What was already known
The earlier depth-two profile supplied part of the depth-three high tail; cyclic and complete-ideal results supplied other tools. They did not determine the full depth-three profile.
AI involvement
GPT-5.6 Sol Codex supplied the depth-three reduction, q-Pascal analysis, minor argument, carry closure and formulas. Oleksiy Babanskyy directed the project, challenged derivations and selected the final claims.
Codex supplied the central new depth-three mechanism and formulas under human direction; the author checked and selected the final work.
Importance
The result extends a specialized integral incidence invariant to depth three for all primes.
Limitations
Exact companion calculations cover the exceptional primes and selected formula controls. A complete independent check of the uniform q-Newton and carry argument is not documented.
Technical verification
The repository documents exact exceptional-prime and symbolic formula checks, plus the author's iterative checks of derivations. These do not amount to a completed rigorous review of the uniform q-Newton and cross-chart proof for every prime.
Independent checking
Exact Smith/Bockstein elimination and symbolic formula checks
- Checker
- Babanskyy's exact companion software
- Scope
- Exceptional p=2,3 depth-three profiles, first-transfer controls and symbolic branch-formula identities
- Basis
- Reported by the linked checker
Independent checking
Iterative human challenge and checking of derivations and outputs
- Checker
- Oleksiy Babanskyy
- Scope
- Depth-three derivations and certified outputs during development
- Basis
- Reported by the linked checker
Human understanding
The author challenged and organized the logical spine, but a complete human explanation of the model-generated q-Newton and divided-carry mechanism is not separately documented.
Correction and publication history
A new all-prime depth-three Smith profile for affine incidence, with bounded exact checks.
Read this published revision