What was already known
Finite-field incidence invariants, residue-ring transforms and cyclic diagonal factors were known. They did not supply the integral affine Smith profile at depth two.
AI involvement
GPT-5.6 Sol Codex supplied the central reduction, transfer and carry arguments and all-prime formulas. Oleksiy Babanskyy chose the direction, checked derivations and outputs, and set the final claim boundary.
Codex supplied the central Smith-profile framework and formulas under Babanskyy's direction, with human checking and final selection.
Importance
The all-prime profile adds a new exact invariant for this affine incidence family.
Limitations
The companion software checks selected small primes and transfer controls. Those cases do not certify the uniform proof, for which no completed independent review is documented.
Technical verification
The author reports checking derivations and the exact companion checks p=2,3 depth-two rows, Bockstein and lattice controls. Those bounded checks do not certify the all-prime written proof; no completed whole-proof human review is documented.
Independent checking
Exact finite Smith, Hermite and lattice computations
- Checker
- Babanskyy's exact companion software
- Scope
- Depth-two Smith rows at p=2,3 and selected transfer/Bockstein controls
- Basis
- Reported by the linked checker
Independent checking
Iterative human challenge and checking of derivations and outputs
- Checker
- Oleksiy Babanskyy
- Scope
- Depth-two derivations and certified outputs during development
- Basis
- Reported by the linked checker
Human understanding
The author selected and challenged the central development and set a detailed logical spine, but the disclosure does not separate a complete human explanation of the model-generated carry and all-prime reduction.
Correction and publication history
A distinct depth-two Smith profile with explicit finite checks and an all-prime proof claim.
Read this published revision