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>

js/solutions/life/model.js

@@ -0,0 +1,28 @@
+// m13 life model: the whole world is one value, like the snake and the match.
+
+/** @typedef {{x: number, y: number}} Point */
+/** @typedef {{cells: Point[], running: boolean, seed: number, generation: number}} LifeState */
+/** @typedef {{tag: 'Frame'} | {tag: 'Toggle', cell: Point} | {tag: 'TogglePause'} | {tag: 'Step'} | {tag: 'Clear'} | {tag: 'Randomize'}} LifeAction */
+
+// The board, in cells: LW columns, LH rows, LCELL pixels per cell. Below it the page shows a status strip.
+export const LW = 40
+export const LH = 30
+/** Pixels per cell. */
+export const LCELL = 16
+/** Height of the status strip under the board, in pixels. */
+export const STRIP = 24
+
+/** A fresh world: no live cells, paused, the given seed, generation 0.
+ * @type {(seed: number) => LifeState} */
+export const initialLife = (seed) => ({ cells: [], running: false, seed, generation: 0 })
+
+/** Everything that can happen to the world, as data. `Toggle` carries the cell that was clicked.
+ * @type {{Frame: LifeAction, Toggle: (cell: Point) => LifeAction, TogglePause: LifeAction, Step: LifeAction, Clear: LifeAction, Randomize: LifeAction}} */
+export const LifeAction = {
+  Frame: { tag: 'Frame' },
+  Toggle: (cell) => ({ tag: 'Toggle', cell }),
+  TogglePause: { tag: 'TogglePause' },
+  Step: { tag: 'Step' },
+  Clear: { tag: 'Clear' },
+  Randomize: { tag: 'Randomize' },
+}