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Proof verification can be done locally or can be done in on-chain smart contracts. The proof verification process is not handled by zkLLVM, though mentioned here as the circuit developer is still responsible for publishing the on-chain verifier contracts and wrappers. The lorem-ipsum project manages the on-chain verification flow.
The users/applications will retrieve the proof generated by the counterparty from the proof market. The proof can be verified inside EVM by dApps.
As we see above, the dApp will have an API exposed, which will take details such as circuit address (circuit-specific gates), public inputs and the proof. This smart contract will verify the proof for the circuit by leveraging the placeholder verifier and the circuit-specific logic verifiers.