Tower Topple 3D

Build a tiny browser game called "Tower Topple 3D".

Game spec
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A first-person 3D demolition puzzle written as a single self-contained file with no external requests: a hand-rolled WebGL renderer (one lit shader, per-face shading, fog, specular balls, orbiting idle sway) driving a hand-rolled rigid-body engine — SAT over oriented boxes, two-way vertex contact collection, sequential-impulse normal and bi-directional friction solvers, Baumgarte-free position projection, warm starting via persistent contact points, and sleeping with contact-island wake propagation so a built tower is exactly frozen until something strikes it. Five levels place procedurally stacked block towers (wood, brick, stone, steel, plus a lintel gate spanning a pit) beside trenches; the objective is to knock the glowing amber target blocks into a pit, scoring 500 per target with shot-saved and under-par bonuses, and score is posted to the parent frame. Difficulty via ?difficulty=easy|medium|hard scales shot count and pit width, defaulting to medium when the parameter is missing or unrecognised. Controls are mouse-drag or arrow-key aiming with a crosshair, click or Space to fire, R to retry, plus on-screen aim and FIRE buttons under @media (pointer: coarse).

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.