Rope Walk

Build a tiny browser game called "Rope Walk".

Game spec
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A rope walk where you twist three yarns into a strand and three strands into a rope, and the whole game is twist. Twist is applied by turning a wheel; too little and the rope is soft, opens up and fails under load; too much and the yarns hockle — they kink into loops that cannot be undone and ruin the strand. The correct amount of twist is not a fixed number: it depends on how far the rope has been stretched, so the run is a balance between pulling the ends apart (which takes twist out) and turning the wheel (which puts it in), and holding either one too long loses it. Wind the wheel with the arrow keys, A/D, or a circular mouse drag; hold Shift to tension the lay. A live lay-angle readout and a strand drawn in cross-section show how tightly the yarns are wrapping, and a warning appears as the strand approaches hockle so you can back off. Each finished length pays by strength achieved, twist kept inside the band, and time; then the next rope is thicker, the yarns are stiffer and the band is narrower. Three ruined strands ends the walk, and difficulty sets band width, stretch loss and length. Ropewalk look: a long timber shed with a cobbled floor, pale tarred hemp yarns under a travelling top, a wooden fidge and throttle board, coils of finished rope, hanging dust motes, and a hemp creak plus wheel ratchet 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.