feat(offline): port DAWG cursor + move generator to TS (parity-pinned)

First engine-first step of PWA offline mode (Phase A): the client-side move
generator — the "robot brain" a local vs_ai game will run on-device — with no
runtime wiring yet (Phase B).

- dawg.ts: add the step-by-step cursor (root/final/next/arcs), a faithful port
  of dafsa traverse.go over the reader's existing bitstream.
- generate.ts: the Appel-Jacobson generator (leftPart/extendRight + cross-sets +
  counts-rack + board transpose + moveKey ranking), reusing the cursor and
  validate.ts evaluate/connected. A cross-set LetterSet is a Uint8Array, so the
  33-letter Russian alphabet (index 32) is exact under JS bit ops.
- validate.ts: export connected for the generator's connectivity filter.
- backend/cmd/movegen: dev tool building small sample dictionaries and emitting
  golden move-generation fixtures from the real Go solver (EN + RU).
- tests: dawg.cursor.test.ts (enumeration bijection vs indexOf) and
  generate.parity.test.ts (7/7 vs the Go solver: empty board, mid-game, blank,
  single-word rule, Russian index-32 cross-set). The committed EN sample also
  unblocks the existing skipped dawg.parity.test.ts once wired with DICT_* in CI.

Pure additive library code; no runtime behavior change.

ui/src/lib/dict/generate.ts

@@ -0,0 +1,418 @@
+// Local move generator: every legal play for a rack on a board, ranked by
+// descending score. Ported from the scrabble-solver engine — the Appel-Jacobson
+// two-phase algorithm (LeftPart then ExtendRight) over a plain left-to-right DAWG
+// (scrabble/gen_dawg.go, gen.go, crossset.go, solver.go, key.go). It walks the DAWG
+// with the cursor from dawg.ts and scores each play with evaluate() from validate.ts,
+// so the whole robot brain runs on-device. Faithfulness to the Go solver is pinned by
+// generate.parity.test.ts against golden fixtures (backend/cmd/movegen).
+//
+// Everything works in alphabet-index space, mirroring the Go engine. A letterSet is
+// a per-square cross-set (the letters that form a legal perpendicular word there);
+// it is a boolean membership array rather than a uint64, so alphabet indexes past
+// JS's 31-bit shift boundary (Russian has 33 letters) are handled exactly.
+
+import { Dawg } from './dawg';
+import {
+  evaluate,
+  connected,
+  Horizontal,
+  Vertical,
+  type Board,
+  type Ruleset,
+  type Move,
+  type Placement,
+  type Direction,
+} from './validate';
+
+/** Both generates across plays (on the board) and down plays (on its transpose). */
+export const Both = 0;
+/** OnlyHorizontal generates across plays only. */
+export const OnlyHorizontal = 1;
+/** OnlyVertical generates down plays only (Эрудит plays a single orientation per turn). */
+export const OnlyVertical = 2;
+export type Mode = typeof Both | typeof OnlyHorizontal | typeof OnlyVertical;
+
+function modeIncludes(mode: Mode, dir: Direction): boolean {
+  if (mode === Both) return true;
+  if (mode === OnlyHorizontal) return dir === Horizontal;
+  return dir === Vertical;
+}
+
+/**
+ * GenBoard is the board view the generator needs: the validator's read view plus the
+ * dimensions it iterates over. The whole board is square, so a transposed view (below)
+ * satisfies the same shape.
+ */
+export interface GenBoard extends Board {
+  rows: number;
+  cols: number;
+}
+
+/**
+ * GenRack is a rack as per-letter tile counts plus a blank slot, mirroring
+ * scrabble-solver/rack. The generator mutates a single rack in place — removing a
+ * tile, recursing, putting it back — so the operations are O(1) and allocation-free.
+ */
+export class GenRack {
+  private readonly counts: Int32Array;
+
+  /** Construct an empty rack for an alphabet of the given size (a trailing blank slot). */
+  constructor(size: number) {
+    this.counts = new Int32Array(size + 1);
+  }
+
+  /** from builds a rack from a multiset of letter indexes plus a blank count. */
+  static from(size: number, letters: readonly number[], blanks: number): GenRack {
+    const r = new GenRack(size);
+    for (const l of letters) r.counts[l]++;
+    r.counts[size] += blanks;
+    return r;
+  }
+
+  /** has reports whether at least one tile of the letter index is on the rack. */
+  has(letter: number): boolean {
+    return this.counts[letter] > 0;
+  }
+  /** blanks returns how many blank tiles are on the rack. */
+  blanks(): number {
+    return this.counts[this.counts.length - 1];
+  }
+  remove(letter: number): void {
+    this.counts[letter]--;
+  }
+  add(letter: number): void {
+    this.counts[letter]++;
+  }
+  removeBlank(): void {
+    this.counts[this.counts.length - 1]--;
+  }
+  addBlank(): void {
+    this.counts[this.counts.length - 1]++;
+  }
+  /** clone returns an independent copy. */
+  clone(): GenRack {
+    const c = new GenRack(this.counts.length - 1);
+    c.counts.set(this.counts);
+    return c;
+  }
+}
+
+// --- cross-sets ------------------------------------------------------------------
+//
+// A LetterSet is membership over alphabet letter indexes. Mirrors scrabble.letterSet
+// (a uint64) but as a Uint8Array so index 32 (Russian) is exact under JS bit ops.
