Replace constant-rate velocity rotate with ω0 spin + v_lat curl.
Path samples are (x, y, theta); client time is index/SAMPLE_RATE_HZ.
Ultraworked with [OhMyOpenCode](https://github.com/code-yeongyu/oh-my-opencode)
Co-authored-by: Sisyphus <sisyphus@ohmyopencode>
Extract mutable state from game.ts into a dedicated GameModel class to clarify data flow and state transitions.
Ultraworked with [Sisyphus](https://github.com/code-yeongyu/oh-my-openagent)
Co-authored-by: Sisyphus <clio-agent@sisyphuslabs.ai>
