1fr));
+  grid-template-columns: repeat(auto-fit, minmax(9rem, 1fr));
 }
 
 .helper-controls {
@@ -1545,6 +2094,42 @@ body:has(.toolbox-shell[data-toolbox-theme="dark"]) .fatal-error {
   font-weight: 720;
 }
 
+.sum-lab-guidance {
+  font-size: 0.76rem;
+}
+
+.sum-combination-cloud {
+  align-items: flex-start;
+}
+
+.sum-combination {
+  min-height: 2rem;
+  padding: 0.28rem 0.48rem;
+  border: 1px solid
+    color-mix(in srgb, var(--toolbox-accent) 18%, var(--toolbox-border));
+  border-radius: 0.42rem;
+  background: var(--toolbox-surface);
+  color: var(--toolbox-accent);
+  font-family:
+    ui-monospace, SFMono-Regular, Consolas, "Liberation Mono", monospace;
+  font-size: 0.72rem;
+  font-weight: 720;
+}
+
+.sum-combination:hover,
+.sum-combination:focus-visible {
+  border-color: var(--toolbox-accent);
+  background: var(--toolbox-accent-soft);
+}
+
+.sum-combination.is-eliminated {
+  border-color: var(--toolbox-border);
+  background: color-mix(in srgb, var(--toolbox-surface-soft) 72%, transparent);
+  color: var(--toolbox-muted);
+  opacity: 0.68;
+  text-decoration: line-through;
+}
+
 .residual-equation {
   color: var(--toolbox-muted);
   font-family:
@@ -1558,6 +2143,226 @@ body:has(.toolbox-shell[data-toolbox-theme="dark"]) .fatal-error {
   color: var(--toolbox-accent);
 }
 
+/* Candidate inspection */
+
+.candidate-lab {
+  min-width: 0;
+}
+
+.candidate-lab h3 {
+  font-size: 1.08rem;
+}
+
+.candidate-lab h4 {
+  margin: 0;
+  color: var(--toolbox-text);
+  font-size: 0.84rem;
+}
+
+.candidate-filter {
+  min-width: 0;
+  display: grid;
+  gap: 0.5rem;
+  margin: 0;
+  padding: 0.7rem;
+  border: 1px solid var(--toolbox-border);
+  border-radius: 0.7rem;
+}
+
+.candidate-filter legend {
+  padding-inline: 0.25rem;
+  color: var(--toolbox-muted);
+  font-size: 0.72rem;
+  font-weight: 760;
+}
+
+.candidate-filter__digits {
+  display: grid;
+  grid-template-columns: repeat(auto-fit, minmax(2.15rem, 1fr));
+  gap: 0.3rem;
+}
+
+.candidate-filter__digits--wide {
+  grid-template-columns: repeat(auto-fit, minmax(2rem, 1fr));
+}
+
+.candidate-filter__digits button {
+  min-width: 0;
+  min-height: 2.3rem;
+  padding: 0.3rem;
+}
+
+.candidate-lab__controls {
+  display: grid;
+  grid-template-columns: minmax(12rem, 1.5fr) repeat(3, minmax(8rem, 1fr));
+  align-items: end;
+  gap: 0.55rem 0.8rem;
+}
+
+.candidate-inspection {
+  min-width: 0;
+  display: grid;
+  gap: 0.55rem;
+}
+
+.candidate-cell-list {
+  display: grid;
+  grid-template-columns: repeat(auto-fit, minmax(10rem, 1fr));
+  gap: 0.4rem;
+}
+
+.candidate-cell-list article {
+  min-width: 0;
+  display: grid;
+  grid-template-columns: auto 1fr;
+  gap: 0.18rem 0.55rem;
+  padding: 0.55rem 0.65rem;
+  border: 1px solid var(--toolbox-border);
+  border-radius: 0.58rem;
+  background: var(--toolbox-surface);
+}
+
+.candidate-cell-list article > strong {
+  color: var(--toolbox-accent);
+  font-family:
+    ui-monospace, SFMono-Regular, Consolas, "Liberation Mono", monospace;
+}
+
+.candidate-cell-list article > span {
+  justify-self: end;
+  color: var(--toolbox-text);
+  font-family:
+    ui-monospace, SFMono-Regular, Consolas, "Liberation Mono", monospace;
+  font-weight: 760;
+}
+
+.candidate-cell-list article > small {
+  grid-column: 1 / -1;
+  overflow: hidden;
+  color: var(--toolbox-muted);
+  font-size: 0.67rem;
+  text-overflow: ellipsis;
+  white-space: nowrap;
+}
+
+.candidate-house-list {
+  max-height: 18rem;
+  display: grid;
+  align-content: start;
+  gap: 0.4rem;
+  overflow: auto;
+  scrollbar-color: var(--toolbox-border) transparent;
+}
+
+.candidate-house-list details {
+  border: 1px solid var(--toolbox-border);
+  border-radius: 0.58rem;
+  background: var(--toolbox-surface);
+}
+
+.candidate-house-list summary {
+  display: flex;
+  align-items: center;
+  justify-content: space-between;
+  gap: 0.8rem;
+  padding: 0.55rem 0.65rem;
+  color: var(--toolbox-text);
+  cursor: pointer;
+}
+
+.candidate-house-list summary span {
+  color: var(--toolbox-muted);
+  font-size: 0.7rem;
+}
+
+.candidate-house-list dl {
+  display: grid;
+  gap: 0.22rem;
+  padding: 0 0.65rem 0.65rem;
+}
+
+.candidate-house-list dl > div {
+  display: grid;
+  grid-template-columns: 1.5rem 1fr;
+  gap: 0.45rem;
+  padding: 0.3rem 0.4rem;
+  border-radius: 0.38rem;
+  background: var(--toolbox-surface-soft);
+}
+
+.candidate-house-list dt {
+  color: var(--toolbox-accent);
+  font-weight: 820;
+  text-align: center;
+}
+
+.candidate-house-list dd {
+  margin: 0;
+  color: var(--toolbox-muted);
+  font-family:
+    ui-monospace, SFMono-Regular, Consolas, "Liberation Mono", monospace;
+  font-size: 0.7rem;
+}
+
+.candidate-house-list [data-link-kind="strong"] dd {
+  color: var(--toolbox-accent);
+}
+
+.candidate-section-heading {
+  display: flex;
+  align-items: center;
+  justify-content: space-between;
+  gap: 0.6rem;
+}
+
+.candidate-link-list {
+  max-height: 18rem;
+  display: grid;
+  grid-template-columns: repeat(auto-fit, minmax(13rem, 1fr));
+  align-content: start;
+  gap: 0.35rem;
+  overflow: auto;
+  scrollbar-color: var(--toolbox-border) transparent;
+}
+
+.candidate-link-list .candidate-link {
+  min-width: 0;
+  min-height: 3.2rem;
+  display: grid;
+  justify-items: start;
+  gap: 0.12rem;
+  padding: 0.45rem 0.55rem;
+  border-left-width: 3px;
+  text-align: left;
+}
+
+.candidate-link > span {
+  overflow: hidden;
+  font-family:
+    ui-monospace, SFMono-Regular, Consolas, "Liberation Mono", monospace;
+  font-size: 0.73rem;
+  text-overflow: ellipsis;
+  white-space: nowrap;
+}
+
+.candidate-link > small {
+  max-width: 100%;
+  overflow: hidden;
+  color: var(--toolbox-muted);
+  font-size: 0.65rem;
+  font-weight: 620;
+  text-overflow: ellipsis;
+  white-space: nowrap;
+}
+
+.candidate-link--strong {
+  border-left-color: var(--toolbox-accent) !important;
+}
+
+.candidate-link--weak {
+  border-left-color: var(--sudoku-warning) !important;
+}
+
 .analysis-summary,
 .logical-results {
   display: grid;
@@ -1999,6 +2804,10 @@ body:has(.toolbox-shell[data-toolbox-theme="dark"]) .fatal-error {
   .helper-controls {
     grid-template-columns: repeat(2, minmax(0, 1fr));
   }
+
+  .candidate-lab__controls {
+    grid-template-columns: repeat(2, minmax(0, 1fr));
+  }
 }
 
 @media (max-width: 48rem) {
@@ -2039,7 +2848,24 @@ body:has(.toolbox-shell[data-toolbox-theme="dark"]) .fatal-error {
 
   .subtabs,
   .import-export-grid,
-  .help-grid {
+  .help-grid,
+  .history-dialog-grid {
+    grid-template-columns: minmax(0, 1fr);
+  }
+
+  .history-name-form {
+    grid-template-columns: minmax(0, 1fr);
+  }
+
+  .history-replay {
+    max-height: none;
+  }
+
+  .history-replay-controls {
+    flex-wrap: wrap;
+  }
+
+  .aid-memoire__selected {
     grid-template-columns: minmax(0, 1fr);
   }
 
@@ -2054,7 +2880,8 @@ body:has(.toolbox-shell[data-toolbox-theme="dark"]) .fatal-error {
   }
 
   .field-grid,
-  .helper-controls {
+  .helper-controls,
+  .candidate-lab__controls {
     grid-template-columns: minmax(0, 1fr);
   }
 
@@ -2138,6 +2965,22 @@ body:has(.toolbox-shell[data-toolbox-theme="dark"]) .fatal-error {
     border-radius: 0.55rem;
   }
 
+  .sudoku-board-frame.has-outside-clues {
+    --board-pad: 1.45rem;
+  }
+
+  .constraint-outside text {
+    font-size: 0.26px;
+  }
+
+  .constraint-outside .outside-clue-kinds {
+    font-size: 0.14px;
+  }
+
+  .constraint-outside .outside-clue-value {
+    font-size: 0.255px;
+  }
+
   .mode-switcher {
     grid-template-columns: repeat(2, minmax(0, 1fr));
   }
@@ -2197,6 +3040,7 @@ body:has(.toolbox-shell[data-toolbox-theme="dark"]) .fatal-error {
   }
 
   .constraint-layer :where(path, polyline, line, circle),
+  .candidate-link-layer :where(line, circle),
   .region-boundaries path {
     stroke: CanvasText;
   }
@@ -2238,6 +3082,10 @@ body:has(.toolbox-shell[data-toolbox-theme="dark"]) .fatal-error {
     display: none !important;
   }
 
+  .candidate-link-layer {
+    display: none !important;
+  }
+
   .toolbox-shell__main,
   .sudoku-workbench,
   .workbench-grid,
@@ -2291,6 +3139,11 @@ body:has(.toolbox-shell[data-toolbox-theme="dark"]) .fatal-error {
     print-color-adjust: exact;
   }
 
+  .sudoku-board-frame.has-outside-clues {
+    --board-pad: 0.85cm;
+    width: min(100%, 19.7cm);
+  }
+
   .sudoku-cell,
   .sudoku-cell.is-selected,
   .sudoku-cell.has-conflict,
@@ -2305,13 +3158,6 @@ body:has(.toolbox-shell[data-toolbox-theme="dark"]) .fatal-error {
     display: none !important;
   }
 
-  .constraint-layer {
-    top: 0;
-    left: 0;
-    width: 100%;
-    height: 100%;
-  }
-
   .board-meta,
   .rule-card {
     width: min(100%, 18cm);

tests/browser/workbench.spec.ts

@@ -116,6 +116,12 @@ test("replaces setter cages and generates a rated variant", async ({
 test("uses distinct numbered sum badges and directional inequalities", async ({
   page,
 }) => {
+  const runtimeErrors: string[] = [];
+  page.on("pageerror", (error) => runtimeErrors.push(error.message));
+  page.on("console", (message) => {
+    if (message.type() === "error") runtimeErrors.push(message.text());
+  });
+
   await page.goto("/deep/nested/sudoku/");
   const examples = page.getByLabel("Open built-in puzzle");
 
@@ -136,4 +142,109 @@ test("uses distinct numbered sum badges and directional inequalities", async ({
   await expect(
     page.locator(".constraint-inequality-tip").first(),
   ).toBeVisible();
+
+  await examples.selectOption("truth-and-lies");
+  await expect(
+    page.getByRole("heading", { name: "Truth and lies" }),
+  ).toBeVisible();
+  await expect(page.locator(".constraint-outside")).toHaveCount(4);
+  await expect(page.locator(".constraint-quadruple")).toHaveCount(2);
+  await expect(page.locator(".constraint-maximum")).toHaveCount(2);
+  await expect(page.locator(".constraint-outside.is-negated")).toHaveCount(2);
+
+  await page.setViewportSize({ width: 390, height: 844 });
+  const outsideBox = await page
+    .locator(".constraint-outside")
+    .first()
+    .boundingBox();
+  const maximumBox = await page
+    .locator(".constraint-maximum")
+    .first()
+    .boundingBox();
+  expect(outsideBox?.width ?? 0).toBeGreaterThan(18);
+  expect(outsideBox?.height ?? 0).toBeGreaterThan(12);
+  expect(maximumBox?.width ?? 0).toBeGreaterThan(12);
+  expect(maximumBox?.height ?? 0).toBeGreaterThan(12);
+  await expect(
+    page.locator(".constraint-thermo .constraint-false-mark").first(),
+  ).toBeVisible();
+
+  expect(runtimeErrors).toEqual([]);
+});
+
+test("keeps navigation, scratch work, branches and analysis tools local", async ({
+  page,
+}) => {
+  const runtimeErrors: string[] = [];
+  page.on("pageerror", (error) => runtimeErrors.push(error.message));
+  page.on("console", (message) => {
+    if (message.type() === "error") runtimeErrors.push(message.text());
+  });
+
+  await page.goto("/deep/nested/sudoku/");
+  const grid = page.getByRole("grid", { name: "9 by 9 Sudoku grid" });
+  const first = grid.getByRole("gridcell", {
+    name: "Row 1, column 1, 4",
+  });
+  await first.focus();
+  await first.press("End");
+  await expect(
+    grid.getByRole("gridcell", { name: /Row 1, column 9,/u }),
+  ).toBeFocused();
+  await page.keyboard.press("PageDown");
+  await expect(
+    grid.getByRole("gridcell", { name: /Row 9, column 9,/u }),
+  ).toBeFocused();
+  await page.keyboard.press("Control+Home");
+  await expect(first).toBeFocused();
+
+  await page.getByLabel("Show aid-mémoire scratch cells").check();
+  const scratch = page.getByRole("grid", {
+    name: "9 aid-mémoire scratch cells",
+  });
+  const scratchCell = scratch.getByRole("gridcell").first();
+  await scratchCell.click();
+  await page
+    .getByRole("group", { name: "Digits" })
+    .getByRole("button", { name: "2", exact: true })
+    .click();
+  await expect(scratch.getByRole("gridcell").first()).toHaveAccessibleName(
+    /value 2/u,
+  );
+
+  await page.getByRole("button", { name: "History & branches" }).click();
+  await page.getByLabel("Savepoint name").fill("Before test branch");
+  await page.getByRole("button", { name: "Save current grid" }).click();
+  await expect(
+    page.getByText("Before test branch", { exact: true }),
+  ).toBeVisible();
+  await page.getByLabel("Hypothesis name").fill("Try a two");
+  await page.getByRole("button", { name: "Start hypothesis" }).click();
+
+  const empty = grid.getByRole("gridcell", {
+    name: "Row 1, column 3, empty",
+  });
+  await empty.click();
+  await page
+    .getByRole("group", { name: "Digits" })
+    .getByRole("button", { name: "2", exact: true })
+    .click();
+  await expect(
+    grid.getByRole("gridcell", { name: "Row 1, column 3, 2" }),
+  ).toBeVisible();
+  await page.getByRole("button", { name: "Hypothesis: Try a two" }).click();
+  await page.getByRole("button", { name: "Discard and return" }).click();
+  await expect(empty).toBeVisible();
+
+  await page.getByRole("button", { name: "Helpers" }).click();
+  await page.getByRole("tab", { name: "Sum Lab" }).click();
+  await expect(
+    page.getByRole("heading", { name: "Generalized Sum Lab" }),
+  ).toBeVisible();
+  await page.getByRole("tab", { name: "Candidate links" }).click();
+  await expect(
+    page.getByRole("heading", { name: "Links and houses" }),
+  ).toBeVisible();
+
+  expect(runtimeErrors).toEqual([]);
 });

