If WF=V is conceptually mandatory, then ℘* and ℘* are necessarily co-extensional, and their alleged distinctness under AFA reflects notational inflation rather than real mathematical difference.

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AFA(Set theory; contrasted with FA): The Anti-Foundation Axiom, which permits non-wellfounded sets and under which greatest fixed points typically contain non-wellfounded members
Co-extensional(describing when two things match up but aren't necessarily connected in a meaningful way): Having exactly the same members or applying to exactly the same things, even if for completely different reasons.
Conceptually mandatory(describing logical necessity): Something that must be true based on the definitions and meanings of the words involved, not just because of how the world happens to be.
Necessarily: "Necessarily" means something must be true in all possible situations—it's not just true right now, but couldn't be false under any circumstances. For example, "2+2=4 necessarily" means there's no possible way 2+2 could equal anything other than 4. This contrasts with "contingently" true facts, like "it's raining today," which happen to be true but could have been false.

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