The idea is that, if a staker refuses to include a proof (digital signature) that it has staked on multiple chains, or double spent coins, the network will fork

The idea is that, if a staker refuses to include a proof (digital signature) that it has staked on multiple chains, or double spent coins, the network will fork the chain to a new one which includes this proof. How the network will reach consensus on then following this new chain is not clear to me.