tests/components/aidMemoire.test.tsx

@@ -0,0 +1,148 @@
+import { useState } from "react";
+import { fireEvent, render, screen, within } from "@testing-library/react";
+import userEvent from "@testing-library/user-event";
+import { describe, expect, it, vi } from "vitest";
+import { AidMemoire } from "../../src/components/AidMemoire";
+import {
+  configureAidMemoire,
+  createAidMemoire,
+  type AidMemoireState,
+} from "../../src/state/aidMemoire";
+import type { EntryMode } from "../../src/state/session";
+
+function Harness({
+  initial,
+  readOnly = false,
+}: {
+  initial?: AidMemoireState;
+  readOnly?: boolean;
+}) {
+  const [state, setState] = useState(
+    initial ?? createAidMemoire(9, { enabled: true }),
+  );
+  const [selected, setSelected] = useState(0);
+  const [active, setActive] = useState(false);
+  const [mode, setMode] = useState<EntryMode>("value");
+  return (
+    <AidMemoire
+      size={9}
+      state={state}
+      selectedCell={selected}
+      active={active}
+      readOnly={readOnly}
+      mode={mode}
+      onStateChange={setState}
+      onSelect={(cell) => {
+        setSelected(cell);
+        setActive(true);
+      }}
+      onMode={setMode}
+    />
+  );
+}
+
+describe("aid-mémoire component", () => {
+  it("renders normal-like cells with keyboard entry and full descriptions", async () => {
+    const user = userEvent.setup();
+    render(<Harness />);
+
+    const grid = screen.getByRole("grid", {
+      name: "9 aid-mémoire scratch cells",
+    });
+    expect(within(grid).getAllByRole("row")).toHaveLength(1);
+    const first = within(grid).getByRole("gridcell", {
+      name: "Aid-mémoire cell 1, label 1, empty",
+    });
+    expect(first).toHaveAttribute("aria-colindex", "1");
+    await user.click(first);
+    await user.keyboard("4");
+    expect(
+      within(grid).getByRole("gridcell", {
+        name: "Aid-mémoire cell 1, label 1, value 4",
+      }),
+    ).toHaveAttribute("aria-selected", "true");
+
+    const second = within(grid).getByRole("gridcell", {
+      name: "Aid-mémoire cell 2, label 2, empty",
+    });
+    second.focus();
+    await user.keyboard("c7");
+    expect(
+      within(grid).getByRole("gridcell", {
+        name: "Aid-mémoire cell 2, label 2, empty, centre marks 7",
+      }),
+    ).toBeInTheDocument();
+    expect(screen.getByRole("button", { name: "Centre" })).toHaveAttribute(
+      "aria-pressed",
+      "true",
+    );
+  });
+
+  it("uses row-aware WAI grid navigation without horizontal wrapping", () => {
+    const initial = configureAidMemoire(
+      createAidMemoire(9, { enabled: true }),
+      9,
+      5,
+      2,
+    );
+    render(<Harness initial={initial} />);
+    const cells = screen.getAllByRole("gridcell");
+    const rows = screen.getAllByRole("row");
+    expect(rows[0]).toHaveAttribute("aria-rowindex", "1");
+    expect(rows[2]).toHaveAttribute("aria-rowindex", "3");
+    expect(cells[2]).toHaveAttribute("aria-colindex", "1");
+
+    cells[1]!.focus();
+    fireEvent.keyDown(cells[1]!, { key: "ArrowRight" });
+    expect(document.activeElement).toBe(cells[1]);
+    fireEvent.keyDown(cells[1]!, { key: "Home" });
+    expect(document.activeElement).toBe(cells[0]);
+    fireEvent.keyDown(cells[0]!, { key: "End", ctrlKey: true });
+    expect(document.activeElement).toBe(cells[4]);
+    fireEvent.keyDown(cells[4]!, { key: "PageUp" });
+    expect(document.activeElement).toBe(cells[0]);
+    fireEvent.keyDown(cells[0]!, { key: "PageDown" });
+    expect(document.activeElement).toBe(cells[4]);
+  });
+
+  it("keeps read-only replay cells navigable without allowing edits", () => {
+    const initial = configureAidMemoire(
+      createAidMemoire(9, { enabled: true }),
+      9,
+      4,
+      2,
+    );
+    render(<Harness initial={initial} readOnly />);
+    const cells = screen.getAllByRole("gridcell");
+
+    cells[0]!.focus();
+    fireEvent.keyDown(cells[0]!, { key: "ArrowDown" });
+    expect(document.activeElement).toBe(cells[2]);
+    fireEvent.keyDown(cells[2]!, { key: "5" });
+    expect(cells[2]).toHaveAccessibleName("Aid-mémoire cell 3, label 3, empty");
+  });
+
+  it("edits labels, reflows, clears entries and resets with confirmation", async () => {
+    const user = userEvent.setup();
+    vi.spyOn(window, "confirm").mockReturnValue(true);
+    render(<Harness />);
+
+    const label = screen.getByLabelText("Selected cell label");
+    await user.clear(label);
+    await user.type(label, "Pseudo A");
+    expect(
+      screen.getByRole("gridcell", {
+        name: "Aid-mémoire cell 1, label Pseudo A, empty",
+      }),
+    ).toBeInTheDocument();
+
+    await user.click(screen.getByText("Configure scratch layout"));
+    await user.click(screen.getByRole("button", { name: "Compact grid" }));
+    expect(screen.getByLabelText("Columns")).toHaveValue(3);
+    await user.click(screen.getByRole("button", { name: "Clear entries" }));
+    await user.click(screen.getByRole("button", { name: "Reset all" }));
+    expect(window.confirm).toHaveBeenCalledTimes(2);
+    expect(screen.getByLabelText("Columns")).toHaveValue(9);
+    expect(screen.getByLabelText("Selected cell label")).toHaveValue("1");
+  });
+});

tests/components/aidMemoireWorkbench.test.tsx

@@ -0,0 +1,139 @@
+import { render, screen, within } from "@testing-library/react";
+import userEvent from "@testing-library/user-event";
+import { beforeAll, describe, expect, it, vi } from "vitest";
+import { Workbench } from "../../src/components/Workbench";
+
+class WorkerStub {
+  addEventListener() {}
+  postMessage() {}
+  terminate() {}
+}
+
+beforeAll(() => {
+  vi.stubGlobal("Worker", WorkerStub);
+});
+
+function mainDigit(name: string) {
+  return within(screen.getByRole("group", { name: "Digits" })).getByRole(
+    "button",
+    { name },
+  );
+}
+
+describe("aid-mémoire Workbench integration", () => {
+  it("routes the shared keypad, undo and redo to a selected scratch cell", async () => {
+    const user = userEvent.setup();
+    render(<Workbench />);
+    const toggle = screen.getByLabelText("Show aid-mémoire scratch cells");
+    await user.click(toggle);
+
+    const grid = screen.getByRole("grid", {
+      name: "9 aid-mémoire scratch cells",
+    });
+    await user.click(
+      within(grid).getByRole("gridcell", {
+        name: "Aid-mémoire cell 1, label 1, empty",
+      }),
+    );
+    await user.click(mainDigit("5"));
+    expect(
+      within(grid).getByRole("gridcell", {
+        name: "Aid-mémoire cell 1, label 1, value 5",
+      }),
+    ).toBeInTheDocument();
+
+    await user.click(screen.getByRole("button", { name: "Undo" }));
+    expect(
+      within(grid).getByRole("gridcell", {
+        name: "Aid-mémoire cell 1, label 1, empty",
+      }),
+    ).toBeInTheDocument();
+    await user.click(screen.getByRole("button", { name: "Redo" }));
+    expect(
+      within(grid).getByRole("gridcell", {
+        name: "Aid-mémoire cell 1, label 1, value 5",
+      }),
+    ).toBeInTheDocument();
+
+    await user.click(toggle);
+    expect(
+      screen.queryByRole("grid", { name: "9 aid-mémoire scratch cells" }),
+    ).not.toBeInTheDocument();
+    await user.click(toggle);
+    expect(
+      screen.getByRole("gridcell", {
+        name: "Aid-mémoire cell 1, label 1, value 5",
+      }),
+    ).toBeInTheDocument();
+  });
+
+  it("restores scratch labels and entries from the local Library", async () => {
+    const user = userEvent.setup();
+    render(<Workbench />);
+    await user.click(screen.getByLabelText("Show aid-mémoire scratch cells"));
+    await user.clear(screen.getByLabelText("Selected cell label"));
+    await user.type(screen.getByLabelText("Selected cell label"), "Pseudo A");
+    await user.click(mainDigit("6"));
+
+    await user.click(screen.getByRole("button", { name: "Library" }));
+    await user.click(screen.getByRole("button", { name: "Save current" }));
+    expect(
+      await screen.findByText("Current puzzle and progress saved locally."),
+    ).toBeInTheDocument();
+    await user.click(screen.getByRole("button", { name: "Close" }));
+
+    await user.click(mainDigit("7"));
+    expect(
+      screen.getByRole("gridcell", {
+        name: "Aid-mémoire cell 1, label Pseudo A, value 7",
+      }),
+    ).toBeInTheDocument();
+    await user.click(screen.getByRole("button", { name: "Library" }));
+    await user.click(
+      await screen.findByRole("button", { name: /A first classic/u }),
+    );
+
+    expect(
+      screen.getByRole("gridcell", {
+        name: "Aid-mémoire cell 1, label Pseudo A, value 6",
+      }),
+    ).toBeInTheDocument();
+  });
+
+  it("restores scratch state with a savepoint and reverses that restore", async () => {
+    const user = userEvent.setup();
+    render(<Workbench />);
+    await user.click(screen.getByLabelText("Show aid-mémoire scratch cells"));
+    await user.click(mainDigit("5"));
+
+    await user.click(
+      screen.getByRole("button", { name: "History & branches" }),
+    );
+    await user.type(screen.getByLabelText("Savepoint name"), "Scratch five");
+    await user.click(screen.getByRole("button", { name: "Save current grid" }));
+    await user.click(screen.getByRole("button", { name: "Close" }));
+
+    await user.click(mainDigit("6"));
+    expect(
+      screen.getByRole("gridcell", {
+        name: "Aid-mémoire cell 1, label 1, value 6",
+      }),
+    ).toBeInTheDocument();
+    await user.click(
+      screen.getByRole("button", { name: "History & branches" }),
+    );
+    await user.click(screen.getByRole("button", { name: "Restore" }));
+    expect(
+      screen.getByRole("gridcell", {
+        name: "Aid-mémoire cell 1, label 1, value 5",
+      }),
+    ).toBeInTheDocument();
+
+    await user.click(screen.getByRole("button", { name: "Undo" }));
+    expect(
+      screen.getByRole("gridcell", {
+        name: "Aid-mémoire cell 1, label 1, value 6",
+      }),
+    ).toBeInTheDocument();
+  });
+});

tests/components/candidateLab.test.tsx

@@ -0,0 +1,100 @@
+import { render, screen, waitFor, within } from "@testing-library/react";
+import userEvent from "@testing-library/user-event";
+import { describe, expect, it, vi } from "vitest";
+import { CandidateLab } from "../../src/components/CandidateLab";
+import { createEmptyPuzzle, normalizePuzzle } from "../../src/domain";
+import type { CandidateOverlay } from "../../src/helpers";
+
+function mask(...values: number[]): number {
+  return values.reduce((result, value) => result | (1 << (value - 1)), 0);
+}
+
+const puzzle = normalizePuzzle(createEmptyPuzzle(4));
+
+describe("candidate lab", () => {
+  it("inspects selected cells, filters digits and focuses a link overlay", async () => {
+    const user = userEvent.setup();
+    const overlays: (CandidateOverlay | undefined)[] = [];
+    const candidateMasks = new Array<number>(16).fill(0);
+    candidateMasks[0] = mask(1, 2);
+    candidateMasks[1] = mask(1, 2);
+
+    render(
+      <CandidateLab
+        puzzle={puzzle}
+        values={puzzle.givens}
+        candidateMasks={candidateMasks}
+        selectedCells={[0]}
+        onOverlayChange={(overlay) => overlays.push(overlay)}
+      />,
+    );
+
+    const selected = screen.getByRole("heading", {
+      name: "Selected cells",
+    }).parentElement!;
+    expect(within(selected).getByText("r1c1")).toBeInTheDocument();
+    expect(within(selected).getByText("1 2")).toBeInTheDocument();
+
+    await user.click(
+      screen.getByRole("button", { name: "Filter candidate 1" }),
+    );
+    await waitFor(() => {
+      expect(overlays.at(-1)?.activeValues).toEqual([1]);
+      expect(overlays.at(-1)?.candidateCells).toEqual([0, 1]);
+    });
+
+    const link = screen.getByRole("button", { name: /r1c1\(1\).*r1c2\(1\)/u });
+    await user.click(link);
+    await waitFor(() => expect(overlays.at(-1)?.links).toHaveLength(1));
+    expect(link).toHaveAttribute("aria-pressed", "true");
+    await user.click(screen.getByRole("button", { name: "Show all" }));
+    expect(link).toHaveAttribute("aria-pressed", "false");
+  });
+
+  it("reveals weak links on demand within a chosen house", async () => {
+    const user = userEvent.setup();
+    const candidateMasks = new Array<number>(16).fill(0);
+    candidateMasks[0] = mask(3);
+    candidateMasks[1] = mask(3);
+    candidateMasks[2] = mask(3);
+
+    render(
+      <CandidateLab
+        puzzle={puzzle}
+        values={puzzle.givens}
+        candidateMasks={candidateMasks}
+        selectedCells={[0]}
+      />,
+    );
+
+    await user.selectOptions(
+      screen.getByLabelText("Candidate house scope"),
+      "unit:0",
+    );
+    await user.click(
+      screen.getByRole("button", { name: "Filter candidate 3" }),
+    );
+    expect(screen.getByText(/No links match this scope/u)).toBeInTheDocument();
+    await user.click(screen.getByRole("checkbox", { name: "Weak links" }));
+
+    expect(
+      screen.getAllByRole("button", { name: /weak · Row 1/u }),
+    ).toHaveLength(3);
+  });
+
+  it("clears the board overlay when it unmounts", async () => {
+    const onOverlayChange = vi.fn();
+    const { unmount } = render(
+      <CandidateLab
+        puzzle={puzzle}
+        values={puzzle.givens}
+        candidateMasks={new Array<number>(16).fill(0)}
+        selectedCells={[0]}
+        onOverlayChange={onOverlayChange}
+      />,
+    );
+    await waitFor(() => expect(onOverlayChange).toHaveBeenCalled());
+    unmount();
+    expect(onOverlayChange).toHaveBeenLastCalledWith(undefined);
+  });
+});

tests/components/gameplayHistoryWorkbench.test.tsx

@@ -0,0 +1,104 @@
+import { fireEvent, render, screen, within } from "@testing-library/react";
+import userEvent from "@testing-library/user-event";
+import { beforeAll, describe, expect, it, vi } from "vitest";
+import { Workbench } from "../../src/components/Workbench";
+
+class WorkerStub {
+  addEventListener() {}
+  postMessage() {}
+  terminate() {}
+}
+
+beforeAll(() => {
+  vi.stubGlobal("Worker", WorkerStub);
+});
+
+function digitButton(name: string) {
+  return within(screen.getByRole("group", { name: "Digits" })).getByRole(
+    "button",
+    { name },
+  );
+}
+
+describe("gameplay history integration", () => {
+  it("restores savepoints and preserves discarded hypotheses for replay", async () => {
+    const user = userEvent.setup();
+    render(<Workbench />);
+
+    fireEvent.pointerDown(
+      screen.getByRole("gridcell", {
+        name: "Row 1, column 3, empty",
+      }),
+      { buttons: 1 },
+    );
+    await user.click(digitButton("2"));
+
+    await user.click(
+      screen.getByRole("button", { name: "History & branches" }),
+    );
+    expect(
+      screen.getByRole("heading", {
+        name: "Branches, savepoints and replay",
+      }),
+    ).toBeInTheDocument();
+    await user.type(screen.getByLabelText("Savepoint name"), "After two");
+    await user.click(screen.getByRole("button", { name: "Save current grid" }));
+    expect(screen.getByText("After two")).toBeInTheDocument();
+    await user.click(screen.getByRole("button", { name: "Close" }));
+
+    await user.click(digitButton("3"));
+    expect(
+      screen.getByRole("gridcell", { name: "Row 1, column 3, 3" }),
+    ).toBeInTheDocument();
+    await user.click(
+      screen.getByRole("button", { name: "History & branches" }),
+    );
+    await user.click(screen.getByRole("button", { name: "Restore" }));
+    expect(
+      screen.getByRole("gridcell", { name: "Row 1, column 3, 2" }),
+    ).toBeInTheDocument();
+
+    await user.click(
+      screen.getByRole("button", { name: "History & branches" }),
+    );
+    await user.type(screen.getByLabelText("Hypothesis name"), "Try three");
+    await user.click(screen.getByRole("button", { name: "Start hypothesis" }));
+    expect(
+      screen.getByRole("button", { name: "Hypothesis: Try three" }),
+    ).toBeInTheDocument();
+    await user.click(digitButton("3"));
+
+    await user.click(
+      screen.getByRole("button", { name: "Hypothesis: Try three" }),
+    );
+    await user.click(
+      screen.getByRole("button", { name: "Discard and return" }),
+    );
+    expect(
+      screen.getByRole("gridcell", { name: "Row 1, column 3, 2" }),
+    ).toBeInTheDocument();
+
+    await user.click(
+      screen.getByRole("button", { name: "History & branches" }),
+    );
+    expect(screen.getByText("discarded")).toBeInTheDocument();
+    await user.click(
+      within(screen.getByRole("list", { name: "Solve history" })).getAllByRole(
+        "button",
+        { name: /Set r1c3 to 3/u },
+      )[0]!,
+    );
+    expect(
+      screen.getByRole("heading", { name: "Set r1c3 to 3" }),
+    ).toBeInTheDocument();
+    expect(
+      screen.getByRole("gridcell", { name: "Row 1, column 3, 3" }),
+    ).toBeInTheDocument();
+    await user.click(
+      screen.getByRole("button", { name: "Return to live grid" }),
+    );
+    expect(
+      screen.getByRole("gridcell", { name: "Row 1, column 3, 2" }),
+    ).toBeInTheDocument();
+  }, 15_000);
+});

