Tide Mill

Build a tiny browser game called "Tide Mill".

Game spec
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A tide mill where you fill a pond behind a causeway and release it through the wheel when the tide turns. The tide rises and falls on a fixed cycle printed as a curve along the bottom of the screen, and your pond level is yours: open the sluice to let the sea in when the sea is higher, close it before the tide falls back and drains your head, then open the wheel gate when the pond is high and the channel outside is low. The wheel only produces power while there is a head across it, and the head you have available in any second is the difference between pond and channel, so the whole skill is closing the sluice at the exact top of the tide and opening the wheel exactly when the outside has dropped far enough. The sluice and the wheel gate are both throttles you hold or drag, and both respond sluggishly, so the pond keeps filling for a moment after you shut. A gauge board shows pond level, channel level, head across the wheel and grinding output, and a millstone turns faster the more head you hold. Grinding pays by output integrated over the tide; a pond left open at high tide loses its head back to the sea, and a season of three failed tides ends the run. Difficulty shortens the usable window, adds a leaky pond, and moves the causeway. Harbour look: a stone causeway with weed, dark pond water holding a sky reflection, a wooden undershot wheel with dripping paddles, sackcloth flour sacks, gulls, and wheel splash with a low grind hum 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.