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>

fixtures/m04-tick.json

@@ -22,7 +22,8 @@
           "seed": 0,
           "score": 0,
           "status": "Playing",
-          "frame": 0
+          "frame": 0,
+          "queued": null
         }
       ],
       "expected": {
@@ -47,7 +48,8 @@
         "seed": 1831565813,
         "score": 1,
         "status": "Playing",
-        "frame": 0
+        "frame": 0,
+        "queued": null
       }
     },
     {
@@ -71,7 +73,8 @@
           "seed": 0,
           "score": 0,
           "status": "Playing",
-          "frame": 0
+          "frame": 0,
+          "queued": null
         }
       ],
       "expected": {
@@ -92,7 +95,8 @@
         "seed": 0,
         "score": 0,
         "status": "Playing",
-        "frame": 0
+        "frame": 0,
+        "queued": null
       }
     },
     {
@@ -116,7 +120,8 @@
           "seed": 0,
           "score": 0,
           "status": "Playing",
-          "frame": 0
+          "frame": 0,
+          "queued": null
         }
       ],
       "expected": {
@@ -137,7 +142,8 @@
         "seed": 0,
         "score": 0,
         "status": "GameOver",
-        "frame": 0
+        "frame": 0,
+        "queued": null
       }
     },
     {
@@ -161,7 +167,8 @@
           "seed": 0,
           "score": 0,
           "status": "GameOver",
-          "frame": 0
+          "frame": 0,
+          "queued": null
         }
       ],
       "expected": {
@@ -182,7 +189,72 @@
         "seed": 0,
         "score": 0,
         "status": "GameOver",
-        "frame": 0
+        "frame": 0,
+        "queued": null
+      }
+    },
+    {
+      "name": "eating-the-last-free-cell-wins",
+      "args": [
+        {
+          "width": 2,
+          "height": 2,
+          "snake": [
+            {
+              "x": 0,
+              "y": 0
+            },
+            {
+              "x": 0,
+              "y": 1
+            },
+            {
+              "x": 1,
+              "y": 1
+            }
+          ],
+          "dir": "Up",
+          "nextDir": "Right",
+          "apple": {
+            "x": 1,
+            "y": 0
+          },
+          "seed": 7,
+          "score": 2,
+          "status": "Playing",
+          "frame": 0,
+          "queued": null
+        }
+      ],
+      "expected": {
+        "width": 2,
+        "height": 2,
+        "snake": [
+          {
+            "x": 1,
+            "y": 0
+          },
+          {
+            "x": 0,
+            "y": 0
+          },
+          {
+            "x": 0,
+            "y": 1
+          },
+          {
+            "x": 1,
+            "y": 1
+          }
+        ],
+        "dir": "Right",
+        "nextDir": "Right",
+        "apple": null,
+        "seed": 7,
+        "score": 3,
+        "status": "Won",
+        "frame": 0,
+        "queued": null
       }
     }
   ]