feat(hint): idle-gated wallet-free vs_ai hint on a monotonic clock (B4)

A vs_ai hint is now unlimited and wallet-free, but idle-gated as an anti-frustration
aid: it unlocks only after the player has been stuck ~30 min on a turn (timed from the
robot's last move; the human's first move, before the robot has played, is exempt).
While gated the hint button carries a small lock badge and a tap shows the remaining
minutes ('Available in N min.'); the lock lifts live at the mark.

The gate is enforced CLIENT-SIDE against a MONOTONIC clock (performance.now()), never a
wall-clock timestamp: a device clock the player controls (or an auto-sync) must not be
able to open or freeze it. The wait is therefore session-scoped -- a reload restarts it
(there is no tamper-proof way to carry idle time across a relaunch without a wall clock).
An online vs_ai game will gate the same way but from the server's clock (a follow-up).

- lib/hints.ts: HINT_GATE_MS + pure hintGateRemainingMs (monotonic) + hintLockMinutes;
  removed the wall-clock hintRemainingMs. Unit-tested red->green.
- Game.svelte: the monotonic gate (hintGateStart/monoNow, armed on the turn change), a
  vs_ai hint button (plain: no confirm, no count; lock badge + gated tap -> toast), a
  live 10s tick.
- localgame: removed the wall-clock hint gate and the now-dead robotLastMoveAtUnix field
  from source.ts/serialize.ts (the client is authoritative); hint() just serves the top
  move.
- i18n game.hintLockedIn.
- offline.spec.ts: assert the first move is un-gated and the lock arms after the robot moves.
- Docs FUNCTIONAL(+_ru) + ARCHITECTURE; bundle budget 114->115 (game-screen feature).

docs/ARCHITECTURE.md

@@ -1252,7 +1252,11 @@ an *Offline* chip and confines play to on-device `vs_ai` games. The **offline lo
 device-local games** (reconstructed by replaying the IndexedDB move journal) and its New-vs-AI entry
 creates one through the in-browser engine — the same game screen then drives it, the robot replying
 locally; online-only affordances (the Stats tab, the friend/random options in New Game) are disabled
-or hidden. To have data ready before the switch, the **Profile advertises the current dictionary
+or hidden. A local `vs_ai` hint is unlimited and wallet-free but idle-gated (unlocked ~30 min into a
+stuck turn); the gate is enforced **client-side against a monotonic clock** (`performance.now()`,
+`lib/hints`), never a wall-clock timestamp — a device clock the player controls must not be able to
+open or freeze it, so the wait is session-scoped (a reload restarts it). An online `vs_ai` game will
+gate the same way but from the server's clock (a follow-up). To have data ready before the switch, the **Profile advertises the current dictionary
 version per variant** (`dict_versions`,
 filled from the registry on the existing cold-start profile request — no extra round-trip), and an
 eligible installed PWA (standalone web + confirmed email) **background-preloads** those dictionaries

docs/FUNCTIONAL.md

@@ -215,7 +215,14 @@ unlimited and offers a complaint on any result; for a word it finds, it also lin
 external reference dictionary (gramota.ru for Russian games, scrabblewordfinder.org for
 English) to look it up. Hints are governed per game —
 whether they are allowed and how many each player starts with — and draw on a
-personal hint wallet once the per-game allowance is spent. The game ends when the
+personal hint wallet once the per-game allowance is spent. Against the robot
+(**vs_ai**) hints are instead **unlimited and wallet-free**, but idle-gated as an
+anti-frustration aid: one unlocks only after the player has been **stuck ~30 minutes
+on a turn** (timed from the robot's last move; the very first move, before the robot
+has played, is exempt). While gated the hint button carries a small **🔒 lock** and a
+tap shows how long remains; the lock lifts live at the mark. The wait uses a steady
+in-app timer, not the device clock — changing the clock cannot open or freeze it
+(though a reload restarts the wait). The game ends when the
 bag empties and a player clears their rack, after 6 consecutive scoreless turns,
 by resignation, or by the per-game move timeout (5 minutes to 24 hours, default
 24 hours): a missed turn auto-resigns, except while the player is inside their

docs/FUNCTIONAL_ru.md

@@ -222,7 +222,14 @@ e-mail) либо ввод фразы. Активные игры форфейтя
 внешний справочный словарь (gramota.ru для русских игр, scrabblewordfinder.org для английских),
 чтобы его посмотреть. Подсказки управляются настройками
 партии — разрешены ли они и сколько их у каждого игрока на старте — и расходуют
-личный кошелёк подсказок после исчерпания внутриигрового лимита. Партия
+личный кошелёк подсказок после исчерпания внутриигрового лимита. Против робота
+(**vs_ai**) подсказки, наоборот, **безлимитны и без кошелька**, но с idle-гейтом как
+анти-фрустрация: подсказка открывается, только когда игрок **застрял на ходу ~30 минут**
+(отсчёт от последнего хода робота; самый первый ход, до хода робота, исключён). Пока гейт
+закрыт, кнопка подсказки несёт маленький **🔒 замок**, а тап показывает, сколько осталось;
+замок снимается вживую в нужный момент. Отсчёт идёт по ровному внутриигровому таймеру, а не
+по системным часам — их перевод не откроет и не заморозит гейт (но перезагрузка отсчёт
+начинает заново). Партия
 завершается, когда мешок пуст и игрок выложил стойку, после 6 подряд бесплодных
 ходов, по сдаче, либо по таймауту хода (от 5 минут до 24 часов, дефолт 24 часа):
 пропущенный ход означает авто-сдачу, кроме как когда игрок внутри своего