Chain Pump

Build a tiny browser game called "Chain Pump".

Game spec
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A chain pump on a cattle trough, and the water table is the enemy. The pump is a loop of linked paddles running through a pipe from a low ditch up to the trough, driven by a flywheel you turn. The lift needed is the difference between the ditch level and the trough lip, and the ditch refills from a seep at a rate you cannot see directly, so you learn it by watching how fast the level recovers after you pump. The chain has a limit: run the flywheel too fast and the paddles cavitate, the chain slips and the water falls back, and a dry run with no water to seal the paddles destroys the chain in seconds. Prime the pump by holding Space to pour a bucket in, then throttle with the arrow keys, a click on the wheel, or a touch drag. A gauge shows chain speed, lift height, trough level and a cavitation warning, and the trough must stay between an overflow mark and a dry mark for as long as possible; keeping it in band pays continuously and the band narrows and the seep changes as the day goes on. Breaking the chain or letting the trough run dry ends the run, and difficulty sets band width, seep variability and chain tolerance. Farm look: a weathered galvanized trough with a waterline stain, cast-iron flywheel with a leather belt, oily chain links, a wooden pump house with a slatted roof, and a chain clatter plus a slosh 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.