What was already known
A 2014 question had already stated the basic determinant divisibility bound and asked when the minimum is attained. Small-order observations also predated this work.
AI involvement
GPT-5.4 supplied the reduction, binary criteria and construction under Oleksiy Babanskyy’s direction. Babanskyy checked derivations and outputs and set the final claim boundaries.
The named model supplied the central reduction, criteria and construction, while Babanskyy directed and checked the work.
Importance
The parity test and all-order family narrow a determinant question but do not settle its minimum-attainment problem.
Limitations
The reported full proof review covers a release candidate, while the AI disclosure names a later paper version; their alignment needs confirmation. Exact order-six computations are finite checks only.
Technical verification
The author reports checking the mathematical derivations, and the release-candidate audit reports review of every theorem and proof-local implication. Exact scripts certify the finite order-six artifacts; those computations alone do not prove the all-order statement. The complete-check rating rests on the reported human proof review, not an independent expert endorsement.
Independent checking
Author check of the mathematical derivations and release-candidate theorem review
- Checker
- Oleksiy Babanskyy, author
- Scope
- The binary parity criteria and all-order n ≡ 2 (mod 4) construction
- Basis
- Reported by the linked checker
Independent checking
Exact exhaustive computation and artifact hash/count checks
- Checker
- Public deterministic package verifier and independent order-six exact audit scripts
- Scope
- Order-six determinant census, parity patterns and certified finite outputs supporting the construction
- Basis
- Reported by the linked checker
Human understanding
The author checked the derivations and wrote the claim map distinguishing the centered normalization, parity obstruction and explicit circulant family; this documents human command of the assessed mechanism.
Correction and publication history
A distinct parity criterion with a documented human proof review and limited exact computations.
Read this published revision