tests/components/generatorWorkspace.test.tsx

@@ -59,4 +59,42 @@ describe("Sudoku generator workspace", () => {
     );
     expect(onRate).toHaveBeenCalledOnce();
   });
+
+  it("submits a bounded evidence-backed practice target", async () => {
+    const user = userEvent.setup();
+    const onGenerate = vi.fn();
+    render(
+      <GeneratorWorkspace
+        busy={false}
+        onGenerate={onGenerate}
+        onRate={vi.fn()}
+      />,
+    );
+
+    await user.selectOptions(
+      screen.getByLabelText("Practice technique"),
+      "x-wing",
+    );
+    const attempts = screen.getByLabelText("Mining attempts");
+    await user.clear(attempts);
+    await user.type(attempts, "7");
+    await user.clear(screen.getByLabelText("Seed"));
+    await user.type(screen.getByLabelText("Seed"), "x-wing-training");
+    await user.click(screen.getByRole("button", { name: "Generate Classic" }));
+
+    expect(onGenerate).toHaveBeenCalledWith(
+      expect.objectContaining({
+        requiredTechnique: "x-wing",
+        maxTechniqueAttempts: 7,
+        seed: "x-wing-training",
+      }),
+    );
+
+    await user.selectOptions(screen.getByLabelText("Variant"), "killer");
+    expect(
+      within(screen.getByLabelText("Practice technique")).getByRole("option", {
+        name: "Killer Cage",
+      }),
+    ).toBeInTheDocument();
+  });
 });

tests/components/helpersWorkspace.test.tsx

@@ -0,0 +1,117 @@
+import { render, screen, within } from "@testing-library/react";
+import userEvent from "@testing-library/user-event";
+import { describe, expect, it } from "vitest";
+import { HelpersWorkspace } from "../../src/components/HelpersWorkspace";
+import { createEmptyPuzzle, normalizePuzzle } from "../../src/domain";
+
+function mask(...digits: number[]): number {
+  return digits.reduce((value, digit) => value | (2 ** (digit - 1)), 0);
+}
+
+describe("Sum Lab helper", () => {
+  const puzzle = normalizePuzzle(createEmptyPuzzle(9));
+
+  it("eliminates and restores combinations without changing the inputs", async () => {
+    const user = userEvent.setup();
+    render(
+      <HelpersWorkspace
+        size={9}
+        puzzle={puzzle}
+        values={puzzle.givens}
+        selectedCells={[]}
+        candidateMasks={Array<number>(81).fill(0)}
+      />,
+    );
+
+    await user.click(screen.getByRole("tab", { name: "Sum Lab" }));
+    expect(
+      screen.getByRole("heading", { name: "Generalized Sum Lab" }),
+    ).toBeInTheDocument();
+    expect(screen.getByText("4", { selector: "strong" })).toBeInTheDocument();
+
+    const combination = screen.getByRole("button", {
+      name: "1 + 9; eliminate",
+    });
+    await user.click(combination);
+
+    expect(
+      screen.getByRole("button", { name: "1 + 9; restore" }),
+    ).toHaveAttribute("aria-pressed", "true");
+    expect(
+      screen.getByText("3", { selector: ".metric-row strong" }).parentElement,
+    ).toHaveTextContent("3 active of 4");
+    expect(screen.getByRole("button", { name: "Restore all" })).toBeEnabled();
+
+    await user.click(screen.getByRole("button", { name: "Restore all" }));
+    expect(
+      screen.getByRole("button", { name: "1 + 9; eliminate" }),
+    ).toHaveAttribute("aria-pressed", "false");
+  });
+
+  it("filters through selected board-cell candidate masks", async () => {
+    const user = userEvent.setup();
+    const candidateMasks = Array<number>(81).fill(0);
+    candidateMasks[0] = mask(1, 2);
+    candidateMasks[1] = mask(8, 9);
+    render(
+      <HelpersWorkspace
+        size={9}
+        puzzle={puzzle}
+        values={puzzle.givens}
+        selectedCells={[0, 1]}
+        candidateMasks={candidateMasks}
+      />,
+    );
+
+    await user.click(screen.getByRole("tab", { name: "Sum Lab" }));
+    await user.click(
+      screen.getByRole("checkbox", {
+        name: "Use 2 board cells and candidates",
+      }),
+    );
+
+    const positions = screen.getByRole("list");
+    expect(within(positions).getByText("r1c1: 1 2")).toBeInTheDocument();
+    expect(within(positions).getByText("r1c2: 8 9")).toBeInTheDocument();
+    expect(
+      screen.queryByRole("button", { name: "3 + 7; eliminate" }),
+    ).not.toBeInTheDocument();
+  });
+
+  it("resets digit bounds when the puzzle size changes", async () => {
+    const user = userEvent.setup();
+    const { rerender } = render(
+      <HelpersWorkspace
+        key={9}
+        size={9}
+        puzzle={puzzle}
+        values={puzzle.givens}
+        selectedCells={[]}
+        candidateMasks={Array<number>(81).fill(0)}
+      />,
+    );
+
+    await user.click(screen.getByRole("tab", { name: "Sum Lab" }));
+    expect(
+      screen.getByRole("spinbutton", { name: "Maximum digit" }),
+    ).toHaveValue(9);
+
+    const smallerPuzzle = normalizePuzzle(createEmptyPuzzle(4));
+    rerender(
+      <HelpersWorkspace
+        key={4}
+        size={4}
+        puzzle={smallerPuzzle}
+        values={smallerPuzzle.givens}
+        selectedCells={[]}
+        candidateMasks={Array<number>(16).fill(0)}
+      />,
+    );
+
+    await user.click(screen.getByRole("tab", { name: "Sum Lab" }));
+    expect(
+      screen.getByRole("spinbutton", { name: "Maximum digit" }),
+    ).toHaveValue(4);
+    expect(screen.queryByRole("alert")).not.toBeInTheDocument();
+  });
+});

tests/components/importExportDialog.test.tsx

@@ -0,0 +1,186 @@
+import { fireEvent, render, screen } from "@testing-library/react";
+import userEvent from "@testing-library/user-event";
+import { describe, expect, it, vi } from "vitest";
+import { ImportExportDialog } from "../../src/components/ImportExportDialog";
+import { createEmptyPuzzle } from "../../src/domain";
+import type { PuzzleDefinition } from "../../src/domain/types";
+import { fromDomainPuzzle } from "../../src/formats";
+import type { PortableAidMemoire } from "../../src/state/aidMemoire";
+import { createSession } from "../../src/state/session";
+
+const TEST_AID_MEMOIRE: PortableAidMemoire = {
+  version: 1,
+  enabled: true,
+  columns: 1,
+  cells: [
+    {
+      label: "A",
+      value: 2,
+      cornerMarks: [],
+      centerMarks: [],
+      color: 3,
+    },
+  ],
+};
+
+function localScl(overrides: Record<string, unknown> = {}) {
+  const cells = Array.from({ length: 4 }, () =>
+    Array.from({ length: 4 }, () => ({})),
+  );
+  cells[0]![0] = { value: 1 };
+  return JSON.stringify({
+    id: "synthetic-local-test",
+    cells,
+    metadata: { title: "Synthetic local puzzle" },
+    ...overrides,
+  });
+}
+
+function renderDialog(
+  options: {
+    readonly puzzle?: PuzzleDefinition;
+    readonly aidMemoire?: PortableAidMemoire;
+  } = {},
+) {
+  const puzzle = options.puzzle ?? createEmptyPuzzle(4);
+  const onClose = vi.fn();
+  const onImport = vi.fn();
+  render(
+    <ImportExportDialog
+      open
+      puzzle={puzzle}
+      session={createSession(puzzle.givens)}
+      aidMemoire={options.aidMemoire}
+      onClose={onClose}
+      onImport={onImport}
+    />,
+  );
+  return { onClose, onImport };
+}
+
+describe("ImportExportDialog interoperability", () => {
+  it("reports a detected compatible format before importing it", async () => {
+    const user = userEvent.setup();
+    const { onClose, onImport } = renderDialog();
+    fireEvent.change(screen.getByPlaceholderText(/Paste 81 characters/u), {
+      target: { value: localScl() },
+    });
+
+    await user.click(
+      screen.getByRole("button", { name: "Check compatibility" }),
+    );
+    expect(
+      await screen.findByText(
+        /SudokuPad\/CTC JSON: 4×4, 1 givens and 0 constraints/u,
+      ),
+    ).toBeInTheDocument();
+
+    await user.click(screen.getByRole("button", { name: "Import locally" }));
+    expect(onImport).toHaveBeenCalledWith(
+      expect.objectContaining({ size: 4, givens: expect.any(Array) }),
+      expect.any(Object),
+    );
+    expect(onClose).toHaveBeenCalledOnce();
+  });
+
+  it("reports unsupported constructs and never fetches short IDs", async () => {
+    const user = userEvent.setup();
+    const fetchSpy = vi.fn();
+    vi.stubGlobal("fetch", fetchSpy);
+    renderDialog();
+    const input = screen.getByPlaceholderText(/Paste 81 characters/u);
+
+    fireEvent.change(input, {
+      target: { value: localScl({ overlays: [{ text: "visual only" }] }) },
+    });
+    await user.click(
+      screen.getByRole("button", { name: "Check compatibility" }),
+    );
+    expect(await screen.findByText(/visual overlays/u)).toBeInTheDocument();
+
+    fireEvent.change(input, {
+      target: { value: "https://sudokupad.app/serverOnly42" },
+    });
+    await user.click(
+      screen.getByRole("button", { name: "Check compatibility" }),
+    );
+    expect(
+      await screen.findByText(/server-hosted SudokuPad puzzle ID/u),
+    ).toBeInTheDocument();
+    expect(fetchSpy).not.toHaveBeenCalled();
+    vi.unstubAllGlobals();
+  });
+
+  it("downloads the current puzzle as a self-contained SVG", async () => {
+    const user = userEvent.setup();
+    let downloaded: Blob | undefined;
+    vi.mocked(URL.createObjectURL).mockImplementation((value) => {
+      downloaded = value as Blob;
+      return "blob:visual-export-test";
+    });
+    vi.spyOn(HTMLAnchorElement.prototype, "click").mockImplementation(() => {});
+    renderDialog();
+
+    await user.click(screen.getByRole("button", { name: "Download SVG" }));
+    expect(
+      await screen.findByText("SVG rendered and downloaded locally."),
+    ).toBeInTheDocument();
+    expect(downloaded?.type).toContain("image/svg+xml");
+    expect(await downloaded?.text()).toContain("<svg");
+  });
+
+  it("round-trips aid-mémoire progress through project import and export", async () => {
+    const user = userEvent.setup();
+    const puzzle = createEmptyPuzzle(4);
+    const { onImport } = renderDialog({
+      puzzle,
+      aidMemoire: TEST_AID_MEMOIRE,
+    });
+    let downloaded: Blob | undefined;
+    vi.mocked(URL.createObjectURL).mockImplementation((value) => {
+      downloaded = value as Blob;
+      return "blob:project-export-test";
+    });
+    vi.spyOn(HTMLAnchorElement.prototype, "click").mockImplementation(() => {});
+
+    await user.click(
+      screen.getByRole("button", { name: "Download project JSON" }),
+    );
+    expect(
+      await screen.findByText("Project JSON downloaded locally."),
+    ).toBeInTheDocument();
+    expect(JSON.parse((await downloaded?.text()) ?? "{}").aidMemoire).toEqual(
+      TEST_AID_MEMOIRE,
+    );
+
+    const importedDocument = {
+      ...fromDomainPuzzle(puzzle),
+      aidMemoire: TEST_AID_MEMOIRE,
+    };
+    fireEvent.change(screen.getByPlaceholderText(/Paste 81 characters/u), {
+      target: { value: JSON.stringify(importedDocument) },
+    });
+    await user.click(screen.getByRole("button", { name: "Import locally" }));
+    expect(onImport).toHaveBeenCalledWith(
+      expect.objectContaining({ size: 4 }),
+      expect.objectContaining({ aidMemoire: TEST_AID_MEMOIRE }),
+    );
+  });
+
+  it("reports an f-puzzles export incompatibility without throwing", async () => {
+    const user = userEvent.setup();
+    renderDialog({
+      puzzle: {
+        ...createEmptyPuzzle(4),
+        constraints: [{ type: "xv", a: 0, b: 1, total: 5, negated: true }],
+      },
+    });
+
+    await user.click(
+      screen.getByRole("button", { name: "Download f-puzzles JSON" }),
+    );
+    expect(
+      await screen.findByText(/cannot preserve an individually false clue/u),
+    ).toBeInTheDocument();
+  });
+});

tests/components/solveWorkspace.test.tsx

@@ -0,0 +1,44 @@
+import { render, screen } from "@testing-library/react";
+import { describe, expect, it, vi } from "vitest";
+import { SolveWorkspace } from "../../src/components/SolveWorkspace";
+import type { ExactSolveResult } from "../../src/solver";
+
+const limited: ExactSolveResult = {
+  solutions: [],
+  count: 0,
+  truncated: true,
+  limitReason: "timeout",
+  nodes: 100,
+  elapsedMs: 10_000,
+};
+
+describe("solve result reporting", () => {
+  it("does not report zero solutions at a safety limit as unsatisfiable", () => {
+    const props = {
+      size: 9,
+      busy: false,
+      onLogical: vi.fn(),
+      onExact: vi.fn(),
+      onApplyValues: vi.fn(),
+      onFocusCells: vi.fn(),
+    };
+    const { rerender } = render(<SolveWorkspace {...props} exact={limited} />);
+
+    expect(
+      screen.getByText(/solvability is not established/u),
+    ).toBeInTheDocument();
+    expect(
+      screen.queryByText("No completion satisfies every supported rule."),
+    ).not.toBeInTheDocument();
+
+    rerender(
+      <SolveWorkspace
+        {...props}
+        exact={{ ...limited, truncated: false, limitReason: undefined }}
+      />,
+    );
+    expect(
+      screen.getByText("No completion satisfies every supported rule."),
+    ).toBeInTheDocument();
+  });
+});

