Game session host

Makes every game playable inside the app the same way: the typed game module enters through one generic seam (createGameHost), each run lives in a per-run store that writes the run before the board animates it, a finished run is recorded in one repository transaction before its result shows, and screens see only plain data and commands. The skill ships the host (templates), the wiring around it (examples) and a checker that proves the invariants by running the app's own host modules against a tiny test game, on iOS and Android alike (the host is pure TypeScript and React).

Rules that must hold