when we want to prove ZK we use a simulator to show that we can create a transcript of the protocol despite not knowing the secret.

In the recitation we did this for an honest verifier and added the rewind method for the case of a malicious verifier (that way we could run till we made the correct guess/commitment).

In the end we ended up with a transcript that satisfies the verifier (100% of the time for the case of an honest verifier).

so if we're talking about the quadratic residue like int he homework we would have a convincing transcript regardless of y. But should we not give a transcript that does not pass verification for the case of y not being a quadratic residue?

why is it enough to show a simulator only for the case of the proof being honest?