tests/components/sudokuBoard.test.tsx

@@ -1,4 +1,4 @@
-import { render } from "@testing-library/react";
+import { render, screen } from "@testing-library/react";
 import { describe, expect, it, vi } from "vitest";
 import { normalizePuzzle } from "../../src/domain";
 import { SudokuBoard } from "../../src/components/SudokuBoard";
@@ -41,4 +41,178 @@ describe("Sudoku board constraint visuals", () => {
       container.querySelector(".constraint-inequality-tip"),
     ).toBeInTheDocument();
   });
+
+  it("renders false local clues and combines dual-purpose outside labels", () => {
+    const puzzle = normalizePuzzle({
+      version: 1,
+      size: 4,
+      givens: new Array<number>(16).fill(0),
+      constraints: [
+        { type: "maximum", cell: 5, negated: true },
+        { type: "thermo", cells: [8, 9], negated: true },
+        {
+          type: "quadruple",
+          cells: [0, 1, 4, 5],
+          digits: [1, 3],
+          negated: true,
+        },
+        {
+          type: "x-sum",
+          side: "top",
+          index: 0,
+          sum: 42,
+          negated: true,
+        },
+        {
+          type: "skyscraper",
+          side: "top",
+          index: 0,
+          count: 42,
+          negated: true,
+        },
+      ],
+    });
+
+    const { container } = render(
+      <SudokuBoard
+        puzzle={puzzle}
+        values={puzzle.givens}
+        selected={new Set([0])}
+        activeCell={0}
+        onCellPointerDown={vi.fn()}
+        onCellPointerEnter={vi.fn()}
+        onKeyDown={vi.fn()}
+      />,
+    );
+
+    expect(container.querySelector(".sudoku-board-frame")).toHaveClass(
+      "has-outside-clues",
+    );
+    expect(container.querySelectorAll(".constraint-outside")).toHaveLength(1);
+    expect(container.querySelector(".outside-clue-kinds")).toHaveTextContent(
+      "Σ · ▥",
+    );
+    expect(container.querySelector(".outside-clue-value")).toHaveTextContent(
+      "≠42",
+    );
+    expect(container.querySelectorAll(".is-negated")).toHaveLength(4);
+    expect(
+      container.querySelector(".constraint-thermo.is-negated polyline"),
+    ).toBeInTheDocument();
+    expect(
+      container.querySelector(".constraint-thermo .constraint-false-mark"),
+    ).toHaveTextContent("≠");
+
+    const board = screen.getByRole("grid", { name: "4 by 4 Sudoku grid" });
+    expect(board).toHaveAccessibleDescription(
+      expect.stringContaining("False clue: X-sum 42 from the top, column 1."),
+    );
+    expect(board).toHaveAccessibleDescription(
+      expect.stringContaining("False clue: maximum at row 2, column 2."),
+    );
+  });
+
+  it("renders candidate filters and strong/weak graph overlays", () => {
+    const puzzle = normalizePuzzle({
+      version: 1,
+      size: 4,
+      givens: new Array<number>(16).fill(0),
+    });
+    const { container } = render(
+      <SudokuBoard
+        puzzle={puzzle}
+        values={puzzle.givens}
+        selected={new Set([0])}
+        activeCell={0}
+        candidateOverlay={{
+          activeValues: [1],
+          candidateCells: [0, 1],
+          links: [
+            {
+              id: "strong",
+              kind: "strong",
+              a: { cell: 0, value: 1 },
+              b: { cell: 1, value: 1 },
+              contexts: [{ kind: "house", label: "Row 1" }],
+            },
+            {
+              id: "weak",
+              kind: "weak",
+              a: { cell: 0, value: 2 },
+              b: { cell: 0, value: 3 },
+              contexts: [{ kind: "cell", label: "Cell r1c1" }],
+            },
+          ],
+        }}
+        onCellPointerDown={vi.fn()}
+        onCellPointerEnter={vi.fn()}
+        onKeyDown={vi.fn()}
+      />,
+    );
+
+    expect(
+      container.querySelectorAll(".is-candidate-highlighted"),
+    ).toHaveLength(2);
+    expect(
+      container.querySelectorAll(".candidate-overlay-link--strong"),
+    ).toHaveLength(1);
+    expect(
+      container.querySelectorAll(".candidate-overlay-link--weak"),
+    ).toHaveLength(1);
+    expect(container.querySelectorAll(".candidate-overlay-node")).toHaveLength(
+      4,
+    );
+  });
+
+  it("exposes real row semantics and detailed per-cell state", () => {
+    const puzzle = normalizePuzzle({
+      version: 1,
+      size: 4,
+      givens: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
+      constraints: [{ type: "killer-cage", cells: [0, 1], sum: 3 }],
+    });
+    render(
+      <SudokuBoard
+        puzzle={puzzle}
+        values={[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]}
+        cornerMarks={[0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]}
+        centerMarks={new Array<number>(16).fill(0)}
+        candidates={[0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]}
+        colors={[0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]}
+        selected={new Set([1])}
+        conflicts={new Set([1])}
+        activeCell={1}
+        showCandidates
+        onCellPointerDown={vi.fn()}
+        onCellPointerEnter={vi.fn()}
+        onKeyDown={vi.fn()}
+      />,
+    );
+
+    const board = screen.getByRole("grid", { name: "4 by 4 Sudoku grid" });
+    expect(board).toHaveAttribute("aria-rowcount", "4");
+    expect(board).toHaveAttribute("aria-colcount", "4");
+    expect(board).toHaveAccessibleDescription(
+      expect.stringContaining("Home and End move to the first and last cell"),
+    );
+    expect(screen.getAllByRole("row")).toHaveLength(4);
+    const given = screen.getByRole("gridcell", {
+      name: "Row 1, column 1, 1",
+    });
+    expect(given).toHaveAttribute("aria-readonly", "true");
+    expect(given).toHaveAccessibleDescription(
+      expect.stringMatching(/region 1.*given digit.*killer cage 3/i),
+    );
+    const annotated = screen.getByRole("gridcell", {
+      name: "Row 1, column 2, empty",
+    });
+    expect(annotated).toHaveAccessibleDescription(
+      expect.stringMatching(
+        /region 1.*corner notes 1.*automatic candidates 1, 2.*colour 2.*conflict/i,
+      ),
+    );
+    expect(annotated).toHaveAttribute("aria-colindex", "2");
+    expect(annotated).toHaveAttribute("aria-invalid", "true");
+    expect(annotated).toHaveAttribute("aria-selected", "true");
+  });
 });

tests/components/workbench.test.tsx

@@ -63,6 +63,34 @@ describe("Sudoku workbench", () => {
     expect(undo).toBeDisabled();
   });
 
+  it("supports non-wrapping WAI-ARIA grid navigation", () => {
+    render(<Workbench />);
+
+    const grid = screen.getByRole("grid", { name: "9 by 9 Sudoku grid" });
+    const cell = (row: number, column: number) =>
+      within(grid).getByRole("gridcell", {
+        name: new RegExp(`^Row ${String(row)}, column ${String(column)},`, "u"),
+      });
+
+    cell(1, 1).focus();
+    fireEvent.keyDown(cell(1, 1), { key: "ArrowLeft" });
+    expect(cell(1, 1)).toHaveAttribute("tabindex", "0");
+
+    fireEvent.keyDown(cell(1, 1), { key: "End" });
+    expect(cell(1, 9)).toHaveAttribute("tabindex", "0");
+    fireEvent.keyDown(cell(1, 9), { key: "ArrowRight" });
+    expect(cell(1, 9)).toHaveAttribute("tabindex", "0");
+
+    fireEvent.keyDown(cell(1, 9), { key: "ArrowDown" });
+    expect(cell(2, 9)).toHaveAttribute("tabindex", "0");
+    fireEvent.keyDown(cell(2, 9), { key: "Home" });
+    expect(cell(2, 1)).toHaveAttribute("tabindex", "0");
+    fireEvent.keyDown(cell(2, 1), { key: "PageDown" });
+    expect(cell(9, 1)).toHaveAttribute("tabindex", "0");
+    fireEvent.keyDown(cell(9, 1), { key: "Home", ctrlKey: true });
+    expect(cell(1, 1)).toHaveAttribute("tabindex", "0");
+  });
+
   it("shows digit progress and toggles matching-digit highlights separately from selection", async () => {
     const user = userEvent.setup();
     render(<Workbench />);
@@ -124,6 +152,30 @@ describe("Sudoku workbench", () => {
       screen.getByRole("button", { name: "Remove selected cage" }),
     );
     expect(screen.queryByText("4 cage · 2 cells")).not.toBeInTheDocument();
+
+    await user.click(screen.getByLabelText("Cage digits may repeat"));
+    await user.click(
+      screen.getByLabelText("Newly added clues must be false (Wrogn mode)"),
+    );
+    await user.clear(cageSum);
+    await user.type(cageSum, "2");
+    await user.click(
+      screen.getByRole("button", { name: "Add / replace cage" }),
+    );
+    expect(
+      screen.getByText("false · 2 cage · 2 cells · repeats allowed"),
+    ).toBeInTheDocument();
+
+    await user.click(screen.getByLabelText("Cage digits may repeat"));
+    await user.clear(cageSum);
+    await user.type(cageSum, "3");
+    await user.click(
+      screen.getByRole("button", { name: "Add / replace cage" }),
+    );
+    expect(
+      screen.queryByText("false · 2 cage · 2 cells · repeats allowed"),
+    ).not.toBeInTheDocument();
+    expect(screen.getByText("false · 3 cage · 2 cells")).toBeInTheDocument();
   });
 
   it("opens the expanded built-in variant examples", async () => {
@@ -157,6 +209,66 @@ describe("Sudoku workbench", () => {
     expect(
       container.querySelector(".constraint-xv--10 text"),
     ).toHaveTextContent("10");
+
+    await user.selectOptions(
+      screen.getByLabelText("Open built-in puzzle"),
+      "truth-and-lies",
+    );
+    expect(
+      screen.getByRole("heading", { name: "Truth and lies" }),
+    ).toBeInTheDocument();
+    expect(container.querySelectorAll(".constraint-outside")).toHaveLength(4);
+    expect(container.querySelectorAll(".constraint-quadruple")).toHaveLength(2);
+    expect(container.querySelectorAll(".constraint-maximum")).toHaveLength(2);
+  });
+
+  it("sets and batch-toggles false local and outside clues", async () => {
+    const user = userEvent.setup();
+    const { container } = render(<Workbench />);
+
+    await user.click(screen.getByRole("button", { name: "New blank" }));
+    expect(
+      screen.getByRole("button", { name: "Add quadruple" }),
+    ).toBeDisabled();
+    await user.clear(screen.getByLabelText("Quadruple digits"));
+    await user.type(screen.getByLabelText("Quadruple digits"), "1");
+    expect(
+      screen.getByRole("button", { name: "Add quadruple" }),
+    ).toBeDisabled();
+    await user.click(
+      screen.getByLabelText("Newly added clues must be false (Wrogn mode)"),
+    );
+    await user.click(screen.getByRole("button", { name: "Maximum cell" }));
+    await user.click(
+      screen.getByRole("button", { name: "Add / replace outside clue" }),
+    );
+
+    expect(screen.getByText("false · maximum · r1c1")).toBeInTheDocument();
+    expect(screen.getByText("false · Σ3 · top 1")).toBeInTheDocument();
+    expect(
+      screen.getByRole("button", {
+        name: "Require true for false · maximum · r1c1",
+      }),
+    ).toBeInTheDocument();
+    expect(
+      screen.getByRole("button", {
+        name: "Remove false · Σ3 · top 1",
+      }),
+    ).toBeInTheDocument();
+    expect(container.querySelectorAll(".is-negated")).toHaveLength(2);
+
+    await user.clear(screen.getByLabelText("Clue"));
+    await user.type(screen.getByLabelText("Clue"), "6562");
+    expect(
+      screen.getByRole("button", { name: "Add / replace outside clue" }),
+    ).toBeDisabled();
+
+    await user.click(
+      screen.getByRole("button", { name: "Make all clues true" }),
+    );
+    expect(screen.getByText("maximum · r1c1")).toBeInTheDocument();
+    expect(screen.getByText("Σ3 · top 1")).toBeInTheDocument();
+    expect(container.querySelectorAll(".is-negated")).toHaveLength(0);
   });
 
   it("switches between setting, solving, playing and helper workspaces", async () => {
@@ -206,6 +318,38 @@ describe("Sudoku workbench", () => {
     ).toBeInTheDocument();
   });
 
+  it("projects candidate filters and links onto the board only while inspecting", async () => {
+    const user = userEvent.setup();
+    const { container } = render(<Workbench />);
+
+    await user.click(screen.getByRole("button", { name: "Helpers" }));
+    await user.click(screen.getByRole("tab", { name: "Candidate links" }));
+    expect(
+      screen.getByRole("heading", { name: "Links and houses" }),
+    ).toBeInTheDocument();
+
+    await user.click(screen.getByRole("checkbox", { name: "Weak links" }));
+    expect(
+      container.querySelector(".candidate-link-layer"),
+    ).toBeInTheDocument();
+
+    await user.click(
+      screen.getByRole("button", { name: "Filter candidate 1" }),
+    );
+    expect(
+      container.querySelectorAll(".sudoku-cell.is-candidate-highlighted")
+        .length,
+    ).toBeGreaterThan(0);
+
+    await user.click(screen.getByRole("button", { name: "Play" }));
+    expect(
+      container.querySelector(".candidate-link-layer"),
+    ).not.toBeInTheDocument();
+    expect(
+      container.querySelectorAll(".sudoku-cell.is-candidate-highlighted"),
+    ).toHaveLength(0);
+  });
+
   it("makes the import boundary and self-contained local sharing explicit", async () => {
     const user = userEvent.setup();
     const fetchSpy = vi.fn();

tests/data/samples.test.ts

@@ -11,11 +11,16 @@ import {
 } from "../../src/solver";
 
 describe("bundled original samples", () => {
-  it.each(SAMPLE_PUZZLES)("ships $title as a unique puzzle", (puzzle) => {
+  const fastUniquenessSamples = SAMPLE_CATALOG.map(({ puzzle }) => puzzle);
-    const result = solveExact(puzzle, { maxSolutions: 2 });
+
-    expect(result.count).toBe(1);
+  it.each(fastUniquenessSamples)(
-    expect(result.truncated).toBe(false);
+    "ships $title as a unique puzzle",
-  });
+    (puzzle) => {
+      const result = solveExact(puzzle, { maxSolutions: 2 });
+      expect(result.count).toBe(1);
+      expect(result.truncated).toBe(false);
+    },
+  );
 
   it("solves the generated classic with the supported logical techniques", () => {
     expect(solveLogically(CLASSIC_SAMPLE).status).toBe("solved");
@@ -50,6 +55,10 @@ describe("bundled original samples", () => {
         "inequality",
         "renban",
         "palindrome",
+        "x-sum",
+        "skyscraper",
+        "quadruple",
+        "maximum",
       ]),
     );
   });

