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/Life/App.fs

@@ -0,0 +1,44 @@
+/// m13 life app: the same wiring as Snake and Pong, with a third kind of input, the mouse.
+module Snake.Life.App
+
+open Snake
+open Snake.Model
+open Snake.IO
+open Snake.Stream
+open Snake.Life.Model
+open Snake.Life.Rules
+open Snake.Life.View
+
+let GEN_MS = 150L
+
+let lifeKey (key: string) : LifeAction option =
+    match key with
+    | " " -> Some LifeAction.TogglePause
+    | "n" | "N" -> Some LifeAction.Step
+    | "c" | "C" -> Some LifeAction.Clear
+    | "r" | "R" -> Some LifeAction.Randomize
+    | _ -> None
+
+// Integer division rounds towards zero (-1 / 16 = 0), so the pixel is checked before dividing.
+let lifeClick (x: int) (y: int) : LifeAction option =
+    if x >= 0 && y >= 0 && x / LCELL < LW && y / LCELL < LH then
+        Some(LifeAction.Toggle { X = x / LCELL; Y = y / LCELL })
+    else
+        None
+
+let lifeActions: Stream<LifeAction> =
+    Stream.merge
+        (Stream.merge
+            (Stream.interval GEN_MS |> Stream.map (fun _ -> LifeAction.Frame))
+            (Stream.keyDowns |> Stream.choose lifeKey))
+        (Stream.clicks |> Stream.choose (fun (x, y) -> lifeClick x y))
+
+let lifeStates (seed: uint32) (actions: Stream<LifeAction>) : Stream<LifeState> =
+    actions |> Stream.scan lifeUpdate (initialLife seed) |> Stream.startWith (initialLife seed)
+
+let lifeMain () : IO<Stream<IO<unit>>> =
+    IO.randomSeed ()
+    |> IO.map (fun seed ->
+        lifeStates seed lifeActions
+        |> Stream.map (fun state -> IO.drawScene (lifeView state))
+        |> Stream.clampTime App.MAX_GAP_MS)