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/test/M04State.test.scala

@@ -0,0 +1,77 @@
+package snake
+
+class M04StateSuite extends munit.FunSuite:
+  // Small initial states for the "behaves like" checks: two States behave alike when they give the same pair from each.
+  private val starts = List(0, 1, 7, 42)
+  private def sameOnAll[A](st1: State[Int, A], st2: State[Int, A]): Unit =
+    starts.foreach(s => assertEquals(st1.run(s), st2.run(s), s"from state $s"))
+
+  // A counter step: gives the current number times 10 and adds 1 to the state. A def, so that a stub that throws
+  // fails each test on its own instead of the whole suite at construction time.
+  private def step: State[Int, Int] = State.get[Int].flatMap(n => State.put(n + 1).map(_ => n * 10))
+
+  private def f(a: Int): State[Int, Int] = State.modify[Int](_ * 2).map(_ => a + 1)
+  private def g(b: Int): State[Int, (Int, Int)] = State.get[Int].flatMap(s => State.pure((b, s)))
+
+  test("State pure gives its value and leaves the state alone") {
+    assertEquals(State.pure[Int, String]("x").run(99), ("x", 99))
+  }
+
+  test("State map applies f to the value and keeps the state from the underlying step") {
+    assertEquals(step.map(_ + 1).run(4), (41, 5))
+  }
+
+  test("State flatMap threads the state through both steps") {
+    assertEquals(step.flatMap(a => step.map(b => (a, b))).run(4), ((40, 50), 6))
+  }
+
+  test("State get gives the state as the value and leaves it alone") {
+    assertEquals(State.get[String].run("board"), ("board", "board"))
+  }
+
+  test("State put replaces the state and gives unit") {
+    assertEquals(State.put(5).run(99), ((), 5))
+  }
+
+  test("State modify applies f to the state and gives unit") {
+    assertEquals(State.modify[Int](_ * 2).run(21), ((), 42))
+  }
+
+  test("State law: left identity, flatMap(pure(a), f) behaves like f(a)") {
+    sameOnAll(State.pure[Int, Int](3).flatMap(f), f(3))
+  }
+
+  test("State law: right identity, flatMap(m, pure) behaves like m") {
+    sameOnAll(step.flatMap(State.pure), step)
+  }
+
+  test("State law: associativity, the grouping of flatMap does not matter") {
+    sameOnAll(step.flatMap(f).flatMap(g), step.flatMap(a => f(a).flatMap(g)))
+  }
+
+  test("State a counter hands out fresh labels in order") {
+    val fresh = State.get[Int].flatMap(n => State.put(n + 1).map(_ => s"L$n"))
+    val three = fresh.flatMap(a => fresh.flatMap(b => fresh.map(c => List(a, b, c))))
+    assertEquals(three.run(0), (List("L0", "L1", "L2"), 3))
+    assertEquals(three.run(7), (List("L7", "L8", "L9"), 10))
+  }
+
+  test("State Random is State with the seed as S: the dice give the same values and seeds") {
+    // One draw written only with State's get and put: read the seed, compute, store the next seed.
+    val draw = State.get[Long].flatMap { seed =>
+      val (v, next) = Random.nextUint32.run(seed)
+      State.put(next).map(_ => v)
+    }
+    val d6State = draw.map(v => 1 + (v % 6))
+    val twoDiceState = d6State.flatMap(a => d6State.map(b => a + b))
+    val d6Random = Random.nextUint32.map(v => 1 + (v % 6))
+    val twoDiceRandom = d6Random.flatMap(a => d6Random.map(b => a + b))
+    // A Random step turned into a State by hand: the same function, in the other wrapper.
+    val drawAsState = State[Long, Long](seed => Random.nextUint32.run(seed))
+    List(0L, 1L, 42L, 4294967295L).foreach { seed =>
+      assertEquals(draw.run(seed), Random.nextUint32.run(seed), s"draw from $seed")
+      assertEquals(draw.run(seed), drawAsState.run(seed), s"draw as a State from $seed")
+      assertEquals(d6State.run(seed), d6Random.run(seed), s"d6 from $seed")
+      assertEquals(twoDiceState.run(seed), twoDiceRandom.run(seed), s"twoDice from $seed")
+    }
+  }