tests/domain/extraBusyConstraints.test.ts

@@ -0,0 +1,505 @@
+import { describe, expect, it } from "vitest";
+import {
+  candidatesForCell,
+  classicRegions,
+  compilePuzzle,
+  constraintIsFeasible,
+  findConflicts,
+  normalizePuzzle,
+  validatePuzzle,
+  type PuzzleDefinition,
+  type VariantConstraint,
+} from "../../src/domain";
+
+const solved4 = [1, 2, 3, 4, 3, 4, 1, 2, 4, 3, 2, 1, 2, 1, 4, 3] as const;
+
+function puzzle4(constraints: readonly VariantConstraint[]): PuzzleDefinition {
+  return {
+    version: 1,
+    size: 4,
+    givens: new Array<number>(16).fill(0),
+    regions: classicRegions(4),
+    constraints,
+  };
+}
+
+describe("outside and local clue constraints", () => {
+  it("strictly validates and clones every new bounded shape", () => {
+    const constraints: VariantConstraint[] = [
+      { type: "x-sum", side: "left", index: 0, sum: 6 },
+      { type: "skyscraper", side: "bottom", index: 1, count: 2 },
+      { type: "quadruple", cells: [1, 2, 5, 6], digits: [2, 2, 4] },
+      { type: "maximum", cell: 5 },
+    ];
+    const definition = puzzle4(constraints);
+    expect(validatePuzzle(definition)).toEqual({ valid: true, issues: [] });
+
+    const normalized = normalizePuzzle(definition);
+    expect(normalized.constraints).toEqual(constraints);
+    expect(normalized.constraints).not.toBe(constraints);
+    expect(normalized.constraints[2]).not.toBe(constraints[2]);
+
+    const malformed = [
+      { type: "x-sum", side: "near", index: 0, sum: 6 },
+      { type: "x-sum", side: "left", index: 4, sum: 6 },
+      { type: "x-sum", side: "left", index: 0, sum: 2 },
+      { type: "skyscraper", side: "top", index: 0, count: 0 },
+      { type: "quadruple", cells: [0, 1], digits: [1, 2, 3] },
+      { type: "quadruple", cells: [0, 2, 4, 6], digits: [1, 2] },
+      { type: "maximum", cell: 16 },
+      {
+        type: "maximum",
+        cell: 5,
+        negated: "yes",
+      },
+    ];
+    for (const constraint of malformed) {
+      expect(validatePuzzle(puzzle4([constraint as never])).valid).toBe(false);
+    }
+  });
+
+  it("allows bounded impossible numbers only for false numeric clues", () => {
+    expect(
+      validatePuzzle(
+        puzzle4([
+          {
+            type: "killer-cage",
+            cells: [0, 1, 2],
+            sum: 42,
+            negated: true,
+          },
+        ]),
+      ).valid,
+    ).toBe(true);
+    expect(
+      validatePuzzle(
+        puzzle4([{ type: "killer-cage", cells: [0, 1, 2], sum: 42 }]),
+      ).valid,
+    ).toBe(false);
+
+    for (const constraint of [
+      { type: "x-sum", side: "left", index: 0, sum: 42 },
+      { type: "skyscraper", side: "top", index: 0, count: 42 },
+    ] as const) {
+      expect(
+        validatePuzzle(puzzle4([{ ...constraint, negated: true }])).valid,
+      ).toBe(true);
+      expect(validatePuzzle(puzzle4([constraint])).valid).toBe(false);
+    }
+
+    expect(
+      validatePuzzle(
+        puzzle4([
+          {
+            type: "x-sum",
+            side: "left",
+            index: 0,
+            sum: 257,
+            negated: true,
+          },
+        ]),
+      ).valid,
+    ).toBe(false);
+  });
+
+  it("attaches outside clues to their full lines and local clues to every affected cell", () => {
+    const compiled = compilePuzzle(
+      normalizePuzzle(
+        puzzle4([
+          { type: "x-sum", side: "top", index: 1, sum: 6 },
+          { type: "skyscraper", side: "right", index: 2, count: 2 },
+          { type: "quadruple", cells: [1, 2, 5, 6], digits: [2] },
+          { type: "maximum", cell: 5 },
+        ]),
+      ),
+    );
+
+    expect(compiled.constraintsByCell[13]).toContain(0);
+    expect(compiled.constraintsByCell[8]).toContain(1);
+    expect(compiled.constraintsByCell[6]).toContain(2);
+    for (const cell of [5, 1, 9, 4, 6]) {
+      expect(compiled.constraintsByCell[cell]).toContain(3);
+    }
+  });
+
+  it("uses the first digit and exact distinct subset sums to prune X-sums", () => {
+    const constraint = {
+      type: "x-sum",
+      side: "left",
+      index: 0,
+      sum: 6,
+    } as const;
+    const values = new Array<number>(16).fill(0);
+    values[1] = 4;
+    expect(candidatesForCell(puzzle4([constraint]), values, 0)).toEqual([2]);
+
+    const reusedOutsidePrefix = new Array<number>(16).fill(0);
+    reusedOutsidePrefix.splice(0, 4, 3, 1, 0, 2);
+    expect(constraintIsFeasible(constraint, reusedOutsidePrefix, 4)).toBe(
+      false,
+    );
+
+    expect(
+      constraintIsFeasible(
+        { type: "x-sum", side: "left", index: 0, sum: 1 },
+        solved4,
+        4,
+      ),
+    ).toBe(true);
+    expect(
+      constraintIsFeasible(
+        { type: "x-sum", side: "bottom", index: 0, sum: 6 },
+        solved4,
+        4,
+      ),
+    ).toBe(true);
+    const conflict = findConflicts(
+      puzzle4([{ type: "x-sum", side: "left", index: 0, sum: 6 }]),
+      solved4,
+    ).find(({ kind }) => kind === "constraint");
+    expect(conflict?.cells).toEqual([0, 1, 2, 3]);
+  });
+
+  it("enforces exact skyscraper visibility and safely prunes partial lines", () => {
+    expect(
+      constraintIsFeasible(
+        { type: "skyscraper", side: "left", index: 0, count: 4 },
+        solved4,
+        4,
+      ),
+    ).toBe(true);
+    expect(
+      constraintIsFeasible(
+        { type: "skyscraper", side: "right", index: 0, count: 1 },
+        solved4,
+        4,
+      ),
+    ).toBe(true);
+    expect(
+      constraintIsFeasible(
+        { type: "skyscraper", side: "left", index: 0, count: 3 },
+        solved4,
+        4,
+      ),
+    ).toBe(false);
+
+    expect(
+      candidatesForCell(
+        puzzle4([{ type: "skyscraper", side: "left", index: 0, count: 1 }]),
+        new Array<number>(16).fill(0),
+        0,
+      ),
+    ).toEqual([4]);
+    const impossiblePrefix = new Array<number>(16).fill(0);
+    impossiblePrefix[0] = 2;
+    expect(
+      constraintIsFeasible(
+        { type: "skyscraper", side: "left", index: 0, count: 4 },
+        impossiblePrefix,
+        4,
+      ),
+    ).toBe(false);
+
+    expect(
+      constraintIsFeasible(
+        { type: "skyscraper", side: "top", index: 0, count: 8 },
+        new Array<number>(16 * 16).fill(0),
+        16,
+      ),
+    ).toBe(true);
+  });
+
+  it("honours quadruple multiplicity in candidates and completed boards", () => {
+    const constraint = {
+      type: "quadruple",
+      cells: [1, 2, 5, 6],
+      digits: [2, 2, 4],
+    } as const;
+    const values = new Array<number>(16).fill(0);
+    values[1] = 2;
+    values[2] = 3;
+    values[5] = 4;
+    expect(candidatesForCell(puzzle4([constraint]), values, 6)).toEqual([2]);
+
+    const wrong = [...values];
+    wrong[6] = 1;
+    expect(constraintIsFeasible(constraint, wrong, 4)).toBe(false);
+    const right = [...values];
+    right[6] = 2;
+    expect(constraintIsFeasible(constraint, right, 4)).toBe(true);
+  });
+
+  it("prunes false clues as soon as their positive statement is fixed", () => {
+    const xSumValues = new Array<number>(16).fill(0);
+    xSumValues.splice(0, 3, 3, 1, 2);
+    expect(
+      constraintIsFeasible(
+        { type: "x-sum", side: "left", index: 0, sum: 6, negated: true },
+        xSumValues,
+        4,
+      ),
+    ).toBe(false);
+    expect(
+      constraintIsFeasible(
+        { type: "x-sum", side: "left", index: 0, sum: 7, negated: true },
+        xSumValues,
+        4,
+      ),
+    ).toBe(true);
+
+    const quadrupleValues = new Array<number>(16).fill(0);
+    quadrupleValues[0] = 1;
+    quadrupleValues[1] = 2;
+    expect(
+      constraintIsFeasible(
+        {
+          type: "quadruple",
+          cells: [0, 1, 4, 5],
+          digits: [1, 2],
+          negated: true,
+        },
+        quadrupleValues,
+        4,
+      ),
+    ).toBe(false);
+
+    const maximumValues = new Array<number>(16).fill(0);
+    maximumValues[5] = 4;
+    expect(
+      constraintIsFeasible(
+        { type: "maximum", cell: 5, negated: true },
+        maximumValues,
+        4,
+      ),
+    ).toBe(false);
+  });
+
+  it("requires a maximum cell to exceed every orthogonal neighbour", () => {
+    const values = new Array<number>(16).fill(0);
+    values[1] = 4;
+    expect(
+      candidatesForCell(puzzle4([{ type: "maximum", cell: 5 }]), values, 5),
+    ).toEqual([]);
+
+    expect(constraintIsFeasible({ type: "maximum", cell: 5 }, solved4, 4)).toBe(
+      true,
+    );
+    expect(constraintIsFeasible({ type: "maximum", cell: 6 }, solved4, 4)).toBe(
+      false,
+    );
+    const conflict = findConflicts(
+      puzzle4([{ type: "maximum", cell: 6 }]),
+      solved4,
+    ).find(({ kind }) => kind === "constraint");
+    expect(conflict?.cells).toEqual([6, 2, 10, 5, 7]);
+  });
+});
+
+describe("false-clue semantics", () => {
+  it("validates and clones polarity for every local clue type", () => {
+    const constraints: VariantConstraint[] = [
+      {
+        type: "killer-cage",
+        cells: [0, 6],
+        sum: 42,
+        negated: true,
+      },
+      { type: "thermo", cells: [0, 1], negated: true },
+      { type: "arrow", bulb: [0], line: [1], negated: true },
+      { type: "kropki", a: 0, b: 1, kind: "white", negated: true },
+      { type: "xv", a: 0, b: 1, total: 5, negated: true },
+      { type: "inequality", lesser: 0, greater: 1, negated: true },
+      { type: "renban", cells: [0, 1], negated: true },
+      { type: "palindrome", cells: [0, 1], negated: true },
+      {
+        type: "x-sum",
+        side: "left",
+        index: 0,
+        sum: 2,
+        negated: true,
+      },
+      {
+        type: "skyscraper",
+        side: "left",
+        index: 0,
+        count: 1,
+        negated: true,
+      },
+      {
+        type: "quadruple",
+        cells: [0, 1, 4, 5],
+        digits: [1, 1],
+        negated: true,
+      },
+      { type: "maximum", cell: 5, negated: true },
+    ];
+
+    const definition = puzzle4(constraints);
+    expect(validatePuzzle(definition)).toEqual({ valid: true, issues: [] });
+    const normalized = normalizePuzzle(definition);
+    expect(normalized.constraints).toEqual(constraints);
+    expect(normalized.constraints).not.toBe(constraints);
+    expect(normalized.constraints[0]).not.toBe(constraints[0]);
+  });
+
+  it("does not turn a false cage's no-repeat rule into an unconditional peer", () => {
+    const falseCage = compilePuzzle(
+      normalizePuzzle(
+        puzzle4([
+          {
+            type: "killer-cage",
+            cells: [0, 6],
+            sum: 3,
+            negated: true,
+          },
+        ]),
+      ),
+    );
+    const ordinaryCage = compilePuzzle(
+      normalizePuzzle(
+        puzzle4([{ type: "killer-cage", cells: [0, 6], sum: 3 }]),
+      ),
+    );
+
+    expect(falseCage.peers[0]?.has(6)).toBe(false);
+    expect(ordinaryCage.peers[0]?.has(6)).toBe(true);
+
+    const repeated = new Array<number>(16).fill(0);
+    repeated[0] = 1;
+    repeated[6] = 1;
+    expect(
+      constraintIsFeasible(
+        {
+          type: "killer-cage",
+          cells: [0, 6],
+          sum: 3,
+          negated: true,
+        },
+        repeated,
+        4,
+      ),
+    ).toBe(true);
+  });
+
+  it("inverts completed dots, XV, thermometers and cages", () => {
+    const cases: Array<
+      readonly [VariantConstraint, readonly number[], boolean]
+    > = [
+      [
+        { type: "kropki", a: 0, b: 1, kind: "white", negated: true },
+        [1, 2],
+        false,
+      ],
+      [
+        { type: "kropki", a: 0, b: 1, kind: "white", negated: true },
+        [1, 3],
+        true,
+      ],
+      [{ type: "xv", a: 0, b: 1, total: 5, negated: true }, [1, 4], false],
+      [{ type: "xv", a: 0, b: 1, total: 5, negated: true }, [1, 3], true],
+      [{ type: "thermo", cells: [0, 1, 2], negated: true }, [1, 2, 3], false],
+      [{ type: "thermo", cells: [0, 1, 2], negated: true }, [1, 3, 2], true],
+      [
+        { type: "killer-cage", cells: [0, 1], sum: 3, negated: true },
+        [1, 2],
+        false,
+      ],
+      [
+        { type: "killer-cage", cells: [0, 1], sum: 4, negated: true },
+        [1, 2],
+        true,
+      ],
+    ];
+    for (const [constraint, relevant, expected] of cases) {
+      const values = new Array<number>(16).fill(0);
+      relevant.forEach((value, cell) => {
+        values[cell] = value;
+      });
+      expect(
+        constraintIsFeasible(constraint, values, 4),
+        JSON.stringify(constraint),
+      ).toBe(expected);
+    }
+  });
+
+  it("inverts each completed outside and local clue", () => {
+    const cases: Array<readonly [VariantConstraint, boolean]> = [
+      [{ type: "x-sum", side: "left", index: 0, sum: 1, negated: true }, false],
+      [{ type: "x-sum", side: "left", index: 0, sum: 6, negated: true }, true],
+      [
+        {
+          type: "skyscraper",
+          side: "left",
+          index: 0,
+          count: 4,
+          negated: true,
+        },
+        false,
+      ],
+      [
+        {
+          type: "skyscraper",
+          side: "left",
+          index: 0,
+          count: 3,
+          negated: true,
+        },
+        true,
+      ],
+      [
+        {
+          type: "quadruple",
+          cells: [1, 2, 5, 6],
+          digits: [1, 2, 3, 4],
+          negated: true,
+        },
+        false,
+      ],
+      [
+        {
+          type: "quadruple",
+          cells: [1, 2, 5, 6],
+          digits: [2, 2, 4],
+          negated: true,
+        },
+        true,
+      ],
+      [{ type: "maximum", cell: 5, negated: true }, false],
+      [{ type: "maximum", cell: 6, negated: true }, true],
+    ];
+    for (const [constraint, expected] of cases) {
+      expect(constraintIsFeasible(constraint, solved4, 4)).toBe(expected);
+    }
+  });
+
+  it("keeps partial false clues feasible and prunes a completed true pair", () => {
+    const falseDot = {
+      type: "kropki",
+      a: 0,
+      b: 1,
+      kind: "white",
+      negated: true,
+    } as const;
+    const partial = new Array<number>(16).fill(0);
+    partial[0] = 1;
+    expect(constraintIsFeasible(falseDot, partial, 4)).toBe(true);
+    expect(candidatesForCell(puzzle4([falseDot]), partial, 1)).toEqual([3, 4]);
+
+    const falseThermo = {
+      type: "thermo",
+      cells: [0, 1, 2],
+      negated: true,
+    } as const;
+    partial[1] = 2;
+    expect(constraintIsFeasible(falseThermo, partial, 4)).toBe(true);
+  });
+
+  it("reports a true false-clue as the contradiction", () => {
+    const conflict = findConflicts(
+      puzzle4([{ type: "xv", a: 0, b: 3, total: 5, negated: true }]),
+      solved4,
+    ).find(({ kind }) => kind === "constraint");
+
+    expect(conflict?.message).toBe("xv clue is true but must be false.");
+  });
+});

tests/formats/aidMemoireDocument.test.ts

@@ -0,0 +1,75 @@
+import { describe, expect, it } from "vitest";
+import {
+  SUDOKU_DOCUMENT_SCHEMA,
+  cloneSudokuDocument,
+  normalizeSudokuDocument,
+  parseSudokuDocument,
+  serializeSudokuDocument,
+  type SudokuDocument,
+} from "../../src/formats";
+import {
+  aidMemoireToPortable,
+  createAidMemoire,
+  enterAidMemoireCell,
+  labelAidMemoireCell,
+  MAX_AID_MEMOIRE_CELLS,
+} from "../../src/state/aidMemoire";
+
+function baseDocument(): SudokuDocument {
+  return {
+    schema: SUDOKU_DOCUMENT_SCHEMA,
+    version: 1,
+    size: 9,
+    givens: Array<number>(81).fill(0),
+    constraints: [],
+  };
+}
+
+describe("portable aid-mémoire document data", () => {
+  it("normalizes, serializes and deeply clones scratch cells", () => {
+    let state = createAidMemoire(9, {
+      enabled: true,
+      cellCount: 3,
+      columns: 2,
+    });
+    state = labelAidMemoireCell(state, 0, "Prime");
+    state = enterAidMemoireCell(state, 0, "corner", 2, 9);
+    state = enterAidMemoireCell(state, 0, "center", 7, 9);
+    state = enterAidMemoireCell(state, 0, "color", 4, 9);
+    const source: SudokuDocument = {
+      ...baseDocument(),
+      aidMemoire: aidMemoireToPortable(state, 9),
+    };
+
+    const parsed = parseSudokuDocument(serializeSudokuDocument(source));
+    expect(parsed.aidMemoire).toEqual(source.aidMemoire);
+    const clone = cloneSudokuDocument(parsed);
+    (clone.aidMemoire!.cells[0]!.cornerMarks as number[])[0] = 9;
+    expect(parsed.aidMemoire?.cells[0]?.cornerMarks).toEqual([2]);
+  });
+
+  it("rejects unbounded layouts and out-of-range scratch symbols", () => {
+    expect(() =>
+      normalizeSudokuDocument({
+        ...baseDocument(),
+        aidMemoire: {
+          version: 1,
+          enabled: true,
+          columns: 1,
+          cells: Array.from({ length: MAX_AID_MEMOIRE_CELLS + 1 }, () => ({})),
+        },
+      }),
+    ).toThrow(/aidMemoire.cells must contain 1 to 36/u);
+    expect(() =>
+      normalizeSudokuDocument({
+        ...baseDocument(),
+        aidMemoire: {
+          version: 1,
+          enabled: true,
+          columns: 1,
+          cells: [{ label: "Bad", value: 10 }],
+        },
+      }),
+    ).toThrow(/value must be an integer from 0 to 9/u);
+  });
+});

tests/formats/document.test.ts

@@ -35,7 +35,30 @@ describe("Sudoku Tools document format", () => {
       centerMarks: Array.from({ length: 81 }, () => [7, 4]),
       colors: Array.from({ length: 81 }, (_, index) => index % 9),
       elapsedMs: 12_345,
-      constraints: [{ type: "killer-cage", cells: [0, 1], sum: 3 }],
+      constraints: [
+        { type: "killer-cage", cells: [0, 1], sum: 3 },
+        {
+          type: "x-sum",
+          side: "top",
+          index: 8,
+          sum: 1111,
+          negated: true,
+        },
+        {
+          type: "skyscraper",
+          side: "left",
+          index: 4,
+          count: 898,
+          negated: true,
+        },
+        {
+          type: "quadruple",
+          cells: [0, 1, 9, 10],
+          digits: [1, 3, 8],
+          negated: true,
+        },
+        { type: "maximum", cell: 10, negated: true },
+      ],
     };
     const parsed = parseSudokuDocument(serializeSudokuDocument(source));
     expect(parsed).toEqual({
@@ -59,6 +82,12 @@ describe("Sudoku Tools document format", () => {
         values: [2, ...Array<number>(15).fill(0)],
       }),
     ).toThrow(/preserve its given digit/u);
+    expect(() =>
+      normalizeSudokuDocument({
+        ...document(Array(81).fill(0)),
+        constraints: [{ type: "quadruple", cells: [0], digits: [1, 2] }],
+      }),
+    ).toThrow(/no more digits than clue cells/u);
   });
 
   it("round-trips compact share hashes", () => {

tests/formats/fpuzzles.test.ts

@@ -52,6 +52,12 @@ describe("fpuzzles interoperability", () => {
       inequality: [{ cells: ["R6C1", "R6C2"], value: ">" }],
       renban: [{ lines: [["R7C1", "R7C2"]] }],
       palindrome: [{ lines: [["R8C1", "R8C2"]] }],
+      xsum: [{ cell: "R0C1", value: "15" }],
+      skyscraper: [{ cell: "R2C10", value: "2" }],
+      quadruple: [
+        { cells: ["R1C1", "R1C2", "R2C1", "R2C2"], values: [1, 3, 8] },
+      ],
+      maximum: [{ cell: "R2C2" }],
     });
     expect(puzzle.givens[0]).toBe(5);
     expect(puzzle.values?.[1]).toBe(3);
@@ -64,6 +70,10 @@ describe("fpuzzles interoperability", () => {
         { type: "kropki", a: 27, b: 28, kind: "white" },
         { type: "kropki", a: 28, b: 29, kind: "black" },
         { type: "inequality", lesser: 46, greater: 45 },
+        { type: "x-sum", side: "top", index: 0, sum: 15 },
+        { type: "skyscraper", side: "right", index: 1, count: 2 },
+        { type: "quadruple", cells: [0, 1, 9, 10], digits: [1, 3, 8] },
+        { type: "maximum", cell: 10 },
       ]),
     );
     expect(() => normalizePuzzle(toDomainPuzzle(puzzle))).not.toThrow();
@@ -85,6 +95,10 @@ describe("fpuzzles interoperability", () => {
         { type: "inequality", lesser: 45, greater: 46 },
         { type: "renban", cells: [54, 55] },
         { type: "palindrome", cells: [63, 64] },
+        { type: "x-sum", side: "left", index: 0, sum: 6 },
+        { type: "skyscraper", side: "right", index: 1, count: 2 },
+        { type: "quadruple", cells: [0, 1, 9, 10], digits: [1, 3, 8] },
+        { type: "maximum", cell: 10 },
       ],
       title: "Round trip",
     };
@@ -110,6 +124,53 @@ describe("fpuzzles interoperability", () => {
     ).toThrow(/local-only app cannot fetch/u);
   });
 
