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/Life/Model.fs

@@ -0,0 +1,32 @@
+/// m13 life model: the whole world is one value, like the snake and the match.
+module Snake.Life.Model
+
+open Snake.Model
+
+/// `Cells` is canonical: sorted row-major (by `Y`, then `X`), no duplicates, all on the board.
+type LifeState =
+    { Cells: Point list
+      Running: bool
+      Seed: uint32
+      Generation: int }
+
+[<RequireQualifiedAccess>]
+type LifeAction =
+    | Frame
+    | Toggle of Point
+    | TogglePause
+    | Step
+    | Clear
+    | Randomize
+
+// The board, in cells: LW columns, LH rows, LCELL pixels per cell. Below it the page shows a status strip.
+let LW = 40
+let LH = 30
+let LCELL = 16
+let STRIP = 24
+
+let initialLife (seed: uint32) : LifeState =
+    { Cells = []
+      Running = false
+      Seed = seed
+      Generation = 0 }