When there’s a disagreement in a state channel contract, the contract turns to the blockchain for adjudication. The contract remains private through a zero-knowledge proof setup that allows the blockchain to render a judgment without needing to know the contents of the contract. In this way, the blockchain acts as a blind judicial system for smart contracts.
Interestingly, since the blockchain’s behavior is predictable, there’s no benefit to disputing the results of a state channel contract. The blockchain is likely to confirm the outcome.
Final settlement of accounts in the contract then takes place on the blockchain and the contract closes. The result of off-chain computation is an increase in throughput by several orders of magnitude for the network since only the final settlement needs to be handled on-chain.