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/tests/M09Runtime.fs

@@ -8,17 +8,25 @@ open Snake.Runtime
 open Snake.Tests.M09Helpers
 
 /// A fake platform: records every call and lets the test fire events by hand. (Tests may mutate; src/ may not.)
-type FakePlatform(seed: uint32) =
+type FakePlatform(seed: uint32, best: int) =
     let calls = ResizeArray<obj list>()
     let mutable onTime: int64 -> unit = ignore
     let mutable onDown: string -> unit = ignore
     let mutable onUp: string -> unit = ignore
+    // m13: a runtime from Module 9 does not register this yet; nothing in m09 fires a click.
+    let mutable onClick: int -> int -> unit = fun _ _ -> ()
+    let registered = ResizeArray<string>()
+
+    new(seed: uint32) = FakePlatform(seed, 0)
 
     member _.Calls: obj list list = List.ofSeq calls
     member _.Clear() = calls.Clear()
     member _.FireTime(t: int64) = onTime t
     member _.FireKey(key: string) = onDown key
     member _.FireKeyUp(key: string) = onUp key
+    member _.FireClick(x: int, y: int) = onClick x y
+    /// The names of the handlers the runtime registered ("click", "down", "time", "up"), sorted.
+    member _.Registered: string list = registered |> Seq.distinct |> Seq.sort |> List.ofSeq
 
     member _.Platform: Platform =
         { FillRect = fun x y w h color -> calls.Add [ box "fillRect"; box x; box y; box w; box h; box color ]
@@ -29,9 +37,27 @@ type FakePlatform(seed: uint32) =
             fun () ->
                 calls.Add [ box "randomSeed" ]
                 seed
-          StartClock = fun cb -> onTime <- cb
-          OnKeyDown = fun cb -> onDown <- cb
-          OnKeyUp = fun cb -> onUp <- cb }
+          LoadBest =
+            fun () ->
+                calls.Add [ box "loadBest" ]
+                best
+          SaveBest = fun n -> calls.Add [ box "saveBest"; box n ]
+          StartClock =
+            fun cb ->
+                registered.Add "time"
+                onTime <- cb
+          OnKeyDown =
+            fun cb ->
+                registered.Add "down"
+                onDown <- cb
+          OnKeyUp =
+            fun cb ->
+                registered.Add "up"
+                onUp <- cb
+          OnClick =
+            fun cb ->
+                registered.Add "click"
+                onClick <- cb }
 
 // What the platform should have been asked to draw for a scene.
 let private expectedCalls (scene: Scene) : obj list list =