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/state.js

@@ -0,0 +1,38 @@
+// m04 state (optional, Exercise 4.7): the general pattern behind Random. A State<S, A> is a function
+// s => [A, nextS]: it reads a state, produces a value and hands on a new state. Random<A> is State<seed, A>.
+// Nothing in the game uses this file; it is here to show that Random was one example of a bigger idea.
+/** @import { State } from './types' */
+
+/** A State that gives `a` and leaves the state untouched.
+ * @type {<S, A>(a: A) => State<S, A>} */
+export const pure = (a) => (s) => [a, s]
+
+/** Transform the value a State produces; the state threading is unchanged.
+ * @type {<S, A, B>(st: State<S, A>, f: (a: A) => B) => State<S, B>} */
+export const map = (st, f) => (s) => {
+  const [a, next] = st(s)
+  return [f(a), next]
+}
+
+/** Run `st`, let `f` pick the next State from its value, and run that with the state `st` left behind.
+ * @type {<S, A, B>(st: State<S, A>, f: (a: A) => State<S, B>) => State<S, B>} */
+export const flatMap = (st, f) => (s) => {
+  const [a, next] = st(s)
+  return f(a)(next)
+}
+
+/** A State whose value is the current state, which it leaves untouched.
+ * @type {<S>(s: S) => [S, S]} */
+export const get = (s) => [s, s]
+
+/** A State that replaces the state with `s` and gives `undefined` (there is no interesting value).
+ * @type {<S>(s: S) => State<S, undefined>} */
+export const put = (s) => () => [undefined, s]
+
+/** A State that replaces the state `s` with `f(s)` and gives `undefined`.
+ * @type {<S>(f: (s: S) => S) => State<S, undefined>} */
+export const modify = (f) => (s) => [undefined, f(s)]
+
+/** Run a State from an initial state: `[value, finalState]`.
+ * @type {<S, A>(st: State<S, A>, s: S) => [A, S]} */
+export const run = (st, s) => st(s)