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>

fsharp/solutions/Runtime.fs

@@ -11,14 +11,23 @@ type Platform =
     { FillRect: int -> int -> int -> int -> string -> unit
       FillText: int -> int -> string -> string -> int -> string -> unit
       RandomSeed: unit -> uint32
+      // m10: the stored best score; reading must never fail (anything unreadable is 0).
+      LoadBest: unit -> int
+      SaveBest: int -> unit
       StartClock: (int64 -> unit) -> unit
       OnKeyDown: (string -> unit) -> unit
-      OnKeyUp: (string -> unit) -> unit }
+      OnKeyUp: (string -> unit) -> unit
+      // m13: clicks on the canvas, in canvas pixels.
+      OnClick: (int -> int -> unit) -> unit }
 
 // Perform one op on the platform and return its answer.
 let private perform (p: Platform) (op: Op) : OpResult =
     match op with
     | RandomSeed -> Seed(p.RandomSeed())
+    | LoadBest -> Best(p.LoadBest())
+    | SaveBest score ->
+        p.SaveBest score
+        Done
     | Draw(Rect(x, y, w, h, color)) ->
         p.FillRect x y w h color
         Done
@@ -43,4 +52,6 @@ let runApp (p: Platform) (main: IO<Stream<IO<unit>>>) : unit =
 
     p.OnKeyDown(fun key -> feed (KeyDown key))
     p.OnKeyUp(fun key -> feed (KeyUp key))
+    // m13: a fourth kind of event. Programs that do not listen for clicks simply ignore them.
+    p.OnClick(fun x y -> feed (Click(x, y)))
     p.StartClock(fun t -> feed (Time t))