Barrel Stave

Build a tiny browser game called "Barrel Stave".

Game spec
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A cooper's barrel, built from staves that must be bent, hooped and kept wet. You assemble the barrel over a firing: stand the staves in a raising hoop, drive the chime hoop down to gather them, and heat the wood over the fire until it will bend — cold wood snaps. The bend is a live curve: heat too long and the stave chars and weakens, too little and it springs back and the joint gapes. Once the barrel is up, the hoops have to be driven tight with a hammer, and tightness is a real trade: a slack hoop leaks, a tight hoop crushes the stave and splits it, and the right tightness changes with the wood's moisture, which dries as the barrel sits. Test for leaks by filling it (Space) and reading where it weeps; a leaking barrel is worthless and three failed barrels ends the bench. Score comes from watertight barrels, staves saved, and time, and the next barrel is taller with fewer staves. Difficulty sets wood moisture loss, charring speed and the tolerance on hoop tightness. Cooperage look: oak staves with quarter-sawn grain and a pale sapwood band, a blackened firing with a copper hood, iron hoops with rivet clinks, a driver and a hoop hook, shavings on the bench, and fire crackle plus a hammer ring 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.