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/life/App.scala

@@ -0,0 +1,36 @@
+package snake
+package life
+
+import LifeModel.*
+
+/** m13 life app: the same wiring as Snake and Pong, with a third kind of input, the mouse. */
+object LifeApp:
+
+  val GEN_MS: Long = 150
+
+  def lifeKey(key: String): Option[LifeAction] = key match
+    case " "       => Some(LifeAction.TogglePause)
+    case "n" | "N" => Some(LifeAction.Step)
+    case "c" | "C" => Some(LifeAction.Clear)
+    case "r" | "R" => Some(LifeAction.Randomize)
+    case _         => None
+
+  // The pixel is checked before dividing: integer division rounds towards zero, so -1 / 16 would be cell 0.
+  def lifeClick(x: Int, y: Int): Option[LifeAction] =
+    if x >= 0 && y >= 0 && x / LCELL < LW && y / LCELL < LH then Some(LifeAction.Toggle(Point(x / LCELL, y / LCELL)))
+    else None
+
+  lazy val lifeActions: Stream[LifeAction] =
+    Stream
+      .interval(GEN_MS)
+      .map(_ => LifeAction.Frame)
+      .merge(Stream.keyDowns.filterMap(lifeKey))
+      .merge(Stream.clicks.filterMap(lifeClick(_, _)))
+
+  def lifeStates(seed: Long, actions: Stream[LifeAction]): Stream[LifeState] =
+    actions.scan(initialLife(seed))(LifeRules.lifeUpdate).startWith(initialLife(seed))
+
+  lazy val lifeMain: IO[Stream[IO[Unit]]] =
+    IO.randomSeed.map(seed =>
+      lifeStates(seed, lifeActions).map(state => IO.drawScene(LifeView.lifeView(state))).clampTime(App.MAX_GAP_MS)
+    )