+type LetterSet = Uint8Array;
+
+function fullSet(size: number): LetterSet {
+  return new Uint8Array(size).fill(1);
+}
+
+// walk follows word (alphabet indexes) left to right from the root; -1 if it derails.
+function walk(dawg: Dawg, word: readonly number[]): number {
+  let n = dawg.root();
+  for (const l of word) {
+    n = dawg.next(n, l);
+    if (n < 0) return -1;
+  }
+  return n;
+}
+
+// completers returns the letters X (< size) whose arc from state leads directly to an
+// accepting node — the deterministic cross-set primitive. Mirrors scrabble.completers.
+function completers(dawg: Dawg, state: number, size: number): LetterSet {
+  const set = new Uint8Array(size);
+  dawg.arcs(state, (label, _dest, final) => {
+    if (final && label < size) set[label] = 1;
+    return true;
+  });
+  return set;
+}
+
+// dawgCrossSet returns the letters X for which above·X·below is a stored word. Mirrors
+// scrabble.dawgCrossSet: a right extension (no tiles below) just completes the prefix
+// above; a left extension (tiles below) probes each X. above/below are letter indexes.
+function dawgCrossSet(dawg: Dawg, above: number[], below: number[], size: number): LetterSet {
+  if (above.length === 0 && below.length === 0) return fullSet(size);
+  if (below.length === 0) {
+    const node = walk(dawg, above);
+    if (node < 0) return new Uint8Array(size);
+    return completers(dawg, node, size);
+  }
+  let node = dawg.root();
+  if (above.length > 0) {
+    node = walk(dawg, above);
+    if (node < 0) return new Uint8Array(size);
+  }
+  const set = new Uint8Array(size);
+  for (let x = 0; x < size; x++) {
+    let m = dawg.next(node, x);
+    if (m < 0) continue;
+    let ok = true;
+    for (const l of below) {
+      m = dawg.next(m, l);
+      if (m < 0) {
+        ok = false;
+        break;
+      }
+    }
+    if (ok && dawg.final(m)) set[x] = 1;
+  }
+  return set;
+}
+
+// columnContext returns the contiguous run of filled cells immediately above and below
+// the empty square (r, c), each top to bottom, as letter indexes — the tiles a
+// perpendicular word through (r, c) would include. Mirrors scrabble.columnContext.
+function columnContext(b: GenBoard, r: number, c: number): { above: number[]; below: number[] } {
+  const above: number[] = [];
+  let start = r;
+  while (start - 1 >= 0 && b.filled(start - 1, c)) start--;
+  for (let rr = start; rr < r; rr++) above.push(b.cellAt(rr, c).letter);
+
+  const below: number[] = [];
+  let end = r;
+  while (end + 1 < b.rows && b.filled(end + 1, c)) end++;
+  for (let rr = r + 1; rr <= end; rr++) below.push(b.cellAt(rr, c).letter);
+  return { above, below };
+}
+
+// transpose returns a view of b with rows and columns swapped, so down-play generation
+// runs as across generation. Mirrors board.Transpose (as a lazy view).
+function transpose(b: GenBoard): GenBoard {
+  return {
+    rows: b.cols,
+    cols: b.rows,
+    inBounds: (r, c) => b.inBounds(c, r),
+    filled: (r, c) => b.filled(c, r),
+    cellAt: (r, c) => b.cellAt(c, r),
+    isEmpty: () => b.isEmpty(),
+  };
+}
+
+// A tentatively placed left-part tile; its column is fixed only at record time.
+interface TileInfo {
+  letter: number;
+  blank: boolean;
+}
+
+// AcrossGen carries one across-generation pass over a board. Mirrors scrabble.acrossGen.
