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/Model.scala

@@ -0,0 +1,32 @@
+package snake
+package life
+
+// m13 life model: the whole world is one value, like the snake and the match.
+
+/**
+ * The whole world. `cells` are the live cells, always kept canonical: sorted row-major (by `y`, then by `x`), each cell
+ * at most once, all on the board. `seed` is the unsigned 32-bit seed that `Randomize` draws from; `generation` counts
+ * the generations since the board was last cleared or randomized.
+ */
+final case class LifeState(cells: List[Point], running: Boolean, seed: Long, generation: Int)
+
+/** Everything that can happen to the world, as data. `Toggle` carries the cell that was clicked. */
+enum LifeAction:
+  case Frame
+  case Toggle(cell: Point)
+  case TogglePause, Step, Clear, Randomize
+
+object LifeModel:
+
+  // The board, in cells: LW columns, LH rows, LCELL pixels per cell. Below it the page shows a status strip.
+  val LW = 40
+  val LH = 30
+
+  /** Pixels per cell. */
+  val LCELL = 16
+
+  /** Height of the status strip under the board, in pixels. */
+  val STRIP = 24
+
+  /** A fresh world: no live cells, paused, the given seed, generation 0. */
+  def initialLife(seed: Long): LifeState = LifeState(Nil, running = false, seed, generation = 0)