+  it("refuses to weaken false clues during fpuzzles export", () => {
+    const source: SudokuDocument = {
+      schema: SUDOKU_DOCUMENT_SCHEMA,
+      version: 1,
+      size: 9,
+      givens: Array<number>(81).fill(0),
+      constraints: [
+        {
+          type: "x-sum",
+          side: "top",
+          index: 0,
+          sum: 11,
+          negated: true,
+        },
+      ],
+    };
+
+    expect(() => exportFpuzzles(source)).toThrow(/individually false clue/u);
+  });
+
+  it("rejects out-of-range outside clues during fpuzzles export", () => {
+    const source = {
+      schema: SUDOKU_DOCUMENT_SCHEMA,
+      version: 1,
+      size: 9,
+      givens: Array<number>(81).fill(0),
+    } as const;
+
+    for (const constraint of [
+      { type: "x-sum", side: "top", index: -1, sum: 15 },
+      { type: "x-sum", side: "bottom", index: 9, sum: 15 },
+      { type: "x-sum", side: "right", index: 0, sum: 0 },
+      { type: "x-sum", side: "left", index: 0, sum: 46 },
+      { type: "skyscraper", side: "right", index: -1, count: 2 },
+      { type: "skyscraper", side: "left", index: 9, count: 2 },
+      { type: "skyscraper", side: "bottom", index: 0, count: 0 },
+      { type: "skyscraper", side: "top", index: 0, count: 10 },
+    ] as const) {
+      expect(() =>
+        exportFpuzzles({
+          ...source,
+          constraints: [constraint],
+        }),
+      ).toThrow(/outside the supported range/u);
+    }
+  });
+
   it("rejects unsupported generalized dots instead of weakening them", () => {
     expect(() =>
       parseFpuzzles({
@@ -120,6 +181,40 @@ describe("fpuzzles interoperability", () => {
     ).toThrow(/Difference-2 dots are not supported/u);
   });
 
+  it("rejects quadruples spanning more than four cells", () => {
+    expect(() =>
+      parseFpuzzles({
+        size: 9,
+        grid: emptyGrid(),
+        quadruple: [
+          {
+            cells: ["R1C1", "R1C2", "R2C1", "R2C2", "R3C3"],
+            values: [1, 2],
+          },
+        ],
+      }),
+    ).toThrow(/one to four cells and clue digits/u);
+    expect(() =>
+      parseFpuzzles({
+        size: 9,
+        grid: emptyGrid(),
+        quadruple: [{ cells: ["R1C1"], values: [1, 2] }],
+      }),
+    ).toThrow(/one to four cells and clue digits/u);
+    expect(() =>
+      parseFpuzzles({
+        size: 9,
+        grid: emptyGrid(),
+        quadruple: [
+          {
+            cells: ["R1C1", "R1C3", "R2C1", "R2C3"],
+            values: [1, 2],
+          },
+        ],
+      }),
+    ).toThrow(/four cells surrounding one grid intersection/u);
+  });
+
   it("rejects unsupported or unknown rules instead of silently weakening them", () => {
     expect(() =>
       parseFpuzzles({

tests/formats/importSecurity.test.ts

@@ -0,0 +1,160 @@
+import fc from "fast-check";
+import { compressToBase64, compressToEncodedURIComponent } from "lz-string";
+import { describe, expect, it } from "vitest";
+import {
+  LzStringOutputLimitError,
+  decompressFromBase64Bounded,
+  decompressFromBase64OrUriComponentBounded,
+  decompressFromEncodedURIComponentBounded,
+} from "../../src/formats/boundedLz";
+import {
+  MAX_DOCUMENT_BYTES,
+  PUZZLE_HASH_PREFIX,
+  SudokuFormatError,
+  decodePuzzleHash,
+  importFpuzzles,
+  importPuzzle,
+  importSudokuPad,
+  parseFpuzzles,
+} from "../../src/formats";
+
+function emptyGrid(size = 4) {
+  return Array.from({ length: size }, () =>
+    Array.from({ length: size }, () => ({})),
+  );
+}
+
+function expectLimitExceeded(action: () => unknown): void {
+  try {
+    action();
+  } catch (error) {
+    expect(error).toBeInstanceOf(SudokuFormatError);
+    expect(error).toMatchObject({ code: "LIMIT_EXCEEDED" });
+    return;
+  }
+  throw new Error("Expected the import to reject an oversized payload.");
+}
+
+describe("bounded puzzle imports", () => {
+  it("keeps both LZ-String wire formats compatible for arbitrary text", () => {
+    fc.assert(
+      fc.property(fc.string({ maxLength: 512 }), (source) => {
+        const byteLength = new TextEncoder().encode(source).byteLength;
+        const limit = Math.max(1, byteLength);
+        expect(
+          decompressFromBase64Bounded(compressToBase64(source), limit),
+        ).toBe(source);
+        expect(
+          decompressFromEncodedURIComponentBounded(
+            compressToEncodedURIComponent(source),
+            limit,
+          ),
+        ).toBe(source);
+      }),
+      { numRuns: 100 },
+    );
+  });
+
+  it("counts UTF-8 bytes while expanding and stops before oversized output", () => {
+    const source = "🧩".repeat(1_024);
+    const compressed = compressToEncodedURIComponent(source);
+    const exactBytes = new TextEncoder().encode(source).byteLength;
+
+    expect(
+      decompressFromEncodedURIComponentBounded(compressed, exactBytes),
+    ).toBe(source);
+    expect(() =>
+      decompressFromEncodedURIComponentBounded(compressed, exactBytes - 1),
+    ).toThrow(LzStringOutputLimitError);
+  });
+
+  it("selects URI-safe payloads before an invalid Base64 interpretation", () => {
+    const title = "AE(a^'XS2pclC*+Q: ?8IJnG(Fe-nR";
+    const grid = emptyGrid();
+    const fpuzzlesJson = JSON.stringify({ size: 4, grid, title });
+    const fpuzzlesPayload = compressToEncodedURIComponent(fpuzzlesJson);
+    const sudokuPadJson = JSON.stringify({
+      id: "local-scl",
+      cells: grid,
+      metadata: {
+        title,
+        author: "Tester",
+        rules: "Normal rules apply.",
+        antiknight: true,
+      },
+      cages: [
+        {
+          cells: [
+            [0, 0],
+            [0, 1],
+          ],
+          value: "3",
+          unique: true,
+        },
+      ],
+    });
+    const sudokuPadPayload = compressToEncodedURIComponent(sudokuPadJson);
+
+    expect(fpuzzlesPayload).toMatch(/[-$]/u);
+    expect(sudokuPadPayload).toMatch(/[-$]/u);
+    expect(
+      decompressFromBase64Bounded(fpuzzlesPayload, MAX_DOCUMENT_BYTES),
+    ).not.toBe(fpuzzlesJson);
+    expect(
+      decompressFromBase64Bounded(sudokuPadPayload, MAX_DOCUMENT_BYTES),
+    ).not.toBe(sudokuPadJson);
+    expect(
+      decompressFromBase64OrUriComponentBounded(
+        fpuzzlesPayload,
+        MAX_DOCUMENT_BYTES,
+      ),
+    ).toBe(fpuzzlesJson);
+    expect(importFpuzzles(`fpuzzles${fpuzzlesPayload}`).title).toBe(title);
+    expect(importSudokuPad(`ctc${sudokuPadPayload}`).title).toBe(title);
+  });
+
+  it("rejects compressed bombs in every LZ-backed import format", () => {
+    const oversized = " ".repeat(MAX_DOCUMENT_BYTES + 1);
+    const base64 = compressToBase64(oversized);
+    const uri = compressToEncodedURIComponent(oversized);
+
+    expectLimitExceeded(() => importFpuzzles(`fpuzzles${base64}`));
+    expectLimitExceeded(() => importSudokuPad(`ctc${base64}`));
+    expectLimitExceeded(() => decodePuzzleHash(`${PUZZLE_HASH_PREFIX}${uri}`));
+  });
+
+  it("checks raw JSON character and byte limits before parsing", async () => {
+    const tooManyCharacters = `{${" ".repeat(MAX_DOCUMENT_BYTES)}}`;
+    await expect(importPuzzle(tooManyCharacters)).rejects.toMatchObject({
+      code: "LIMIT_EXCEEDED",
+    });
+
+    const tooManyUtf8Bytes = `{"future":"${"é".repeat(
+      Math.floor(MAX_DOCUMENT_BYTES / 2),
+    )}"}`;
+    expect(tooManyUtf8Bytes.length).toBeLessThan(MAX_DOCUMENT_BYTES);
+    await expect(importPuzzle(tooManyUtf8Bytes)).rejects.toMatchObject({
+      code: "LIMIT_EXCEEDED",
+    });
+  });
+
+  it("rejects unknown fpuzzles inequality markers", () => {
+    for (const value of [undefined, "≤", "left", 1]) {
+      expect(() =>
+        parseFpuzzles({
+          size: 4,
+          grid: emptyGrid(),
+          inequality: [{ cells: ["R1C1", "R1C2"], value }],
+        }),
+      ).toThrow(/inequality\.value must be either/u);
+    }
+
+    expect(
+      parseFpuzzles({
+        size: 4,
+        grid: emptyGrid(),
+        inequality: [{ cells: ["R1C1", "R1C2"], value: "<" }],
+      }).constraints,
+    ).toContainEqual({ type: "inequality", lesser: 0, greater: 1 });
+  });
+});

tests/formats/interoperability.test.ts

@@ -0,0 +1,175 @@
+import { compressToBase64 } from "lz-string";
+import { describe, expect, it, vi } from "vitest";
+import {
+  NetworkPuzzleIdError,
+  UnsupportedPuzzleConstructsError,
+  importPenpa,
+  importPuzzle,
+  importSudokuPad,
+  parsePenpaText,
+  parseSudokuPadPuzzle,
+} from "../../src/formats";
+
+const penpaText = [
+  "square,4,4,40,0,1,1,320,320,18,18,1,1,1,1,Title: Tiny,Author: Test,,Normal Sudoku rules apply.,ON,false",
+  "[0,0,0,0]",
+  "{}",
+  JSON.stringify({
+    number: { 18: [1, 1, "1"], 45: [4, 1, "1"] },
+    thermo: [[19, 20]],
+    arrows: [[26, 27]],
+  }),
+  JSON.stringify({ number: { 21: [2, 2, "1"] } }),
+  "[18,1,1,1,5,1,1,1,5,1,1,1,5,1,1,1]",
+  "[]",
+].join("\n");
+
+const compressedPenpa =
+  "bY/LCsIwEEX3+Yow64sksb6y8wd0YXchi4gRxbTRpEGk9N+lKoIgZ4bLncWBybfikkc1IiAgITFV4rVy+ZoP9bkLXvP63D6wLt0pJs1rnztgE1PjAt+VQ7wUnkrwmbvrNTwm2G5wdCF7Zka5gLCsH1hPbWn2PpHuSS5Jm9FPkiyompE21acOoO7kUxNJGyNXUMJakEsp3vN4UnOohbW/QiVJGwX1NgzMfH+Y/U/LjH0C";
+
+function sclPuzzle() {
+  const cells = Array.from({ length: 4 }, () =>
+    Array.from({ length: 4 }, () => ({})),
+  );
+  cells[0]![0] = { value: "1" };
+  cells[0]![1] = {
+    value: 2,
+    given: false,
+    pencilMarks: [4, 3],
+    centremarks: [2],
+  };
+  return {
+    id: "local-scl",
+    cells,
+    metadata: {
+      title: "Local SCL",
+      author: "Tester",
+      rules: "Normal rules apply.",
+      antiknight: true,
+    },
+    cages: [
+      {
+        cells: [
+          [0, 0],
+          [0, 1],
+        ],
+        value: "3",
+        unique: true,
+      },
+    ],
+  };
+}
+
+describe("local puzzle interoperability", () => {
+  it("imports bounded SudokuPad/CTC data and retains semantic features", () => {
+    const parsed = parseSudokuPadPuzzle(sclPuzzle());
+
+    expect(parsed.size).toBe(4);
+    expect(parsed.givens.slice(0, 2)).toEqual([1, 0]);
+    expect(parsed.values?.slice(0, 2)).toEqual([1, 2]);
+    expect(parsed.cornerMarks?.[1]).toEqual([3, 4]);
+    expect(parsed.constraints).toEqual(
+      expect.arrayContaining([
+        {
+          type: "killer-cage",
+          cells: [0, 1],
+          sum: 3,
+          noRepeat: true,
+        },
+        { type: "anti-knight" },
+      ]),
+    );
+  });
+
+  it("imports a self-contained ctc payload locally", async () => {
+    const inline = `ctc${compressToBase64(JSON.stringify(sclPuzzle()))}`;
+    const direct = importSudokuPad(inline);
+    const detected = await importPuzzle(`https://sudokupad.app/${inline}`);
+
+    expect(direct.title).toBe("Local SCL");
+    expect(detected.format).toBe("sudokupad");
+    expect(detected.document.givens[0]).toBe(1);
+  });
+
+  it("rejects visual-only SCL constructs instead of weakening them", () => {
+    expect(() =>
+      parseSudokuPadPuzzle({
+        ...sclPuzzle(),
+        lines: [
+          {
+            wayPoints: [
+              [0.5, 0.5],
+              [1.5, 1.5],
+            ],
+          },
+        ],
+        overlays: [{ text: "?" }],
+      }),
+    ).toThrow(UnsupportedPuzzleConstructsError);
+    expect(() =>
+      parseSudokuPadPuzzle({
+        ...sclPuzzle(),
+        lines: [{}],
+      }),
+    ).toThrow(/visual lines/u);
+  });
+
+  it("parses semantic Penpa+ Sudoku layers and local progress", () => {
+    const parsed = parsePenpaText(penpaText);
+
+    expect(parsed.size).toBe(4);
+    expect(parsed.title).toBe("Tiny");
+    expect(parsed.author).toBe("Test");
+    expect(parsed.givens[0]).toBe(1);
+    expect(parsed.givens[15]).toBe(4);
+    expect(parsed.values?.[3]).toBe(2);
+    expect(parsed.constraints).toEqual([
+      { type: "thermo", cells: [1, 2] },
+      { type: "arrow", bulb: [4], line: [5] },
+    ]);
+  });
+
+  it("detects an already-decompressed Penpa+ text record", async () => {
+    const parsed = await importPuzzle(penpaText);
+
+    expect(parsed.format).toBe("penpa");
+    expect(parsed.label).toBe("Penpa+ text");
+    expect(parsed.document.constraints).toHaveLength(2);
+  });
+
+  it("decompresses a complete Penpa+ long URL without fetching", async () => {
+    const fetchSpy = vi.fn();
+    vi.stubGlobal("fetch", fetchSpy);
+    const parsed = await importPenpa(
+      `https://swaroopg92.github.io/penpa-edit/#m=solve&p=${compressedPenpa}`,
+    );
+
+    expect(parsed.givens[0]).toBe(1);
+    expect(fetchSpy).not.toHaveBeenCalled();
+    vi.unstubAllGlobals();
+  });
+
+  it("rejects unsupported Penpa+ drawings with a compatibility list", () => {
+    const rows = penpaText.split("\n");
+    rows[3] = JSON.stringify({
+      number: { 18: [1, 1, "1"] },
+      line: { "18,19": 3 },
+      symbol: { 20: [1, "circle_L", 1] },
+    });
+
+    expect(() => parsePenpaText(rows.join("\n"))).toThrow(
+      /problem line, problem symbol/u,
+    );
+  });
+
+  it("never resolves a server-only SudokuPad short ID", async () => {
+    const fetchSpy = vi.fn();
+    vi.stubGlobal("fetch", fetchSpy);
+
+    await expect(
+      importPuzzle("https://sudokupad.app/serverOnly42"),
+    ).rejects.toBeInstanceOf(NetworkPuzzleIdError);
+    expect(fetchSpy).not.toHaveBeenCalled();
+    vi.unstubAllGlobals();
+  });
+});