+class AcrossGen {
+  private row = 0;
+  private readonly left: TileInfo[] = [];
+  private readonly right: Placement[] = [];
+
+  constructor(
+    private readonly dawg: Dawg,
+    private readonly bd: GenBoard,
+    private readonly rk: GenRack,
+    private readonly cross: (r: number, c: number) => LetterSet,
+    private readonly emit: (placements: Placement[]) => void,
+  ) {}
+
+  generateRow(row: number, firstMove: boolean, centerRow: number, centerCol: number): void {
+    this.row = row;
+    let limit = 0;
+    for (let col = 0; col < this.bd.cols; col++) {
+      if (this.bd.filled(row, col)) {
+        limit = 0;
+        continue;
+      }
+      const anchor = firstMove ? row === centerRow && col === centerCol : this.hasFilledNeighbor(row, col);
+      if (!anchor) {
+        limit++;
+        continue;
+      }
+      this.left.length = 0;
+      this.right.length = 0;
+      if (col > 0 && this.bd.filled(row, col - 1)) {
+        const pre = this.walkPrefix(row, col);
+        if (pre.ok) this.extendRight(pre.node, col, col);
+      } else {
+        this.leftPart(this.dawg.root(), col, limit);
+      }
+      limit = 0;
+    }
+  }
+
+  private hasFilledNeighbor(r: number, c: number): boolean {
+    return this.bd.filled(r - 1, c) || this.bd.filled(r + 1, c) || this.bd.filled(r, c - 1) || this.bd.filled(r, c + 1);
+  }
+
+  // walkPrefix walks the DAWG through the filled run ending at col-1, returning the
+  // node reached and whether that prefix exists. Mirrors scrabble.acrossGen.walkPrefix.
+  private walkPrefix(row: number, col: number): { node: number; ok: boolean } {
+    let start = col - 1;
+    while (start - 1 >= 0 && this.bd.filled(row, start - 1)) start--;
+    let node = this.dawg.root();
+    for (let c = start; c < col; c++) {
+      node = this.dawg.next(node, this.bd.cellAt(row, c).letter);
+      if (node < 0) return { node, ok: false };
+    }
+    return { node, ok: true };
+  }
+
+  // leftPart places left-part tiles from the rack (up to limit), calling extendRight
+  // after each prefix. Mirrors scrabble.acrossGen.leftPart.
+  private leftPart(node: number, anchorCol: number, limit: number): void {
+    this.extendRight(node, anchorCol, anchorCol);
+    if (limit === 0) return;
+    this.dawg.arcs(node, (label, dest) => {
+      if (this.rk.has(label)) {
+        this.rk.remove(label);
+        this.left.push({ letter: label, blank: false });
+        this.leftPart(dest, anchorCol, limit - 1);
+        this.left.pop();
+        this.rk.add(label);
+      }
+      if (this.rk.blanks() > 0) {
+        this.rk.removeBlank();
+        this.left.push({ letter: label, blank: true });
+        this.leftPart(dest, anchorCol, limit - 1);
+        this.left.pop();
+        this.rk.addBlank();
+      }
+      return true;
+    });
+  }
+
+  // extendRight extends the word rightward from col, placing rack tiles on empty
+  // squares (constrained by cross-sets) and following board tiles. A word is recorded
+  // only past the anchor. Mirrors scrabble.acrossGen.extendRight.
+  private extendRight(node: number, col: number, anchorCol: number): void {
+    if (col >= this.bd.cols) {
+      if (col > anchorCol && this.dawg.final(node)) this.record(anchorCol);
+      return;
+    }
+    if (this.bd.filled(this.row, col)) {
+      const dest = this.dawg.next(node, this.bd.cellAt(this.row, col).letter);
+      if (dest >= 0) this.extendRight(dest, col + 1, anchorCol);
+      return;
+    }
+
+    if (col > anchorCol && this.dawg.final(node)) this.record(anchorCol);
+    const cross = this.cross(this.row, col);
+    this.dawg.arcs(node, (label, dest) => {
+      if (cross[label] !== 1) return true;
+      if (this.rk.has(label)) {
+        this.rk.remove(label);
+        this.right.push({ row: this.row, col, letter: label, blank: false });
+        this.extendRight(dest, col + 1, anchorCol);
+        this.right.pop();
+        this.rk.add(label);
+      }
+      if (this.rk.blanks() > 0) {
+        this.rk.removeBlank();
+        this.right.push({ row: this.row, col, letter: label, blank: true });
+        this.extendRight(dest, col + 1, anchorCol);
+        this.right.pop();
+        this.rk.addBlank();
+      }
+      return true;
+    });
+  }
+
+  // record assembles the play (left part at fixed columns, then the right part) and
+  // reports it, skipping plays that lay no new tile. Mirrors scrabble.acrossGen.record.
