feat(course): audit fixes and twelve extensions (Modules 7b, 12, 13)

Audit pass:
- Frame rule counts frames since the last move, so every step lasts
  exactly movesEvery(score) frames, also right after a speed-up
- clampTime + MAX_GAP_MS: a hidden tab no longer replays the whole gap
- Pong Restart keeps held keys
- Fact corrections (mulberry32 output coverage, Haskell IO, uniform)
- New fixture cases from a mutation analysis

Extensions (all three tracks, shared fixtures, course text):
- Turn queue (Exercise 10.6), persisted high score (10.7),
  replay viewer (10.8), play() end-to-end helper (9.5)
- Optional State (4.7) and optional Module 7b, stack-safe IO
- Module 12, property-based testing with generators, shrinking,
  invariants and a model-based oracle
- Module 13, Conway's Life with a Click event
- JS type checking via jsconfig, JSDoc and types.d.ts
- Maintainer tools: scripts/mutate.mjs, scripts/typecheck-js.sh,
  Playwright end-to-end suite (e2e/, scripts/e2e.sh)

Docs: docs/contract.md is the canonical contract; specs and build log
under docs/superpowers.

Verified: JS 728, Scala 689, F# 691 unit tests; stubs and progression
M01-M13 and M07b; 176 end-to-end tests on Chromium and WebKit.

Co-Authored-By: Claude Fable 5.2 <noreply@anthropic.com>

scala/solutions/Game.scala

@@ -2,19 +2,41 @@ package snake
 
 /**
  * m05 game: one `update` turns every action into a new state; replaying a game is a fold over its actions.
- * m10 adds pause, restart and a frame clock that speeds up as the score grows.
+ * m10 adds pause, restart, a frame counter that makes the snake speed up as the score grows, and a turn queue.
  */
 object Game:
 
+  /**
+   * What `update` does with `Turn(dir)` from Module 10 on. With no turn pending (`nextDir == dir`) it is the Module 3
+   * `turn`. With a turn pending, a key that is neither `nextDir` nor its opposite is remembered in `queued`
+   * (replacing an earlier one) and taken on the step after; any other key changes nothing.
+   */
+  def steer(state: GameState, dir: Direction): GameState =
+    if state.status != Status.Playing then state
+    else if state.nextDir == state.dir then Rules.turn(state, dir)
+    else if dir != state.nextDir && dir != Model.opposite(state.nextDir) then state.copy(queued = Some(dir))
+    else state
+
+  // After a step: a game still in play takes the queued turn, if there is one. It is always a legal turn, because the
+  // step just made `dir` equal to the old `nextDir`, and `queued` is neither that nor its opposite.
+  private def takeQueued(state: GameState): GameState = state.queued match
+    case Some(dir) if state.status == Status.Playing => state.copy(nextDir = dir, queued = None)
+    case _                                           => state
+
+  // One game step as `update` takes it: `tick`, then the queued turn.
+  private def step(state: GameState): GameState = takeQueued(Spawn.tick(state))
+
   /** How many frames pass between game steps: 8 at first, one fewer every 3 points, never fewer than 2. */
   def movesEvery(score: Int): Int = math.max(2, 8 - score / 3)
 
-  // One animation frame: count it, and every `movesEvery(score)`-th frame run a game step.
+  // One animation frame. `frame` counts the frames since the snake last moved; when it reaches
+  // `movesEvery(score)` the count starts again and the game takes a step. Counting from the last move
+  // (not from the start of the game) keeps every step exactly `movesEvery` frames long, also right after a speed-up.
   private def frame(state: GameState): GameState =
     if state.status != Status.Playing then state
     else
-      val counted = state.copy(frame = state.frame + 1)
-      if counted.frame % movesEvery(counted.score) == 0 then Spawn.tick(counted) else counted
+      val n = state.frame + 1
+      if n >= movesEvery(state.score) then step(state.copy(frame = 0)) else state.copy(frame = n)
 
   // Pause and resume only make sense in those two statuses; a finished game stays finished.
   private def togglePause(state: GameState): GameState = state.status match
@@ -24,8 +46,8 @@ object Game:
 
   // Every case is listed (no `case _`): adding an Action later makes the compiler point here.
   def update(state: GameState, action: Action): GameState = action match
-    case Action.Tick        => Spawn.tick(state)
-    case Action.Turn(dir)   => Rules.turn(state, dir)
+    case Action.Tick        => step(state)
+    case Action.Turn(dir)   => steer(state, dir)
     case Action.TogglePause => togglePause(state)
     case Action.Restart     => Spawn.newGame(state.seed)
     case Action.Frame       => frame(state)