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/dawg.ts

@@ -95,6 +95,85 @@ export class Dawg {
     return this.indexOf(word) >= 0;
   }
 
+  // --- Step-by-step traversal (the move generator's primitive) ---------------
+  //
+  // A `Node` is a bit offset into the graph; 0 denotes the root (which resolves
+  // to firstNodeOffset). These mirror dafsa's traverse.go Cursor (Root/Final/
+  // Next/Arcs) over the same bitstream this reader already decodes, so the ported
+  // generator can drive the automaton one transition at a time. Single-threaded
+  // JS shares this reader's position across calls; every method re-seeks to its
+  // node on entry, and arcs brackets the callback with a save/restore, so nested
+  // use during a walk is safe. Mirrors dafsa (*Cursor).
+
+  /** root returns the start state of the automaton. */
+  root(): number {
+    return 0;
+  }
+
+  /** final reports whether node is an accepting state (a stored word ends there). */
+  final(node: number): boolean {
+    if (this.numEdges <= 0) {
+      return this.hasEmptyWord && node === 0;
+    }
+    this.p = node === 0 ? this.firstNodeOffset : node;
+    return this.readBits(1) === 1;
+  }
+
+  /**
+   * next follows the edge labelled ch (an alphabet index) from node, returning the
+   * destination node, or -1 when no such edge exists.
+   */
+  next(node: number, ch: number): number {
+    return this.getEdge(node, ch) ? this.eNode : -1;
+  }
+
+  /**
+   * arcs calls fn for each out-edge of node in ascending label order, passing the
+   * edge's label, its destination node and whether that destination is accepting.
+   * It stops early if fn returns false. Mirrors dafsa (*Cursor).Arcs.
+   */
+  arcs(node: number, fn: (label: number, dest: number, final: boolean) => boolean): void {
+    if (this.numEdges <= 0) {
+      return;
+    }
+    this.p = node === 0 ? this.firstNodeOffset : node;
+    this.readBits(1); // node final flag — not needed here
+    const fallthrough = this.readBits(1);
+
+    if (fallthrough === 1) {
+      const label = this.readBits(this.cbits);
+      // The reader now sits at the destination node, whose first bit is its final flag.
+      const dest = this.p;
+      const final = this.readBits(1) === 1;
+      fn(label, dest, final);
+      return;
+    }
+
+    const nskiplen = bitsLen(this.wbits);
+    let nskip = 0;
+    let numEdges = 1;
+    if (this.readBits(1) !== 1) {
+      // not a single edge
+      numEdges = this.readUnsigned();
+      nskip = this.readBits(nskiplen);
+    }
+
+    for (let i = 0; i < numEdges; i++) {
+      const label = this.readBits(this.cbits);
+      if (i > 0) {
+        this.readBits(nskip); // per-edge skip count, unused for traversal
+      }
+      const dest = this.readBits(this.abits);
+      const resume = this.p;
+      this.p = dest;
+      const final = this.readBits(1) === 1;
+      if (!fn(label, dest, final)) {
+        return;
+      }
+      this.p = resume;
+    }
+  }
+
   // getEdge resolves the outgoing edge for ch from the node at the given bit
   // offset. On success it fills eNode/eCount/eFinal and returns true. Mirrors
   // dafsa (*dawg).getEdge.