A central-point-of-failure (CPF) refers to a single entity or component that, if compromised or failed, would cause the entire system or process to fail or be compromised. In the context of trust-based bridges, the custodian or central authority is the CPF.

If the custodian or central authority is compromised, the entire bridge is at risk because:

1. _Single point of attack_: Attackers only need to target the custodian or central authority to gain control over the entire bridge.

2. _Unlimited access_: A compromised custodian or central authority would have unlimited access to all assets and user information.

3. _Total control_: An attacker could manipulate or steal assets, alter transactions, or shut down the bridge entirely.

4. _Systemic risk_: The failure of the CPF could lead to a systemic collapse of the entire bridge, causing widespread damage and loss of trust.

To mitigate this risk, trustless bridges and decentralized solutions are being developed, which aim to eliminate the CPF and provide a more secure and resilient infrastructure for cross-chain interactions.