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/solutions/State.scala

@@ -0,0 +1,32 @@
+package snake
+
+/**
+ * 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[Long, A].
+ * Nothing in the game uses this file; it is here to show that Random was one example of a bigger idea.
+ */
+final case class State[S, A](run: S => (A, S)):
+
+  def map[B](f: A => B): State[S, B] =
+    State { s =>
+      val (a, next) = run(s)
+      (f(a), next)
+    }
+
+  def flatMap[B](f: A => State[S, B]): State[S, B] =
+    State { s =>
+      val (a, next) = run(s)
+      f(a).run(next)
+    }
+
+object State:
+
+  def pure[S, A](a: A): State[S, A] = State(s => (a, s))
+
+  /** The current state as the value; the state is left untouched. */
+  def get[S]: State[S, S] = State(s => (s, s))
+
+  /** Replace the state with `s`; there is no interesting value, so it is `()`. */
+  def put[S](s: S): State[S, Unit] = State(_ => ((), s))
+
+  def modify[S](f: S => S): State[S, Unit] = State(s => ((), f(s)))