Slingshot

Build a tiny browser game called "Slingshot".

Game spec
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A top-down gravity-golf game in one self-contained canvas file. Each hole is procedurally seeded (mulberry32 keyed on hole number) with a tee on the left, a pulsing wormhole on the right, difficulty-scaled planets (some orbiting anchors on visible rails from hole 3+), and drifting jagged asteroids from hole 2+. The player drags anywhere and releases: pull-back distance sets power (capped, colour-coded amber/red at max), and the flight is an honest preview — up to 220 simulated steps of the same integrator shown as fading cyan dots that terminate in a red X on a predicted crash or a green X on a predicted capture, since movers and asteroids are deterministic functions of world time. Physics is semi-implicit Euler with softened inverse-square gravity (capped acceleration), wall bounces at 0.88 restitution, velocity cap, and sub-stepped collision: planets and asteroids kill the probe (explosion, life lost, back to the tee), entering the wormhole completes the hole. Scoring rewards par: max(100, 400 - 100*overPar) plus 100 per stroke under par; an ace is called out. Strokes are unlimited but cost score; lives are lost probes. Zero lives ends the run with a score card, holes cleared, localStorage best (try/catch for the sandbox) and re-fly button. WebAudio for launches, bounces, crashes, capture and hole fanfares. HUD plates show hole/par/strokes, score, probe lives and the difficulty tag; score posts via parent.postMessage({source:'ai-arcade',type:'score',score}). ?difficulty=easy|medium|hard (default medium) scales lives, planet/asteroid counts, gravity, power cap, par and orbit speeds. Touch works via the same pointer-drag aiming.

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.