What was already known
Carlet proposed the cyclic-additive count; the Kasami instance remained open beyond known APN and related pair-correlation facts when this partial result appeared.
AI involvement
Nagy and Vajda supplied the problem context and hints, then credited Claude Fable 5 with the new derivations and proofs. Aristotle formalized the k=2 result in Lean 4. The authors maintained the report and inspected background assumptions; a separate human proof check is not documented.
The central new k=2 proof and reductions are credited to Claude Fable 5, prompted with substantial mathematical background.
Importance
The proof settles infinite parameter families and supplies reductions used by later work.
Limitations
The four classes are the scope of this earlier result. A later separate paper reports a full proof for all admissible parameters. The repository reports Lean verification of the k=2 case; a theorem-by-theorem match of every paper reduction to Lean declarations is not documented.
Technical verification
The paper reports Lean 4 verification by Aristotle; the companion repository reports a clean build and axiom checks for the k=2/n−2 headline. The rating applies to the proved partial classes, not the general conjecture.
Formal checking
Reported clean Lean build and standard-axiom check of the k=2 and n−2 headline result; not independently rerun.
- Checker
- Aristotle and Lean 4 kernel
- Scope
- k=2 and n−2 partial triple-count theorem
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The paper explains the argument, but it attributes those explanations to Claude; independent human grasp of the central k=2 mechanism is not explicitly documented.
Correction and publication history
Earlier four-class result and finite check; the public general Kasami proof is a later, stronger, separately credited contribution.
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