This repose contains a library which is used to authorize signature generation on the MPC side. Currently it's a wrapper around RPC calls to a different blockchains.
Usual data flow would be making a single call to a NEAR blockchain, then calling a target chain.
The message can be signed if there's a "proof." For example, we want to sign a message "Record a deposit of 5 XLM" which is sent to the Hot Bridge. The proof would be a transaction identifier – unique nonce. Then we check if a transaction with this exact nonce and parameters took place.
In the code this proof and proof verification implemented through quite abstract hot_verify methods in smart contract.