Kiln Draw

Build a tiny browser game called "Kiln Draw".

Game spec
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A pottery kiln you load, not fire. Twelve shelves have to be filled with pots so that the whole stack fires evenly: every pot has a clay body and a glaze, and the kiln has hot zones near the elements and cold zones near the door, printed as a heat map you can toggle. A pot that is too thick for a cold zone underfires and is scrap; a thin glazed pot in a hot zone melts and fuses to the shelf. Pots must not touch each other or the elements, and stacking them requires ordering by height so taller pieces sit where they will not hit the roof. Place a pot by dragging it from the bench to a shelf cell, or with the cursor keys plus Enter, and rotate it to change its footprint. A live evenness score shows how close the planned load is to uniform firing, and the firing itself is a short animation of the cone bending. An even load pays by pots fired, scraps avoided, and how full the kiln got, then the next load is a different mix with a hotter element map; three scrapped pots ends the run and difficulty sets the mix, the heat spread and the number of shelves. Kiln look: cordierite shelves with kiln-wash grit, orange element glow through a peephole, a stack of unfired grey-green pots with a paper label, cone pack with bent cones, and a rising burner 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.