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>

fsharp/solutions/Game.fs

@@ -1,19 +1,40 @@
 /// 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.
 module Snake.Game
 
 open Snake.Model
 
+/// What `update` does with `Turn dir` from m10 on. With no turn pending (`NextDir = Dir`) it is the m03 `Rules.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.
+let steer (state: GameState) (dir: Direction) : GameState =
+    if state.Status <> Playing then state
+    elif state.NextDir = state.Dir then Rules.turn state dir
+    elif dir <> state.NextDir && dir <> opposite state.NextDir then { state with 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.
+let private takeQueued (state: GameState) : GameState =
+    match state.Queued with
+    | Some d when state.Status = Playing -> { state with NextDir = d; Queued = None }
+    | _ -> state
+
+// One game step as `update` takes it: `Spawn.tick`, then the queued turn.
+let private 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.
 let movesEvery (score: int) : int = 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.
 let private frame (state: GameState) : GameState =
     if state.Status <> Playing then
         state
     else
-        let counted = { state with Frame = state.Frame + 1 }
-        if counted.Frame % movesEvery counted.Score = 0 then Spawn.tick counted else counted
+        let n = state.Frame + 1
+        if n >= movesEvery state.Score then step { state with Frame = 0 } else { state with Frame = n }
 
 // Pause and resume only make sense in those two statuses; a finished game stays finished.
 let private togglePause (state: GameState) : GameState =
@@ -26,8 +47,8 @@ let private togglePause (state: GameState) : GameState =
 // Every case is listed (no `| _ ->`): adding an Action later makes the compiler point here.
 let update (state: GameState) (action: Action) : GameState =
     match action with
-    | Tick -> Spawn.tick state
-    | Turn dir -> Rules.turn state dir
+    | Tick -> step state
+    | Turn dir -> steer state dir
     | TogglePause -> togglePause state
     | Restart -> Spawn.newGame state.Seed
     | Frame -> frame state