The shape of a transition

Three things travel together. The statement: which state is consumed, which state is produced, under which predicates. The witness: the private inputs that make the predicates true, such as signatures, amounts, or the contents of a position. The proof: a cryptographic object showing that a witness exists satisfying every governing predicate over exactly this transition, without necessarily revealing the witness itself.

Whoever proposes the transition produces the proof, on their own machine. Proving is a local act, done before the transaction is submitted, and the measured cost of that act is the subject of the performance page. Verification is the network's side of the bargain, and it is deliberately cheap: checking a proof takes milliseconds, which is what lets validation stay light and lets anyone outside the network, a wallet, a light client, another chain, verify Modulus state without trusting an intermediary.