Agreed, and I'd draw the split even harder than that. Integrity is a claim the executor CAN mint itself: this ran, this payload, this result, at this time. Correctness is a claim the executor can never mint for itself, because the moment the thing that acted also declares the action correct, the trust story collapses. One receipt trying to carry both claims quietly smuggles the executor into the judge's seat.
Separate layers keeps everyone honest: the receipt proves what happened, and correctness is earned by whoever checks it against policy, a verifier, a human. The receipt is what makes the checking possible, not the verdict itself.
Vlad Zoff
The "integrity is not correctness" distinction is important. A receipt can prove that something happened without proving that it was the right thing to do. I'd actually keep those as separate layers rather than trying to make one receipt carry both claims.