What was already known
Naslund’s Conjecture 13 predicted the upper bound 3^(3n/4) for these parameters.
AI involvement
Jones directed the task; the disclosure credits Claude, GPT-6 and Grok with work on the construction and proof. It does not identify one model as the sole originator.
The disclosure credits multiple AI systems with the central construction under Jones’s direction.
Importance
The infinite family disproves the stated bound and raises the known growth exponent in this setting.
Limitations
The construction gives no optimal value and makes no claim for other q. No independent human mathematical check is documented.
Technical verification
The released verification report lists Lean proofs of the infinite families and growth bound; finite Python checks are corroboration.
Formal checking
Complete Lean proof build, trust/axiom audit and source guard; exact finite code property by kernel decide
- Checker
- Lean 4 kernel in Jones’s reported local build
- Scope
- Six selected polynomial-set, conjecture-refutation and liminf statements over F₃
- 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 of the code-and-lift mechanism is documented; Few is the evidence default.
Correction and publication history
The q=3, k=2 infinite-family refutation is distinct from other coded-set and Lean publications.
Read this published revision