Lock Keeper

Build a tiny browser game called "Lock Keeper".

Game spec
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A canal lock you operate by hand. A barge waits at one end of a stone lock chamber and you must get it to the other side, where the water sits a metre higher or lower. The chamber has a pair of upper gates, a pair of lower gates, two paddle wheels that admit or drain water through sluices, and a set of bollards. Click or tap a mechanism to work it, or use the arrow keys to move a highlight and Enter to operate it. The order matters and the water is the hazard: gates can only be opened when the water is level with the far side, opening a gate against a head of water bursts the paddles and floods the towpath (that costs a lock-keeper's badge, and three ends the shift), and the barge must be warped in and moored before the water moves or it slams the chamber wall. A live gauge shows chamber level against both reaches, and the HUD lists which mechanisms are locked out and why. Each passage pays by time taken and badges kept; the next lock has a bigger rise, leakier paddles and a shorter shift, and hard adds a second barge waiting behind. Dusk canal look: wet stone coping with a waterline stain, timber gates with iron corner braces, rippling green water with reflections, a brass paddle wheel, lantern light on the towpath, and a creaking gate sound 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.