What was already known
Chen and Gendron’s spin-parity classification was conditional on their number-theoretic Conjecture A.10.
AI involvement
The authors report giving AxiomProver the conjecture without references, geometry or method hints. It found the key reduction and later formalized the identity; human authors completed and explained the argument and geometric application.
The central reformulation and missing reduction were obtained from the conjecture alone, without method hints or proof, before the authors' exposition and geometric application.
Importance
Supplies the missing reduction that removes the conjectural condition from the stated spin-parity formulas.
Limitations
The reported Lean proof covers the floor-sum identity, not the Jacobi-symbol bridge or geometric corollaries. No explicit full human proof check of all steps is documented.
Technical verification
Lean 4.26 reports a complete check of Lemma 2.5's floor-sum identity, but the Jacobi-symbol reduction from that identity to the parity conjecture and the geometric consequences are not formalized. The paper explains those steps; an explicit complete human proof check is not documented.
Formal checking
Formal proof of main_theorem matching the displayed counting and floor-sum definitions; source-reported.
- Checker
- Lean proof assistant through AxiomProver's solution.lean, as reported by the authors
- Scope
- Lemma 2.5: N_k(n) = F_k(n+1) - F_k(n) for odd k >= 3, under the stated coprimality assumptions
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The authors explain the Jacobi-symbol reformulation, the floor-sum identity, and how classical number theory completes the stated parity formula in Section 2.
Correction and publication history
Supplies the missing reduction that removes the conjectural condition from the stated spin-parity formulas.
Read this published revision