feat(hint): persist the vs_ai idle-hint wait (wall-clock + read sanitiser)

Per the owner's call, the idle-hint gate now PERSISTS across leaving and reopening the
app, instead of the session-scoped monotonic clock: the unlock is a wall-clock instant
(hintUnlockAtMs) stamped from the robot's reply, stored on the local record, carried on
the game view + the opponent_moved move delta, and read through a sanitiser that caps it
at now + the window. So:
- the wait survives a relaunch (a stuck turn is not forgotten);
- a device clock set BACK cannot freeze the gate (the cap bounds the remaining to the
  window and self-heals on the next read);
- a clock set FORWARD just opens the hint early -- accepted as harmless for a solo game.

- lib/hints.ts hintGateRemainingMs now takes the unlock instant + clamps to the window.
- localgame: re-add hintUnlockAtMs to the record/meta; stamp it off the robot's reply;
  sanitise on read (a shared hintUnlock helper feeds stateView + the opponent_moved event).
- gamedelta + PushEvent: the move delta carries hintUnlockAtMs so the view stays fresh.
- Game.svelte: hintUnlockAt derives from the view; the tick + lock + toast unchanged.
- offline.spec.ts: also assert the lock survives a reload (the wait persisted).
- Docs FUNCTIONAL(+_ru)/ARCHITECTURE updated (persist + sanitiser, not monotonic-resets).

ui/src/lib/localgame/source.ts

@@ -13,6 +13,7 @@ import { serializeGame, replayGame, type LocalGameRecord, type Seat as LocalSeat
 import { getLocalGame, saveLocalGame, listLocalGames, deleteLocalGame } from './store';
 import { RULESETS } from './ruleset';
 import { getDawg } from '../dict';
+import { HINT_GATE_MS } from '../hints';
 import { LOCAL_ID_PREFIX, isLocalGameId } from './id';
 import { decide } from '../robot/strategy';
 import { GatewayError, type PlacedTile } from '../client';
@@ -120,6 +121,7 @@ export class LocalSource implements GameLoopSource {
       seats: opts.seats.map((s) => ({ kind: s.kind, name: s.name, accountId: s.accountId })),
       createdAtUnix: now,
       updatedAtUnix: now,
+      hintUnlockAtMs: 0, // no robot move yet: a human-first opening's hint is open at once
     });
     const entry: Live = { game, record };
     this.live.set(opts.id, entry);
@@ -277,15 +279,20 @@ export class LocalSource implements GameLoopSource {
       else if (dec.kind === 'exchange' && g.bagLength >= RULESETS[entry.record.variant].rackSize) out.push(g.exchange(dec.exchange));
       else out.push(g.pass());
     }
+    // Arm the idle hint gate from the robot's reply: a wall-clock unlock time, persisted so the wait
+    // survives a relaunch. Read back through a sanitiser (lib/hints / stateView) so a clock set back
+    // cannot freeze it.
+    if (out.length > 0) entry.record.hintUnlockAtMs = Date.now() + HINT_GATE_MS;
     return out;
   }
 
   private emitRobot(entry: Live, moves: LocalMove[]): void {
     const set = this.listeners.get(entry.record.id);
     if (!set) return;
+    const hintUnlockAtMs = this.hintUnlock(entry);
     for (const m of moves) {
       const game = this.gameView(entry);
-      const ev: PushEvent = { kind: 'opponent_moved', gameId: entry.record.id, move: this.moveRecord(entry.record.variant, m), game, bagLen: entry.game.bagLength };
+      const ev: PushEvent = { kind: 'opponent_moved', gameId: entry.record.id, move: this.moveRecord(entry.record.variant, m), game, bagLen: entry.game.bagLength, hintUnlockAtMs };
       for (const cb of set) cb(ev);
     }
     if (entry.game.isOver) {
@@ -301,6 +308,7 @@ export class LocalSource implements GameLoopSource {
       seats: entry.record.seats,
       createdAtUnix: entry.record.createdAtUnix,
       updatedAtUnix: nowUnix(),
+      hintUnlockAtMs: entry.record.hintUnlockAtMs,
     });
     await saveLocalGame(entry.record);
   }
@@ -333,10 +341,25 @@ export class LocalSource implements GameLoopSource {
 
   // --- shape builders --------------------------------------------------------
 
+  // The vs_ai idle-hint unlock instant, sanitised on read: capped at now + the window so a device
+  // clock set back cannot push it far ahead and freeze the gate (the client counts down from here).
+  // 0 while open (a human-first opening, no robot move yet).
+  private hintUnlock(entry: Live): number {
+    return entry.record.hintUnlockAtMs ? Math.min(entry.record.hintUnlockAtMs, Date.now() + HINT_GATE_MS) : 0;
+  }
+
   private stateView(entry: Live): StateView {
     const seat = this.humanSeat(entry);
     const rack = entry.game.handOf(seat).map((t) => indexToLetter(entry.record.variant, t));
-    return { game: this.gameView(entry), seat, rack, bagLen: entry.game.bagLength, hintsRemaining: 1, walletBalance: 0 };
+    return {
+      game: this.gameView(entry),
+      seat,
+      rack,
+      bagLen: entry.game.bagLength,
+      hintsRemaining: 1,
+      walletBalance: 0,
+      hintUnlockAtMs: this.hintUnlock(entry),
+    };
   }
 
   private gameView(entry: Live): GameView {