+  private record(anchorCol: number): void {
+    if (this.left.length + this.right.length === 0) return;
+    const placements: Placement[] = [];
+    const leftStart = anchorCol - this.left.length;
+    for (let i = 0; i < this.left.length; i++) {
+      placements.push({ row: this.row, col: leftStart + i, letter: this.left[i].letter, blank: this.left[i].blank });
+    }
+    for (const p of this.right) placements.push(p);
+    this.emit(placements);
+  }
+}
+
+// runAcross generates all across plays on bd and reports each via emit in bd's
+// coordinates. Cross-sets are computed lazily (vertical words on bd) and cached.
+// Mirrors DAWGGenerator.runAcross.
+function runAcross(
+  dawg: Dawg,
+  bd: GenBoard,
+  rk: GenRack,
+  size: number,
+  rs: Ruleset,
+  centerRow: number,
+  centerCol: number,
+  emit: (placements: Placement[]) => void,
+): void {
+  let crossFn: (r: number, c: number) => LetterSet;
+  if (rs.ignoreCrossWords) {
+    const full = fullSet(size);
+    crossFn = () => full;
+  } else {
+    const cache = new Array<LetterSet | undefined>(bd.rows * bd.cols);
+    crossFn = (r, c) => {
+      const i = r * bd.cols + c;
+      let s = cache[i];
+      if (!s) {
+        const { above, below } = columnContext(bd, r, c);
+        s = dawgCrossSet(dawg, above, below, size);
+        cache[i] = s;
+      }
+      return s;
+    };
+  }
+
+  const ag = new AcrossGen(dawg, bd, rk, crossFn, emit);
+  const firstMove = bd.isEmpty();
+  for (let row = 0; row < bd.rows; row++) {
+    ag.generateRow(row, firstMove, centerRow, centerCol);
+  }
+}
+
+// moveKey is a canonical string identifying a play (direction plus its placed tiles),
+// used to de-duplicate and rank generated moves. Mirrors scrabble.moveKey.
+export function moveKey(dir: Direction, placements: readonly Placement[]): string {
+  const ps = placements.slice().sort((a, b) => (a.row !== b.row ? a.row - b.row : a.col - b.col));
+  let s = String(dir);
+  for (const p of ps) s += `;${p.row},${p.col},${p.letter}${p.blank ? '*' : ''}`;
+  return s;
+}
+
+/**
+ * generateMoves returns every legal play for rack on board in the mode's orientations,
+ * ranked by descending score (ties broken by the canonical move key). It walks the DAWG
+ * with the cursor and scores each play with evaluate(); the alphabet size is taken from
+ * the ruleset's value table. Mirrors (*Solver).GenerateMovesOpts (the ruleset carries
+ * ignoreCrossWords for the single-word rule).
+ */
+export function generateMoves(dawg: Dawg, board: GenBoard, rack: GenRack, rs: Ruleset, mode: Mode = Both): Move[] {
+  const size = rs.values.length;
+  const rk = rack.clone(); // generation mutates the rack in place and restores it
+  const centerRow = Math.floor(rs.center / rs.cols);
+  const centerCol = rs.center % rs.cols;
+
+  const moves: Move[] = [];
+  const seen = new Set<string>();
+  const emit = (dir: Direction, placements: Placement[]): void => {
+    const key = moveKey(dir, placements);
+    if (seen.has(key)) return;
+    const res = evaluate(board, rs, dir, placements);
+    if (res.err || !res.move) return;
+    seen.add(key);
+    moves.push(res.move);
+  };
+
+  if (modeIncludes(mode, Horizontal)) {
+    runAcross(dawg, board, rk, size, rs, centerRow, centerCol, (p) => emit(Horizontal, p));
+  }
+  if (modeIncludes(mode, Vertical)) {
+    const tb = transpose(board);
+    runAcross(dawg, tb, rk, size, rs, centerCol, centerRow, (p) => {
+      const rp = p.map((pl) => ({ row: pl.col, col: pl.row, letter: pl.letter, blank: pl.blank }));
+      emit(Vertical, rp);
+    });
+  }
+
+  const kept = moves.filter((m) => connected(board, rs, m));
+  kept.sort((a, b) => {
+    if (a.score !== b.score) return b.score - a.score;
+    const ka = moveKey(a.dir, a.tiles);
+    const kb = moveKey(b.dir, b.tiles);
+    return ka < kb ? -1 : ka > kb ? 1 : 0;
+  });
+  return kept;
+}