What was already known
Vaidyanathaswamy and later authors established the unrestricted finite-order criterion ψ(m)≤N. The determinant-negative refinement is separate from that classical result.
AI involvement
JD Jones selected and directed the project. GPT-6 Pro supplied a paper proof of the determinant −1 refinement; Claude agents rederived and formalized it. The unrestricted finite-order criterion is classical and credited to its earlier authors.
GPT-6 Pro supplied the determinant −1 argument and Claude rederived and formalized it under Jones’s direction.
Importance
Adds a precise determinant constraint to a classical finite-order matrix classification.
Limitations
The cited references do not establish priority for the determinant refinement. The formalization also covers classical results, which are credited to their original authors.
Technical verification
The cited verification record reports a Lean build and axiom audit covering the three determinant −1 declarations, including the necessary extra dimension. It does not establish their novelty and was not rerun here.
Formal checking
Lean proof-term check and standard-axiom audit of the determinant-negative statements.
- Checker
- Lean 4 kernel and project axiom audit
- Scope
- exists_orderOf_eq_det_neg_one_iff, isLeast_dimension_det_neg_one, and exists_orderOf_eq_det_neg_one_iff_rat
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
No named human explanation or proof review of the determinant refinement is documented; this is an evidence-gap default.
Correction and publication history
Adds a precise determinant constraint to a classical finite-order matrix classification.
Read this published revision