What was already known
The mixed xz cases and the SU(2) case remained open, although a separate Jacobian counterexample had already ruled out the universal compact-group conjecture.
AI involvement
Long credits ChatGPT 5.6 Sol Pro with the witnesses, SU(2) lift, beta-binomial proof and parameter family. Long checked the identities, explained the mechanism and wrote the paper.
The model supplied the witnesses and symbolic proof during Long’s interactive research session.
Importance
Explicit witnesses settle the mixed xz question and the SU(2) case.
Limitations
The reported Lean audit covers the core counterexamples and integration formula; two optional supporting derivations remain partial.
Technical verification
A reported Lean audit covers the core xz and SU(2) statements, and Long checked the displayed identities.
Independent checking
independent human algebraic verification
- Checker
- Christopher D. Long
- Scope
- Displayed xz and SU(2) moment identities
- Basis
- Reported by the linked checker
Formal checking
proof assistant build, theorem-to-manuscript correspondence ledger and transitive-axiom audit
- Checker
- Lean 4 kernel via the author's formalization repository
- Scope
- Theorem 2.1, Corollary 2.2, Proposition 3.1, Lemma 4.1 and Theorem 4.2, including actual SU(2) Haar moments
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Long explains the beta-binomial cancellation and transfer to SU(2).
Correction and publication history
The same explicit witness connects the mixed xz and SU(2) cases; they form one claim group and do not duplicate the earlier Jacobian result.
Read this published revision