Cart Wheel

Build a tiny browser game called "Cart Wheel".

Game spec
---------
A cartwright's wheel. A wooden wheel rolls across a cobbled road that scrolls toward you, and it wobbles: the wheel is built from spokes of slightly different lengths, so its centre rises and falls once per revolution by an amount set by the worst spoke, and a hard jolt shakes a loose spoke out of its hub. Turn the spoke wrench with the arrow keys, A/D, or a click on a spoke (touch pads work too) to drive a spoke tighter, but every spoke you tighten changes how the load spreads to its neighbours, so tightening one can loosen the two beside it. A runout dial shows the current wobble in millimetres and a spoke map highlights the offenders; drive the runout below tolerance to finish the wheel for a bonus scaled by remaining time and spokes left sound. A spoke that backs out entirely makes the wheel collapse and costs a wheel; three ends the day. Speed is a trade: a faster cart covers ground and banks distance score sooner but every jolt is sharper and spokes back out faster, so hold Up to urge the horse and take the risk. Difficulty sets road roughness, how fast spokes loosen, tolerance and run length. Cartwright look: warm oiled elm felloe and spokes, an iron tyre with hammer marks, ruts and flint in the cobbles, dust puffs at each jolt, a leather apron and a wrench in the foreground, and a rhythmicclop-clip in WebAudio.

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.