tests/formats/visual.test.ts

@@ -0,0 +1,117 @@
+import { describe, expect, it } from "vitest";
+import {
+  SUDOKU_DOCUMENT_SCHEMA,
+  SUDOKU_DOCUMENT_VERSION,
+  buildJpegPdf,
+  renderPuzzleSvg,
+  type SudokuDocument,
+} from "../../src/formats";
+
+function visualDocument(): SudokuDocument {
+  const values = Array.from({ length: 16 }, () => 0);
+  values[0] = 1;
+  values[15] = 4;
+  const cornerMarks = Array.from({ length: 16 }, () => [] as number[]);
+  cornerMarks[1] = [2, 3];
+  const centerMarks = Array.from({ length: 16 }, () => [] as number[]);
+  centerMarks[2] = [1, 4];
+  return {
+    schema: SUDOKU_DOCUMENT_SCHEMA,
+    version: SUDOKU_DOCUMENT_VERSION,
+    size: 4,
+    givens: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
+    values,
+    cornerMarks,
+    centerMarks,
+    colors: [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
+    constraints: [
+      { type: "diagonal", direction: "main" },
+      { type: "killer-cage", cells: [0, 1], sum: 3 },
+      { type: "thermo", cells: [4, 5] },
+      { type: "arrow", bulb: [8], line: [9, 10] },
+      { type: "kropki", a: 2, b: 3, kind: "white" },
+      { type: "xv", a: 6, b: 7, total: 5 },
+      { type: "inequality", lesser: 10, greater: 11 },
+      { type: "renban", cells: [12, 13] },
+      { type: "palindrome", cells: [14, 15] },
+      { type: "maximum", cell: 5 },
+      { type: "quadruple", cells: [0, 1, 4, 5], digits: [1, 2] },
+      { type: "x-sum", side: "top", index: 0, sum: 1 },
+      { type: "skyscraper", side: "left", index: 2, count: 2 },
+      { type: "anti-knight" },
+    ],
+    title: 'A < B & "C"',
+    author: "Synthetic test",
+  };
+}
+
+describe("visual puzzle export", () => {
+  it("renders a standalone SVG with clues, regions, givens and progress", () => {
+    const svg = renderPuzzleSvg(visualDocument());
+    const parsed = new DOMParser().parseFromString(svg, "image/svg+xml");
+
+    expect(parsed.querySelector("parsererror")).toBeNull();
+    expect(parsed.documentElement.localName).toBe("svg");
+    expect(svg).toContain("A &lt; B &amp; &quot;C&quot;");
+    expect(svg).toContain('class="constraint diagonal" x1="58" y1="132"');
+    expect(svg).toContain('class="constraint cage"');
+    expect(svg).toContain('class="constraint thermo"');
+    expect(svg).toContain('class="constraint arrow"');
+    expect(svg).toContain('class="constraint outside x-sum"');
+    expect(svg).toContain('class="constraint xv total-5"');
+    expect(svg).toContain(">5</text>");
+    expect(svg).not.toContain(">V</text>");
+    expect(svg).toContain('class="inequality-tip"');
+    expect(svg).toContain('class="cell-value given"');
+    expect(svg).toContain('class="cell-value progress"');
+    expect(svg).toContain('class="corner-note" x=');
+    expect(svg).toContain('class="center-note" x=');
+    expect(svg).not.toMatch(/<(?:script|image)|(?:href|src)=/iu);
+  });
+
+  it("can omit all solving progress from the visual", () => {
+    const svg = renderPuzzleSvg(visualDocument(), {
+      includeProgress: false,
+      includeNotes: false,
+    });
+
+    expect(svg).toContain('class="cell-value given"');
+    expect(svg).not.toContain('class="cell-value progress"');
+    expect(svg).not.toContain('class="corner-note" x=');
+    expect(svg).not.toContain('class="center-note" x=');
+    expect(svg).not.toContain('class="cell-color"');
+  });
+
+  it("builds a bounded single-page PDF around local JPEG bytes", () => {
+    const pdf = buildJpegPdf(
+      new Uint8Array([0xff, 0xd8, 0xff, 0xd9]),
+      320,
+      240,
+    );
+    const text = new TextDecoder("latin1").decode(pdf);
+
+    expect(text.startsWith("%PDF-1.4")).toBe(true);
+    expect(text).toContain("/DCTDecode");
+    expect(text).toContain("xref\n0 6");
+    expect(text.endsWith("%%EOF\n")).toBe(true);
+  });
+
+  it("rejects invalid or unbounded PDF image input", () => {
+    expect(() => buildJpegPdf(new Uint8Array([0, 1, 2, 3]), 320, 240)).toThrow(
+      /JPEG/u,
+    );
+    expect(() =>
+      buildJpegPdf(new Uint8Array([0xff, 0xd8, 0xff, 0xd9]), 99_999, 240),
+    ).toThrow(/dimensions/u);
+  });
+
+  it("validates progress before embedding it in a visual", () => {
+    const document = visualDocument();
+    const invalidMarks = Array.from({ length: 16 }, () => [] as number[]);
+    invalidMarks[0] = [99];
+
+    expect(() =>
+      renderPuzzleSvg({ ...document, cornerMarks: invalidMarks }),
+    ).toThrow(/cornerMarks/u);
+  });
+});

tests/helpers/candidates.test.ts

@@ -0,0 +1,97 @@
+import { describe, expect, it } from "vitest";
+import { createEmptyPuzzle, normalizePuzzle } from "../../src/domain";
+import {
+  candidateCellsForValues,
+  candidateUnitIndicesForCells,
+  candidateValuesFromMask,
+  deriveCandidateLinks,
+  inspectCandidateCells,
+  inspectCandidateHouse,
+} from "../../src/helpers";
+
+function mask(...values: number[]): number {
+  return values.reduce((result, value) => result | (1 << (value - 1)), 0);
+}
+
+const puzzle = normalizePuzzle(createEmptyPuzzle(4));
+
+describe("candidate inspection", () => {
+  it("decodes masks and identifies the houses touching selected cells", () => {
+    expect(candidateValuesFromMask(mask(1, 3, 4), 4)).toEqual([1, 3, 4]);
+    expect(candidateUnitIndicesForCells(puzzle, [0])).toEqual([0, 1, 2]);
+
+    const cells = inspectCandidateCells(
+      puzzle,
+      [mask(1, 4), ...new Array<number>(15).fill(0)],
+      [0],
+    );
+    expect(cells).toEqual([
+      {
+        cell: 0,
+        values: [1, 4],
+        houseLabels: ["Row 1", "Column 1", "Region 1"],
+      },
+    ]);
+  });
+
+  it("reports missing values, candidate positions and conjugate pairs in a house", () => {
+    const values = [4, 0, 0, 2, ...new Array<number>(12).fill(0)];
+    const masks = new Array<number>(16).fill(0);
+    masks[1] = mask(1, 3);
+    masks[2] = mask(1, 3);
+
+    expect(inspectCandidateHouse(puzzle, values, masks, 0)).toMatchObject({
+      label: "Row 1",
+      missingValues: [1, 3],
+      positions: [
+        { value: 1, cells: [1, 2], linkKind: "strong" },
+        { value: 3, cells: [1, 2], linkKind: "strong" },
+      ],
+    });
+  });
+});
+
+describe("candidate link graph", () => {
+  it("derives strong house and bivalue links and merges shared contexts", () => {
+    const masks = new Array<number>(16).fill(0);
+    masks[0] = mask(1, 2);
+    masks[1] = mask(1, 3);
+
+    const links = deriveCandidateLinks(puzzle, masks);
+    const houseLink = links.find(
+      ({ a, b }) =>
+        a.cell === 0 && a.value === 1 && b.cell === 1 && b.value === 1,
+    );
+    expect(houseLink).toMatchObject({ kind: "strong" });
+    expect(houseLink?.contexts.map(({ label }) => label)).toEqual([
+      "Row 1",
+      "Region 1",
+    ]);
+    expect(links).toContainEqual(
+      expect.objectContaining({
+        kind: "strong",
+        a: { cell: 0, value: 1 },
+        b: { cell: 0, value: 2 },
+      }),
+    );
+  });
+
+  it("keeps larger candidate groups weak and supports digit and house scopes", () => {
+    const masks = new Array<number>(16).fill(0);
+    masks[0] = mask(2, 4);
+    masks[1] = mask(2);
+    masks[2] = mask(2);
+    masks[3] = mask(3, 4);
+
+    const links = deriveCandidateLinks(puzzle, masks, {
+      unitIndices: [0],
+      values: [2],
+    });
+    expect(links).toHaveLength(3);
+    expect(links.every(({ kind }) => kind === "weak")).toBe(true);
+    expect(links.every(({ a, b }) => a.value === 2 && b.value === 2)).toBe(
+      true,
+    );
+    expect(candidateCellsForValues(masks, [4])).toEqual([0, 3]);
+  });
+});

tests/helpers/sumLab.test.ts

@@ -0,0 +1,146 @@
+import fc from "fast-check";
+import { describe, expect, it } from "vitest";
+import { analyzeSumLab, sumCombinationKey } from "../../src/helpers/sumLab";
+
+function mask(...digits: number[]): number {
+  return digits.reduce((value, digit) => value | (2 ** (digit - 1)), 0);
+}
+
+describe("generalized sum lab", () => {
+  it("enumerates deterministic, sorted combinations", () => {
+    const result = analyzeSumLab({ cellCount: 2, target: 10 });
+
+    expect(result.combinations.map(({ digits }) => digits)).toEqual([
+      [1, 9],
+      [2, 8],
+      [3, 7],
+      [4, 6],
+    ]);
+    expect(result.truncated).toBe(false);
+  });
+
+  it("supports a digit range, repeats, required and excluded digits", () => {
+    const result = analyzeSumLab({
+      cellCount: 3,
+      target: 15,
+      minimumDigit: 3,
+      maximumDigit: 7,
+      allowRepeats: true,
+      requiredDigits: [3],
+      excludedDigits: [4],
+    });
+
+    expect(result.combinations.map(({ digits }) => digits)).toEqual([
+      [3, 5, 7],
+      [3, 6, 6],
+    ]);
+  });
+
+  it("uses per-cell candidate masks and derives positional possibilities", () => {
+    const result = analyzeSumLab({
+      cellCount: 2,
+      target: 10,
+      candidateMasks: [mask(1, 2), mask(8, 9)],
+    });
+
+    expect(result.combinations.map(({ digits }) => digits)).toEqual([
+      [1, 9],
+      [2, 8],
+    ]);
+    expect(result.assignments).toEqual([
+      [1, 9],
+      [2, 8],
+    ]);
+    expect(result.possibleByCell).toEqual([
+      [1, 2],
+      [8, 9],
+    ]);
+  });
+
+  it("removes toggled combinations from every live deduction", () => {
+    const eliminatedKeys = new Set([sumCombinationKey([1, 9])]);
+    const result = analyzeSumLab({
+      cellCount: 2,
+      target: 10,
+      eliminatedKeys,
+    });
+
+    expect(result.combinations).toHaveLength(4);
+    expect(result.eliminatedCombinations.map(({ digits }) => digits)).toEqual([
+      [1, 9],
+    ]);
+    expect(result.activeCombinations.map(({ digits }) => digits)).toEqual([
+      [2, 8],
+      [3, 7],
+      [4, 6],
+    ]);
+    expect(result.possibleDigits).not.toContain(1);
+    expect(result.possibleDigits).not.toContain(9);
+  });
+
+  it("reports which independent safety bound stopped an analysis", () => {
+    const result = analyzeSumLab({
+      cellCount: 8,
+      target: 36,
+      allowRepeats: true,
+      maxSearchNodes: 1,
+    });
+
+    expect(result.truncated).toBe(true);
+    expect(result.truncationReason).toBe("search");
+    expect(result.exploredNodes).toBe(2);
+  });
+
+  it("validates positional candidates and contradictory digit filters", () => {
+    expect(() =>
+      analyzeSumLab({ cellCount: 2, target: 3, candidateMasks: [mask(1)] }),
+    ).toThrow(/exactly 2/u);
+    expect(
+      analyzeSumLab({
+        cellCount: 2,
+        target: 3,
+        requiredDigits: [1],
+        excludedDigits: [1],
+      }).combinations,
+    ).toEqual([]);
+  });
+
+  it("preserves combination invariants over generated inputs", () => {
+    fc.assert(
+      fc.property(
+        fc.integer({ min: 3, max: 12 }),
+        fc.integer({ min: 1, max: 6 }),
+        fc.integer({ min: 0, max: 72 }),
+        fc.boolean(),
+        (maximumDigit, cellCount, target, allowRepeats) => {
+          if (target > maximumDigit * cellCount) return;
+          const result = analyzeSumLab({
+            cellCount,
+            target,
+            maximumDigit,
+            allowRepeats,
+          });
+          const keys = new Set<string>();
+          for (const combination of result.combinations) {
+            expect(combination.digits).toHaveLength(cellCount);
+            expect(
+              combination.digits.reduce((total, digit) => total + digit, 0),
+            ).toBe(target);
+            expect(combination.digits).toEqual(
+              [...combination.digits].sort((left, right) => left - right),
+            );
+            if (!allowRepeats) {
+              expect(new Set(combination.digits)).toHaveProperty(
+                "size",
+                cellCount,
+              );
+            }
+            keys.add(combination.key);
+          }
+          expect(keys.size).toBe(result.combinations.length);
+        },
+      ),
+      { numRuns: 100 },
+    );
+  });
+});

tests/solver/logical.test.ts

@@ -38,6 +38,28 @@ describe("logical solver", () => {
     expect(result.steps).toHaveLength(1);
   });
 
+  it("does not apply positive cage reductions to a false cage", () => {
+    const result = solveLogically({
+      version: 1,
+      size: 4,
+      givens: Array<number>(16).fill(0),
+      regions: classicRegions(4),
+      constraints: [
+        {
+          type: "killer-cage",
+          cells: [0, 1],
+          sum: 3,
+          noRepeat: false,
+          negated: true,
+        },
+      ],
+    });
+
+    expect(result.status).toBe("stuck");
+    expect(result.steps).toEqual([]);
+    expect(result.candidates[0]).toEqual([1, 2, 3, 4]);
+  });
+
   it("returns bounded killer combinations", () => {
     expect(
       killerDigitCombinations({ size: 9, count: 2, sum: 10 }).combinations,

tests/solver/variantGenerator.test.ts

@@ -196,6 +196,35 @@ describe("variant generator", () => {
     expect(generated.puzzle.rules).not.toMatch(/Kropki|negative/i);
   });
 
