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/src/State.scala

@@ -0,0 +1,31 @@
+package snake
+
+/**
+ * Optional (Exercise 4.7). A `State[S, A]` is a plain function from a state to a pair: `s => (value, nextS)`.
+ * It is `Random[A]` with the seed replaced by any state type `S`. Nothing in the game uses this file.
+ * `run` is the case class's field, so there is nothing to write for it.
+ */
+final case class State[S, A](run: S => (A, S)):
+
+  /** Transform the value this State produces; the state threading is unchanged. */
+  def map[B](f: A => B): State[S, B] = ???
+
+  /** Run this State, feed its value to `f` to pick the next State, and run that with the state this one left behind. */
+  def flatMap[B](f: A => State[S, B]): State[S, B] = ???
+
+object State:
+
+  /** A State that gives `a` and leaves the state untouched: `s => (a, s)`. */
+  def pure[S, A](a: A): State[S, A] = ???
+
+  /**
+   * A State whose value is the current state, which it leaves untouched: `s => (s, s)`. When nothing else fixes the
+   * state type, give it at the call site: `State.get[Int]`.
+   */
+  def get[S]: State[S, S] = ???
+
+  /** A State that replaces the state with `s` and gives `()`: whatever the old state, `((), s)`. */
+  def put[S](s: S): State[S, Unit] = ???
+
+  /** A State that replaces the state `s` with `f(s)` and gives `()`. */
+  def modify[S](f: S => S): State[S, Unit] = ???