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/App.fs

@@ -0,0 +1,34 @@
+/// m13 life app: the same wiring as Snake and Pong, with a third kind of input, the mouse.
+module Snake.Life.App
+
+open Snake
+open Snake.IO
+open Snake.Stream
+open Snake.Life.Model
+open Snake.Life.Rules
+open Snake.Life.View
+
+/// Milliseconds between two generations while the world runs.
+let GEN_MS = 150L
+
+/// A key press to a `LifeAction`, if any: " " -> TogglePause, "n"/"N" -> Step, "c"/"C" -> Clear,
+/// "r"/"R" -> Randomize. Any other key -> `None`.
+let lifeKey (key: string) : LifeAction option = failwith "TODO m13"
+
+/// A click at canvas pixel `(x, y)` to `Toggle` of the cell under it (`x / LCELL` and `y / LCELL`, rounded down),
+/// or `None` when the pixel is not on the board (left of it, above it, right of it, or in the status strip below it).
+/// Careful: F# integer division rounds towards zero, so `-1 / 16` is 0. Check the pixel before you divide.
+let lifeClick (x: int) (y: int) : LifeAction option = failwith "TODO m13"
+
+/// Everything that can happen to the world: `Frame` every GEN_MS (from `Stream.interval`), merged with `lifeKey` of
+/// every key press, merged with `lifeClick` of every click (`Stream.clicks`), in that order.
+/// (The stub is wrapped in `Stream` so the TODO only fires when the stream is stepped.)
+let lifeActions: Stream<LifeAction> = Stream(fun _ -> failwith "TODO m13")
+
+/// Fold the actions into a stream of states: start from `initialLife seed`, `lifeUpdate` for each action, emit the
+/// initial state first.
+let lifeStates (seed: uint32) (actions: Stream<LifeAction>) : Stream<LifeState> = failwith "TODO m13"
+
+/// The whole program as a value, like `App.main`: ask for a seed, turn the stream of states into a stream of drawings
+/// of `lifeView`, and wrap that stream in `Stream.clampTime App.MAX_GAP_MS`. A function of `unit`, like `App.main`.
+let lifeMain () : IO<Stream<IO<unit>>> = failwith "TODO m13"