All the code and calls to run it is stored on chain. When it's committed to chain every single validator node suppose not just record results of the execution, but run the code.

To host validator node you stake ETH which is serve as collateral in case your node misbehave, go offline, etc.

If specific validator cheats at any point and end up approving bogus data he'll be punished by loss of staked ETH and penalty grows with each attempt to cheat. If multiple validators commit the same bogus data they'll get even more severe punishment for coordinated attack on chain.

It doesn't take a supercomputer to host ETH node so there is absolutely no incentive to cheat unless you actual bad actor who is attempting 51% attack. And to perform said 50% attack you will need like $75-100B+ of ETH stacked since currently there is $150B of ETH stacked for Proof of Stake. So this kind of attack really doesn't make any financial sense.