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>

e2e/tests/replay.spec.mjs

@@ -0,0 +1,58 @@
+// The replay viewer (replay.html) on every track, judged against the pure model. The recording is
+// fixtures/replay-sample.json, which the pages fetch and the oracle reads from disk.
+import { test, expect, TRACKS } from '../lib/app.mjs'
+import { FRAME } from '../lib/clock.mjs'
+import { recording, REPLAY_MS } from '../lib/oracle.mjs'
+
+const LAST = recording.actions.length
+const lastScene = (shapes) => shapes.slice(Math.max(0, shapes.findLastIndex((s) => s.tag === 'Rect' && s.x === 0 && s.y === 0 && s.w === 400)))
+const stepOf = (shapes) => {
+  const t = lastScene(shapes).find((s) => s.tag === 'Text' && s.text.startsWith('step '))
+  return Number(/^step (\d+) \//.exec(t.text)[1])
+}
+const textsOf = (shapes) => lastScene(shapes).filter((s) => s.tag === 'Text').map((s) => s.text)
+// Multiples of `ms` in (a, b]: how many beats of a `ms` interval fall between two frames at times a and b.
+const beats = (ms, a, b) => Math.floor(b / ms) - Math.floor(a / ms)
+// Time of the last animation frame so far, in the page's own clock (ms since its first frame).
+const lastFrameTime = (a) => Math.floor(a.clock.now / FRAME) * FRAME - a.clock.t0
+
+for (const track of TRACKS) {
+  test.describe(`${track}: replay`, () => {
+    test('Right, Left, Home and End show the model\'s frames', async ({ app }) => {
+      const a = await (await app(track, 'replay')).start()
+      expect(stepOf(await a.expectInSync())).toBe(0)
+      const seen = []
+      for (const key of ['ArrowRight', 'ArrowRight', 'ArrowRight', 'ArrowLeft', 'End', 'ArrowRight', 'ArrowLeft', 'Home', 'ArrowLeft']) {
+        await a.press(key)
+        seen.push(stepOf(await a.expectInSync(`after ${key}`)))
+        await a.advance(50)
+      }
+      await a.expectInSync()
+      expect(seen).toEqual([1, 2, 3, 2, LAST, LAST, LAST - 1, 0, 0])
+      expect(textsOf(a.lastPageFrame)).toContain(`step 0 / ${LAST}`)
+    })
+
+    test('autoplay advances one frame per 100 ms of fake time and stops on the last frame', async ({ app }) => {
+      const a = await (await app(track, 'replay')).start()
+      await a.advance(130)
+      await a.press(' ')
+      const pressedAt = lastFrameTime(a)
+      expect(textsOf(await a.expectInSync('play'))).toContain('Space: pause')
+      // For a while, check every 100 ms: the step shown is the number of 100 ms beats since the key.
+      for (let i = 0; i < 12; i++) {
+        await a.advance(REPLAY_MS)
+        expect(stepOf(await a.expectInSync(`playing, ${i}`))).toBe(beats(REPLAY_MS, pressedAt, lastFrameTime(a)))
+      }
+      // Then run to the end and beyond, a second at a time; it stops on the last frame.
+      while (a.state.playing) {
+        await a.advance(1000)
+        await a.expectInSync('playing on')
+      }
+      await a.advance(1000)
+      const end = await a.expectInSync('stopped')
+      expect(stepOf(end)).toBe(LAST)
+      expect(textsOf(end)).toContain('Left/Right: step   Home/End: jump   Space: play')
+      expect(beats(REPLAY_MS, pressedAt, lastFrameTime(a))).toBeGreaterThan(LAST)
+    })
+  })
+}