Gimbal

Build a tiny browser game called "Gimbal".

Game spec
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A marble labyrinth on a tilting gimbal, drawn as real 3D: a pinhole camera over perspective-projected slab, rim, walls and pits, depth-sorted far to near. THE PROMISE: one geometry, in slab-local coordinates, pushed through ONE world()->project() transform — the slab, its walls, its pits, the goal pad and the marble are all that transform, so the pit you fall into and the pit the screen paints are the same (u,v,r) tuple and cannot drift apart. Gravity is not a painted animation over separate physics either: the sim's acceleration is the world gravity vector projected onto the SAME rotation's in-plane axes, G*sin(tiltV)*cos(tiltU) along u and G*sin(tiltU) along v, so what you see is what pulls. Tilt eases toward the held direction (a gimbal, not a toggle) and difficulty IS the max tilt angle (0.16/0.21/0.27 rad), which makes hard turns and the speed ceiling a difficulty dial rather than a number. Walls are circle-vs-AABB with reflection and energy loss; a marble whose centre gets inside a wall is ejected through the nearest face, never left embedded. Pits swallow a marble below a difficulty-scaled SAFE speed and a fast marble skips the same tuple — the risk reward. The rim is a low lip: arrive above SAFE speed and you carry over it and are gone. The clock is DERIVED, not invented: a calibration bot that plans a real BFS route over the 20px grid and escapes walls at random clears a slab in ~22 s at any tilt, so budgets are 55/30/24 s — comfortable, tight, and out of time. The generator refuses to emit an unreachable slab: BFS with a marble-radius pad must connect start to goal, and it is seeded so probes reproduce any layout. The probes re-implement the camera outside the game, read the painted pixel at every pit centre and demand black (this caught a real painter-sort bug — sorting by centroid let the giant slab plate paint over a far pit, so a pit vanished from screen while the sim still swallowed marbles there; sorting by farthest vertex fixes it), drop a marble at each tuple and demand the sim takes it, fire marbles at walls and demand zero penetration, and mutation-test by offsetting the painted pit and requiring the pixel probe to notice. Six rounds, lives, time bonus, tilt dials reading the same tiltU/tiltV as world(). Keyboard, WASD and an on-screen pad; score via postMessage; audio synthesised; no external requests.

Hard constraints — the game will be embedded in a sandboxed iframe on a static gallery site, and a headless browser will screenshot it:

1. Output exactly ONE self-contained HTML file. All CSS and JS inline. Zero external requests: no CDNs, no external fonts, images, or sounds, no fetch/XHR/WebSocket. Any sound must be synthesized with WebAudio.
2. The iframe sandbox is "allow-scripts allow-pointer-lock" (plus an autoplay permission). So: no localStorage, cookies, or indexedDB (opaque origin — access throws); no popups, window.open, or navigation; no access to the parent page; alert()/prompt()/confirm() are silently blocked.
3. The playfield must be visible within 800 ms of load — that is when the screenshot is taken. No dead white screen. If there is a start screen, make it visually rich.
4. Controls: keyboard AND mouse must both work, plus on-screen touch buttons for phones. Call preventDefault() on game keys (arrows, space) so the page never scrolls.
5. The view is 16:9 and must scale to fill the viewport with no overflow or scrollbars.
6. Show a visible score. If the genre has a losing state, show a game-over screen with a restart (button and a key). Idle/clicker games skip game over but still need clear numeric feedback.
7. If you track a score, report it to the arcade shell so the player's best is remembered between visits: on every score change, call parent.postMessage({ source: "ai-arcade", type: "score", score: <number> }, "*"). It is safe to call it no matter what the parent does with it.
8. Keep it tiny: aim for under 400 lines, 60 fps, no frameworks. That 400-line target does not apply to 3D games — true 3D (a camera and perspective-projected world) or pseudo-3D (projected road/track, depth-sorted sprites) — which need their own software renderer and typically land at 800–1400 lines. The rest of this constraint still binds every game: 60 fps, no frameworks, no external assets, and no padding to reach a length.
9. Difficulty: the arcade shell passes the player's chosen difficulty as a URL query parameter. Read it with new URLSearchParams(location.search).get("difficulty") — the value is "easy", "medium", or "hard" (missing or unknown means "medium"). Make the three levels meaningfully different — speed, lives, enemy pressure, reaction time, whatever fits the genre; clicker/idle games with no losing state use starting resources and upgrade cost curves instead. Show the active level in the HUD. Without the parameter the game must be fully playable at its default (medium) tuning.

Return only the complete HTML file, no commentary.