+  it("mines deterministically for a requested practice technique", () => {
+    const options = {
+      variant: "classic",
+      size: 9,
+      seed: "mine-practice",
+      targetDifficulty: "hard",
+      requiredTechnique: "naked-pair",
+      maxTechniqueAttempts: 6,
+      maxChecks: 72,
+    } as const;
+    const generated = generateVariant(options);
+    expect(generated.requestedTechnique).toBe("naked-pair");
+    expect(generated.generationAttempts).toBe(4);
+    expect(generated.difficulty.techniqueCounts["naked-pair"]).toBeGreaterThan(
+      0,
+    );
+    expect(generateVariant(options)).toEqual(generated);
+  });
+
+  it("keeps Killer-cage practice tied to the Killer generator", () => {
+    expect(() =>
+      generateVariant({
+        variant: "classic",
+        size: 4,
+        requiredTechnique: "killer-cage",
+      }),
+    ).toThrow(/requires the Killer generator/i);
+  });
+
   it("keeps the public variant ID type exhaustive", () => {
     const ids: GeneratorVariant[] = GENERATOR_VARIANTS.map(({ id }) => id);
     expect(new Set(ids).size).toBe(GENERATOR_VARIANTS.length);

tests/state/aidMemoire.test.ts

@@ -0,0 +1,149 @@
+import { describe, expect, it } from "vitest";
+import {
+  aidMemoireCellDescription,
+  aidMemoireFromPortable,
+  aidMemoireToPortable,
+  clearAidMemoireEntries,
+  compactAidMemoireColumns,
+  configureAidMemoire,
+  createAidMemoire,
+  enterAidMemoireCell,
+  eraseAidMemoireCell,
+  labelAidMemoireCell,
+  MAX_AID_MEMOIRE_CELLS,
+  normalizePortableAidMemoire,
+  resetAidMemoire,
+} from "../../src/state/aidMemoire";
+import { maskValues } from "../../src/state/session";
+
+describe("aid-mémoire state", () => {
+  it("creates a bounded row and preserves existing cells while reflowing", () => {
+    let state = createAidMemoire(9, { enabled: true });
+    expect(state.cells).toHaveLength(9);
+    expect(state.columns).toBe(9);
+    expect(state.cells.map((cell) => cell.label)).toEqual([
+      "1",
+      "2",
+      "3",
+      "4",
+      "5",
+      "6",
+      "7",
+      "8",
+      "9",
+    ]);
+
+    state = labelAidMemoireCell(state, 0, "Prime");
+    state = enterAidMemoireCell(state, 0, "value", 7, 9);
+    state = configureAidMemoire(state, 9, 12, 4);
+    expect(state.cells).toHaveLength(12);
+    expect(state.columns).toBe(4);
+    expect(state.cells[0]).toMatchObject({ label: "Prime", value: 7 });
+    expect(state.cells[11]?.label).toBe("12");
+
+    state = configureAidMemoire(state, 9, 1_000, 1_000);
+    expect(state.cells).toHaveLength(MAX_AID_MEMOIRE_CELLS);
+    expect(state.columns).toBe(MAX_AID_MEMOIRE_CELLS);
+    state = configureAidMemoire(state, 9, Number.NaN, Number.NaN);
+    expect(state.cells).toHaveLength(9);
+    expect(state.columns).toBe(1);
+    state = configureAidMemoire(state, 9, 3.9, 2.8);
+    expect(state.cells).toHaveLength(3);
+    expect(state.columns).toBe(2);
+    expect(compactAidMemoireColumns(9)).toBe(3);
+    expect(compactAidMemoireColumns(Number.NaN)).toBe(1);
+  });
+
+  it("edits values, both mark types and colours like normal cells", () => {
+    let state = createAidMemoire(9, { enabled: true, cellCount: 1 });
+    state = enterAidMemoireCell(state, 0, "corner", 2, 9);
+    state = enterAidMemoireCell(state, 0, "corner", 8, 9);
+    state = enterAidMemoireCell(state, 0, "center", 4, 9);
+    state = enterAidMemoireCell(state, 0, "color", 6, 9);
+    expect(maskValues(state.cells[0]!.cornerMarks, 9)).toEqual([2, 8]);
+    expect(maskValues(state.cells[0]!.centerMarks, 9)).toEqual([4]);
+    expect(state.cells[0]?.color).toBe(6);
+
+    state = enterAidMemoireCell(state, 0, "value", 5, 9);
+    expect(state.cells[0]).toMatchObject({
+      value: 5,
+      cornerMarks: 0,
+      centerMarks: 0,
+      color: 6,
+    });
+    expect(enterAidMemoireCell(state, 0, "center", 3, 9)).toBe(state);
+    expect(enterAidMemoireCell(state, 0, "value", 2.5, 9)).toBe(state);
+    state = eraseAidMemoireCell(state, 0, "value");
+    state = enterAidMemoireCell(state, 0, "color", 6, 9);
+    expect(state.cells[0]).toMatchObject({ value: 0, color: 0 });
+  });
+
+  it("clears entries without losing layout or labels and can reset all", () => {
+    let state = createAidMemoire(6, {
+      enabled: true,
+      cellCount: 4,
+      columns: 2,
+    });
+    state = labelAidMemoireCell(state, 0, "Used");
+    state = enterAidMemoireCell(state, 0, "value", 3, 6);
+    const cleared = clearAidMemoireEntries(state);
+    expect(cleared).toMatchObject({ enabled: true, columns: 2 });
+    expect(cleared.cells[0]).toMatchObject({ label: "Used", value: 0 });
+
+    const reset = resetAidMemoire(cleared, 6);
+    expect(reset).toMatchObject({ enabled: true, columns: 6 });
+    expect(reset.cells).toHaveLength(6);
+    expect(reset.cells[0]?.label).toBe("1");
+  });
+
+  it("round-trips a stable portable representation", () => {
+    const portable = normalizePortableAidMemoire(
+      {
+        version: 1,
+        enabled: true,
+        columns: 2,
+        cells: [
+          {
+            label: "Primes",
+            value: 0,
+            cornerMarks: [7, 2, 2],
+            centerMarks: [5, 3],
+            color: 4,
+          },
+          { label: "Used", value: 8, color: 0 },
+        ],
+      },
+      9,
+    );
+    expect(portable.cells[0]).toMatchObject({
+      cornerMarks: [2, 7],
+      centerMarks: [3, 5],
+    });
+    expect(
+      aidMemoireToPortable(aidMemoireFromPortable(portable, 9), 9),
+    ).toEqual(portable);
+  });
+
+  it("rejects unsafe portable layouts and provides complete cell narration", () => {
+    expect(() =>
+      normalizePortableAidMemoire(
+        {
+          version: 1,
+          enabled: true,
+          columns: 1,
+          cells: Array.from({ length: MAX_AID_MEMOIRE_CELLS + 1 }, () => ({})),
+        },
+        9,
+      ),
+    ).toThrow(/1 to 36/u);
+
+    let state = createAidMemoire(9, { cellCount: 1 });
+    state = labelAidMemoireCell(state, 0, "Odd candidates");
+    state = enterAidMemoireCell(state, 0, "corner", 1, 9);
+    state = enterAidMemoireCell(state, 0, "center", 7, 9);
+    state = enterAidMemoireCell(state, 0, "color", 3, 9);
+    expect(aidMemoireCellDescription(state.cells[0]!, 0, 9)).toBe(
+      "Aid-mémoire cell 1, label Odd candidates, empty, corner marks 1, centre marks 7, colour 3",
+    );
+  });
+});

tests/state/gridNavigation.test.ts

@@ -0,0 +1,27 @@
+import { describe, expect, it } from "vitest";
+import { navigateGridCell } from "../../src/state/gridNavigation";
+
+describe("accessible grid navigation", () => {
+  it("moves with arrows without wrapping at edges", () => {
+    expect(navigateGridCell(4, 3, "ArrowRight")).toBe(5);
+    expect(navigateGridCell(5, 3, "ArrowRight")).toBe(5);
+    expect(navigateGridCell(3, 3, "ArrowLeft")).toBe(3);
+    expect(navigateGridCell(1, 3, "ArrowUp")).toBe(1);
+    expect(navigateGridCell(7, 3, "ArrowDown")).toBe(7);
+  });
+
+  it("supports row, grid and column-edge shortcuts", () => {
+    expect(navigateGridCell(4, 3, "Home")).toBe(3);
+    expect(navigateGridCell(4, 3, "End")).toBe(5);
+    expect(navigateGridCell(4, 3, "Home", true)).toBe(0);
+    expect(navigateGridCell(4, 3, "End", true)).toBe(8);
+    expect(navigateGridCell(4, 3, "PageUp")).toBe(1);
+    expect(navigateGridCell(4, 3, "PageDown")).toBe(7);
+  });
+
+  it("ignores non-navigation keys and rejects unsafe inputs", () => {
+    expect(navigateGridCell(0, 9, "Enter")).toBeNull();
+    expect(() => navigateGridCell(-1, 9, "Home")).toThrow(/outside/i);
+    expect(() => navigateGridCell(0, 0, "Home")).toThrow(/size/i);
+  });
+});

tests/state/playHistory.test.ts

@@ -0,0 +1,176 @@
+import { describe, expect, it } from "vitest";
+import {
+  activeHypothesis,
+  beginHypothesis,
+  createGameplayHistory,
+  createSavepoint,
+  deleteSavepoint,
+  describeGameplayChange,
+  finishHypothesis,
+  gameplayMoment,
+  recordGameplayMoment,
+  restoreSavepoint,
+  sessionFromGameplayState,
+} from "../../src/state/playHistory";
+import {
+  createAidMemoire,
+  enterAidMemoireCell,
+} from "../../src/state/aidMemoire";
+import { createSession } from "../../src/state/session";
+
+describe("gameplay history", () => {
+  it("records immutable states with useful move labels", () => {
+    const initial = createSession([0, 0, 0, 0]);
+    const changed = { ...initial, values: [0, 3, 0, 0] };
+    const label = describeGameplayChange(initial, changed, 2);
+    const history = recordGameplayMoment(
+      createGameplayHistory(initial),
+      changed,
+      label,
+    );
+
+    expect(label).toBe("Set r1c2 to 3");
+    expect(history.moments.map((moment) => moment.label)).toEqual([
+      "Puzzle opened",
+      "Set r1c2 to 3",
+    ]);
+    changed.values[1] = 4;
+    expect(history.moments[1]!.state.values[1]).toBe(3);
+  });
+
+  it("creates, restores and deletes full named savepoints", () => {
+    const session = createSession([0, 0, 0, 0]);
+    session.values[1] = 2;
+    session.centerMarks[2] = 5;
+    session.colors[3] = 4;
+    session.elapsedSeconds = 75;
+    let history = createSavepoint(
+      createGameplayHistory(session),
+      session,
+      "Before chain",
+    );
+
+    session.values[1] = 4;
+    session.centerMarks[2] = 0;
+    const transition = restoreSavepoint(history, history.savepoints[0]!.id);
+    const restored = sessionFromGameplayState(transition.state);
+    expect(restored.values[1]).toBe(2);
+    expect(restored.centerMarks[2]).toBe(5);
+    expect(restored.colors[3]).toBe(4);
+    expect(restored.elapsedSeconds).toBe(75);
+    expect(transition.history.moments.at(-1)?.label).toBe(
+      "Restored “Before chain”",
+    );
+
+    history = deleteSavepoint(
+      transition.history,
+      transition.history.savepoints[0]!.id,
+    );
+    expect(history.savepoints).toHaveLength(0);
+  });
+
+  it("captures aid-mémoire state in moments and savepoints", () => {
+    const session = createSession([0, 0, 0, 0]);
+    let aidMemoire = createAidMemoire(2, {
+      enabled: true,
+      cellCount: 2,
+    });
+    aidMemoire = enterAidMemoireCell(aidMemoire, 0, "value", 1, 2);
+    const history = createSavepoint(
+      createGameplayHistory(session, aidMemoire),
+      session,
+      "Scratch one",
+      aidMemoire,
+    );
+
+    aidMemoire = enterAidMemoireCell(aidMemoire, 0, "value", 2, 2);
+    const restored = restoreSavepoint(history, history.savepoints[0]!.id);
+    expect(restored.state.aidMemoire?.cells[0]?.value).toBe(1);
+    expect(history.moments[0]?.state.aidMemoire?.cells[0]?.value).toBe(1);
+    expect(aidMemoire.cells[0]?.value).toBe(2);
+  });
+
+  it("keeps discarded hypotheses available while restoring their exact base", () => {
+    const session = createSession([0, 0, 0, 0]);
+    session.values[0] = 1;
+    let transition = beginHypothesis(
+      createGameplayHistory(session),
+      session,
+      "Try a 2",
+    );
+    expect(activeHypothesis(transition.history)?.name).toBe("Try a 2");
+
+    const branchSession = sessionFromGameplayState(transition.state);
+    branchSession.values[1] = 2;
+    transition = {
+      history: recordGameplayMoment(
+        transition.history,
+        branchSession,
+        "Set r1c2 to 2",
+      ),
+      state: transition.state,
+    };
+    const result = finishHypothesis(
+      transition.history,
+      branchSession,
+      "discard",
+    );
+
+    expect(result.state.values).toEqual([1, 0, 0, 0]);
+    expect(result.history.branches[0]?.status).toBe("discarded");
+    expect(
+      result.history.moments.some(
+        (moment) =>
+          moment.branchId === result.history.branches[0]!.id &&
+          moment.state.values[1] === 2,
+      ),
+    ).toBe(true);
+    expect(result.history.moments.at(-1)?.label).toBe(
+      "Discarded hypothesis “Try a 2”",
+    );
+  });
+
+  it("can branch from a replayed moment and merge accepted changes", () => {
+    const initial = createSession([0, 0, 0, 0]);
+    const first = { ...initial, values: [1, 0, 0, 0] };
+    const second = { ...initial, values: [1, 2, 0, 0] };
+    let history = recordGameplayMoment(
+      createGameplayHistory(initial),
+      first,
+      "First move",
+    );
+    const replayId = history.currentMomentId;
+    history = recordGameplayMoment(history, second, "Second move");
+
+    let transition = beginHypothesis(history, second, "Alternative", replayId);
+    expect(transition.state.values).toEqual([1, 0, 0, 0]);
+    const alternative = sessionFromGameplayState(transition.state);
+    alternative.values[2] = 3;
+    transition = {
+      history: recordGameplayMoment(
+        transition.history,
+        alternative,
+        "Alternative move",
+      ),
+      state: transition.state,
+    };
+    const kept = finishHypothesis(transition.history, alternative, "keep");
+
+    expect(kept.state.values).toEqual([1, 0, 3, 0]);
+    expect(kept.history.branches.at(-1)?.status).toBe("kept");
+    expect(
+      gameplayMoment(kept.history, kept.history.currentMomentId)?.label,
+    ).toBe("Kept hypothesis “Alternative”");
+  });
+
+  it("rejects blank checkpoint and hypothesis names", () => {
+    const session = createSession([0, 0, 0, 0]);
+    const history = createGameplayHistory(session);
+    expect(() => createSavepoint(history, session, "   ")).toThrow(
+      "Savepoint name cannot be empty",
+    );
+    expect(() => beginHypothesis(history, session, "   ")).toThrow(
+      "Hypothesis name cannot be empty",
+    );
+  });
+});

tests/storage/aidMemoireProgress.test.ts

@@ -0,0 +1,72 @@
+import { describe, expect, it } from "vitest";
+import { SUDOKU_DOCUMENT_SCHEMA } from "../../src/formats";
+import {
+  ProjectLibrary,
+  createProjectRecord,
+  normalizeProjectRecord,
+} from "../../src/storage";
+import {
+  aidMemoireToPortable,
+  createAidMemoire,
+  enterAidMemoireCell,
+} from "../../src/state/aidMemoire";
+
+const puzzle = {
+  schema: SUDOKU_DOCUMENT_SCHEMA,
+  version: 1 as const,
+  size: 9,
+  givens: Array<number>(81).fill(0),
+  constraints: [],
+};
+
+describe("aid-mémoire Library progress", () => {
+  it("persists bounded scratch state in an independent local clone", async () => {
+    let aidMemoire = createAidMemoire(9, {
+      enabled: true,
+      cellCount: 4,
+      columns: 2,
+    });
+    aidMemoire = enterAidMemoireCell(aidMemoire, 2, "value", 6, 9);
+    const record = createProjectRecord(puzzle, {
+      id: "aid-progress",
+      now: 10,
+      progress: {
+        version: 1,
+        values: Array<number>(81).fill(0),
+        aidMemoire: aidMemoireToPortable(aidMemoire, 9),
+      },
+    });
+    const library = new ProjectLibrary({ indexedDB: null });
+    await library.put(record);
+
+    const loaded = await library.get("aid-progress");
+    expect(loaded?.progress?.aidMemoire).toEqual(record.progress?.aidMemoire);
+    (loaded!.progress!.aidMemoire!.cells[2]!.centerMarks as number[]).push(4);
+    expect(
+      (await library.get("aid-progress"))?.progress?.aidMemoire?.cells[2]
+        ?.centerMarks,
+    ).toEqual([]);
+  });
+
+  it("rejects malformed scratch progress at the storage boundary", () => {
+    const record = createProjectRecord(puzzle, {
+      id: "bad-aid-progress",
+      now: 1,
+    });
+    expect(() =>
+      normalizeProjectRecord({
+        ...record,
+        progress: {
+          version: 1,
+          values: Array<number>(81).fill(0),
+          aidMemoire: {
+            version: 1,
+            enabled: true,
+            columns: 2,
+            cells: [{}],
+          },
+        },
+      }),
+    ).toThrow(/columns must be an integer from 1 to 1/u);
+  });
+});