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/src/Life/Rules.fs

@@ -0,0 +1,27 @@
+/// m13 life rules: the next generation is a function of the whole old board, and nothing else.
+module Snake.Life.Rules
+
+open Snake
+open Snake.Model
+open Snake.Life.Model
+
+/// One generation of Conway's Life on the LW x LH board (B3/S23), from a canonical list of live cells to a canonical
+/// list (sorted row-major: by `Y`, then `X`; no duplicates).
+/// - A live cell with 2 or 3 live neighbours stays alive; a dead cell with exactly 3 live neighbours is born;
+///   every other cell is dead in the next generation.
+/// - The neighbours of a cell are the up to 8 cells around it that are on the board: the edges are dead,
+///   nothing wraps around.
+/// - Every cell is judged by the *old* board only.
+let lifeStep (cells: Point list) : Point list = failwith "TODO m13"
+
+/// The one function that says how the world changes.
+/// - `Frame`: when running, the next generation (`lifeStep`) and `Generation + 1`; when paused, unchanged.
+/// - `Step`: when paused, the next generation and `Generation + 1`; when running, unchanged.
+/// - `TogglePause`: `Running` flips.
+/// - `Toggle cell`: a dead cell becomes alive, a live one dead, whether the world runs or not; `Cells` stays canonical
+///   (insert the new cell at its row-major place). A cell off the board changes nothing. `Generation` is unchanged.
+/// - `Clear`: no live cells, generation 0; `Running` and `Seed` are kept.
+/// - `Randomize`: draw `Random.intBelow 4` (Module 4) once for every cell of the board, in row-major order
+///   (y = 0..LH-1, and within a row x = 0..LW-1), threading the seed from `state.Seed`; a cell is alive when its draw
+///   is 0. The state gets those cells, the seed after the last draw, and generation 0; `Running` is kept.
+let lifeUpdate (state: LifeState) (action: LifeAction) : LifeState = failwith "TODO m13"