What was already known
Gallardo proposed this equivalence in OEIS A071642. Classical trace criteria for irreducibility of binary polynomial compositions predate the proof.
AI involvement
Brandon Yates chose Gallardo’s question and reviewed the informal proof. GPT 6 Astra derived the trace-based argument; Claude Fable 5.1 independently rederived it and Claude Opus agents formalized it. Gallardo and the classical trace criterion retain separate credit.
The original proof for the stated conjecture is expressly attributed to GPT 6 Astra, with human target choice and later review; other AI agents supplied independent derivation and formalization.
Importance
Settles a specific polynomial irreducibility conjecture using a classical composition criterion.
Limitations
The result does not introduce a general composition criterion. The available record does not establish whether an earlier criterion already stated this exact consequence.
Technical verification
The stated per-n equivalence and set form are reported checked by Lean's kernel with standard axioms, including independent TheoremDB checking. The unnamed hand check is retained as context but not counted as a documented human method.
Formal checking
Lean proof build and axiom audit, followed by a second kernel check of the same statements.
- Checker
- Lean 4 kernel and TheoremDB verifier
- Scope
- AllOnesGallardo.main, A071642_terms_ge_two and boundary_one
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Yates reviewed the informal proof, but the available record does not provide a named human explanation of the central trace argument; Few is an evidence-gap default, not a finding of inability.
Correction and publication history
Settles a specific polynomial irreducibility conjecture using a classical composition criterion.
Read this published revision