What was already known
Glauberman and Norton ruled out p≥5 and gave p=2 examples, leaving the p=3 case as Péterfalvi’s question. Bender and Glauberman later repeated it.
AI involvement
Ishida selected and directed the problem. Claude agents found and formalized the proof, retaining a GPT-5.6 Hua-identity idea; no human mathematical proof review is documented.
Claude agents are explicitly credited with finding the negative proof under Ishida's direction; the retained Hua-identity idea also came from GPT-5.6.
Importance
Answers the remaining p=3 case for the stated group-theoretic hypothesis.
Limitations
The q=2 case is excluded by the hypothesis. The older p=2 example is a consistency check, not a new result; historical priority remains incompletely searched.
Technical verification
Palomar v1 reports Comparator matching not_hypothesisB_three to the cited challenge under standard axioms, with Lean, NanoDa and con-ron accepting the exported proof. Finite-field numerical checks support intermediate identities but are not the reason for Formal. The review did not rerun these checkers.
Formal checking
statement/solution comparison, permitted-axiom audit and exported-proof replay by three kernels
- Checker
- Palomar Comparator, Lean kernel, NanoDa and con-ron
- Scope
- PeterfalviProblem.not_hypothesisB_three, with PeterfalviProblem.hypothesisB_two checked separately
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The available proof outline was written by agents and no named human explanation or review of the long finite-field mechanism is documented. Few is the missing-evidence default, not a finding that Ishida cannot understand it.
Correction and publication history
Answers the remaining p=3 case for the stated group-theoretic hypothesis.
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