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/runtime.js

@@ -1,10 +1,13 @@
 // The single impure place in the course (with browser.js and main.js): everything else only builds values.
 // Here we interpret IO descriptions against a Platform and hold the one mutable variable, the current stream.
-// Platform = { fillRect, fillText, randomSeed, startClock, onKeyDown, onKeyUp }
+// Platform = { fillRect, fillText, randomSeed, loadBest, saveBest, startClock, onKeyDown, onKeyUp, onClick }
+/** @import { IO, Platform, Program } from './types' */
 
 // Perform one op on the platform and return its result.
 const perform = (op, platform) => {
   if (op.tag === 'RandomSeed') return platform.randomSeed()
+  if (op.tag === 'LoadBest') return platform.loadBest()
+  if (op.tag === 'SaveBest') return platform.saveBest(op.score)
   const s = op.shape
   return s.tag === 'Rect'
     ? platform.fillRect(s.x, s.y, s.w, s.h, s.color)
@@ -12,12 +15,14 @@ const perform = (op, platform) => {
 }
 
 // A loop, not recursion: a scene is hundreds of ops and the stack must not grow with them.
+/** @type {<A>(io: IO<A>, platform: Platform) => A} */
 export const runIO = (io, platform) => {
   let current = io
   while (current.tag === 'Effect') current = current.k(perform(current.op, platform))
   return current.value
 }
 
+/** @type {(main: Program, platform: Platform) => void} */
 export const runApp = (main, platform) => {
   let stream = runIO(main, platform)
   const feed = (input) => {
@@ -27,5 +32,7 @@ export const runApp = (main, platform) => {
   }
   platform.onKeyDown((key) => feed({ tag: 'KeyDown', key }))
   platform.onKeyUp((key) => feed({ tag: 'KeyUp', key }))
+  // m13: a fourth kind of input. Programs that do not listen for clicks simply ignore them.
+  platform.onClick((x, y) => feed({ tag: 'Click', x, y }))
   platform.startClock((t) => feed({ tag: 'Time', t }))
 }