What was already known
Carlet proposed the Kasami cyclic-additive condition. Nagy and Vajda proved selected residue classes of k and checked n≤13; their reductions and averaging argument are inputs to the new general proof.
AI involvement
The project disclosure credits interactive GPT work with the main new argument, and Claude agents with later formal development. Nagy, McNeil and Vajda reviewed and edited the paper and retain credit for earlier partial results. The paper names a different GPT version than the code disclosure.
The cited disclosure calls GPT interactive discovery the main source of the new mathematical argument, while human authors guided the work and supplied significant antecedents. The named model version conflicts with the later paper and prevents a stronger attribution to one system.
- Supporting source (arxiv.org) — Nagy–Vajda partial cases and exhaustive n≤13 baseline
- Supporting source (github.com) — exact count and proof architecture
Importance
Resolves the cyclic-additive count for all admissible Kasami parameters.
Limitations
The formal development reports a complete proof of the count and a separate statement comparison. The code disclosure names GPT-5.6 Sol while the later paper names ChatGPT 6 Pro for the present proof; the model identity and phases need reconciliation. The authors’ editing does not document a complete human proof check.
Technical verification
The cited revision reports a complete Lean proof of the coefficient-count statement, a separate Mathlib-only literature specification and semantic bridge, standard-axiom audit, Comparator matching and NanoDa replay. Earlier exhaustive n≤13 tests are not the basis of the universal Formal rating. This review did not rerun Lean.
Independent checking
complete formal proof, semantic statement bridge, axiom audit, protected statement comparison and independent proof replay
- Checker
- Lean kernel, Comparator and NanoDa, with reported Aristotle statement review
- Scope
- KasamiCyclicAdditive.carlet_kasami_cyclic_additive for all admissible n, k and distinct nonzero coefficients
- Basis
- Reported by the linked checker
Human understanding
The named authors give an explicit, detailed explanation of the Fourier correction, Fermat-cubic incidence and exact-average forcing mechanism in their later paper, which they reviewed and edited. Their review is evidence of understanding, not a separately documented complete human proof check.
Correction and publication history
Resolves the cyclic-additive count for all admissible Kasami parameters.
Read this published revision