Validity proofs compress thousands of transactions into a single cryptographic attestation. Each batch sealed on-chain carries the weight of every operation it contains, verified in constant time.
Data availability is ensured through calldata compression. The rollup posts only the minimal delta required to reconstruct state, reducing L1 costs by orders of magnitude.
The sequencer orders transactions, executes them against the current state, and produces a new state root. This root becomes the claim that the validity proof must verify. Every operation is deterministic -- replay the inputs, get the same output.
The proof encodes the entire batch computation into a polynomial commitment scheme. A single elliptic curve pairing on L1 verifies what took millions of operations to compute. This is the fundamental asymmetry that makes rollups possible.
The final proof is submitted to L1. A single on-chain transaction verifies the entire batch, updating the canonical state root. Finality is inherited from the base layer -- once confirmed, the batch is irreversible. The rollup has compressed time itself.