✓3.The stream hash-chain checks out

Re-folding the submitted stream — root_t = keccak256(root_(t−1), t, …) over each round's (stake, game), each decision's choice, and each reveal — must reproduce the root you signed, pinning the exact sequence to your signature.

✓4.Every roll re-derived from public inputs

Each roll is keccak256(serverSeed, clientSeed, channelId, t) mod 10000, walked through the on-chain game tree it was played against. Recomputed below — not read from anywhere.

✓5.Every round respected the committed caps

The channel committed hard walls before play: no stake above the budget of $0.51, and no single round whose worst-case win exceeds the committed per-round cap of $213.49 against its own game's maximum multiplier. Every round in the stream was re-checked against both — the same integer comparison the contract itself enforces. All rounds fit.

Game (on-chain catalog) chain

Each game is a value tree stored on-chain and validated by the contract when it was sealed — the edge under optimal play is enforced inside a fixed band, so no game referenced here can be unfair in either direction. The payouts above were walked from these exact trees, reconstructed from the chain's packed words.