High-level overview of how it can work:

Selection of Relayers: In a decentralized network of relayers, anyone who meets certain criteria (e.g., staking a certain amount of tokens) can become a relayer. This forms a decentralized network of nodes that can participate in the relaying process.

Submission of Proofs: When a user initiates a transaction on one chain (let's say BSC), the event will be emitted. Any relayer can pick up this event, construct a cryptographic proof, and submit it to the contract on the other chain (Arbitrum in your case).

Incentivization: To incentivize relayers to participate and behave honestly, they are usually rewarded with transaction fees or protocol-specific tokens.

Slashing: If a relayer submits fraudulent information, their staked tokens could be slashed as a penalty. This incentivizes them to be honest.

Consensus Mechanism: To prevent multiple relayers from submitting the same transaction or a fraudulent relayer from submitting a false transaction, a consensus mechanism is used. This could be as simple as the first relayer to submit gets the reward, or it could be more complex, like a committee-based system where multiple relayers have to agree on a transaction before it is confirmed.