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/web/BrowserPlatform.fs

@@ -41,7 +41,48 @@ let private randomSeed () : uint32 =
     crypto?getRandomValues (buf)
     buf[0]
 
-/// A Platform drawing on `canvas` (an HTML canvas element) and listening to the window's keys and frames.
+// m10: where the best score survives a reload.
+let private bestKey = "pure-snake-best"
+
+// Storage can be missing, blocked (privacy settings; some browsers throw as soon as localStorage is touched) or hold
+// anything: all of that reads as 0, and nothing throws. Only a non-negative whole number counts.
+let private loadBest () : int =
+    try
+        let raw: string = window?localStorage?getItem (bestKey)
+
+        if isNull raw then
+            0
+        else
+            // Only what saveBest writes counts: decimal digits, at most 2147483647 (so all three tracks read alike).
+            let digits = raw.Length >= 1 && raw.Length <= 10 && Seq.forall (fun c -> c >= '0' && c <= '9') raw
+
+            if digits && float raw <= 2147483647.0 then int (float raw) else 0
+    with _ ->
+        0
+
+// A record that cannot be stored is lost; the game goes on.
+let private saveBest (score: int) : unit =
+    try
+        window?localStorage?setItem (bestKey, string score)
+    with _ ->
+        ()
+
+// m13: a click on the canvas, in canvas pixels. The page may show the canvas larger or smaller than its width and
+// height (CSS, zoom) and draws a border round it, so the window coordinates of the mouse are made relative to the
+// drawing area (inside the border) and then scaled. The listener is added when the runtime asks, not before.
+let private onClick (canvas: obj) (cb: int -> int -> unit) : unit =
+    canvas?addEventListener ("click",
+                             fun (e: obj) ->
+                                 let r = canvas?getBoundingClientRect ()
+                                 let scale (client: float) (start: float) (border: float) (size: float) (shown: float) =
+                                     int (System.Math.Floor((client - start - border) * size / shown))
+
+                                 cb
+                                     (scale e?clientX r?left canvas?clientLeft canvas?width canvas?clientWidth)
+                                     (scale e?clientY r?top canvas?clientTop canvas?height canvas?clientHeight))
+
+/// A Platform drawing on `canvas` (an HTML canvas element) and listening to the window's keys and frames, and from
+/// m13 to clicks on the canvas.
 let create (canvas: obj) : Platform =
     let ctx = canvas?getContext ("2d")
 
@@ -56,9 +97,12 @@ let create (canvas: obj) : Platform =
             ctx?textAlign <- align
             ctx?fillText (text, x, y)
       RandomSeed = randomSeed
+      LoadBest = loadBest
+      SaveBest = saveBest
       StartClock = startClock
       OnKeyDown = listen "keydown"
-      OnKeyUp = listen "keyup" }
+      OnKeyUp = listen "keyup"
+      OnClick = onClick canvas }
 
 /// The page's `<canvas id="game">`.
 let gameCanvas () : obj = window?document?getElementById ("game")