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/Stream.scala

@@ -1,10 +1,14 @@
 package snake
 
-/** Something that happens to the program: time passing (ms since start) or a key going down or up. */
+/**
+ * Something that happens to the program: time passing (ms since start), a key going down or up, or (from Module 13)
+ * a mouse click at canvas pixel (x, y). Every stream ignores the kinds of event it does not use.
+ */
 enum Event:
   case Time(t: Long)
   case KeyDown(key: String)
   case KeyUp(key: String)
+  case Click(x: Int, y: Int)
 
 /**
  * m08 stream: an event stream is a pure automaton (a Mealy machine).
@@ -54,6 +58,21 @@ final case class Stream[A](step: Event => (List[A], Stream[A])):
       (v :: out, next)
     }
 
+  // (m10) `last` is the previous real time, `clock` the time this stream has been told. A long silence
+  // (a background tab) moves `clock` by at most `maxGap`, so this stream never has to catch up on minutes of beats.
+  private def clampFrom(maxGap: Long, last: Long, clock: Long): Stream[A] =
+    Stream {
+      case Event.Time(t) =>
+        val now = clock + math.min(math.max(t - last, 0L), maxGap)
+        val (out, next) = step(Event.Time(now))
+        (out, next.clampFrom(maxGap, t, now))
+      case e =>
+        val (out, next) = step(e)
+        (out, next.clampFrom(maxGap, last, clock))
+    }
+
+  def clampTime(maxGap: Long): Stream[A] = clampFrom(maxGap, 0, 0)
+
   def run(events: List[Event]): List[A] =
     events
       .foldLeft((List.empty[A], this)) { case ((outs, stream), e) =>
@@ -75,6 +94,12 @@ object Stream:
     case _                => (Nil, keyUps)
   }
 
+  // (m13, given in src/) The position of every Click event, in canvas pixels. Like the key sources it remembers nothing.
+  lazy val clicks: Stream[(Int, Int)] = Stream {
+    case Event.Click(x, y) => (List((x, y)), clicks)
+    case _                 => (Nil, clicks)
+  }
+
   // `last` is the time of the previous Time event. Multiples of ms in (last, t] fire, ascending.
   private def intervalFrom(ms: Long, last: Long): Stream[Long] = Stream {
     case Event.Time(t) => ((last / ms + 1 to t / ms).map(_ * ms).toList, intervalFrom(ms, t))