Note, typically, only the hash of the state is kept on-chain. To enforce the trustless nature of the system, the on-chain state can only be updated by a proof attesting to the validity of the state transition. StarkWare's SHARP provides this proof.
Typically, several requests are batched together into a single statement (step 2 in the diagram). For example, a batch can compile 1000 financial transactions to be sent for proving.
To ensure the transition's validity (i.e., that SHARP verified it), the customer application's smart contract corroborates that the transition statement is registered in the Verifier smart contract (step 5 in the diagram).