Lead Sink

Build a tiny browser game called "Lead Sink".

Game spec
---------
A plumbers shop making sheet lead into a weather pan, and the whole craft is beating the lead into a compound curve without thinning it. A flat sheet sits over a wooden bunch and you raise the shape with a set of hammers, each of which spreads the metal differently; the crown of the pan needs the metal stretched evenly, and any place you beat too much goes thin and, past the limit, cracks through. The thickness map is drawn live over the work as a heat overlay, so thinning is visible before it becomes a hole. Hammer with a click or tap on the pan, or move a cursor with the arrows and strike with Space, and switch hammer with the number keys to change spread and force. Once raised, the pan is planished flat on the stake to true it, and a pan whose rim will not sit on the flat bar is scrap. A finished pan pays by thickness kept above tolerance, how true the rim sits, and strokes used, then the next pattern is deeper with a tighter tolerance; three cracked pans ends the day and difficulty sets tolerance, depth and sheet thickness. Lead shop look: dull grey sheet with hammer-dimple texture and a soft sheen, a shaped wooden bunch, a raising mallet and a planishing hammer, a flat bar with a straightedge, swarf on the bench, and dull lead taps 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.