What was already known
The unrestricted Banks–Martin claim is false when Q may contain 2. Lichtman proposed the odd-prime restriction; special cases were known, but the general revised inequality remained open.
AI involvement
GPT-5.4 Pro suggested the shared Markov-chain method and GPT-5.5 Pro assisted an initial proof. Eight human authors developed, explained and reviewed the final odd-prime argument.
A model-origin Markov-chain method is central to this theorem and GPT-5.5 Pro assisted its initial proof; human authors supplied the final argument.
Importance
Proves the corrected odd-prime form of the primitive-set conjecture.
Limitations
The result does not restore the unrestricted claim. The model-origin method is documented, but the source does not identify a proof step unique to the odd-prime adaptation.
Technical verification
The human authors explicitly report reviewing the final proof of Theorem 1.3. This is a source-reported completed human check, not a review reproduced here; the Lean result cited in the paper is for Theorem 1.1 only.
Formal checking
Generation and review of the final mathematical proof
- Checker
- Eight human authors of the primitive-sets paper
- Scope
- Theorem 1.3 for sets of odd primes
- Basis
- Reproduced by AIProofWatch
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The human authors explain the odd-prime chain construction, sub-invariant weights and antichain/chain comparison in Section 6.
Correction and publication history
Proves the corrected odd-prime form of the primitive-set conjecture.
Read this published revision