Game loop skeleton

Build me a game skeleton in one HTML file. Canvas, no libraries, no
build step.

Structure, strictly:
- One `state` object holding everything mutable.
- `update(dt)` — changes state only, never draws. Takes elapsed
  seconds, so movement is speed × dt and not per-frame.
- `draw()` — reads state and renders, changes nothing.
- A requestAnimationFrame loop calling both, with dt clamped so a
  tab returning from the background doesn't teleport everything.

Include a `mode` field with 'playing', 'paused' and 'gameover' from
the start, and a placeholder square I can move with the arrow keys.

Then tell me where I'd add a new entity type, a collision, and a score.