What was already known
Morris proposed the asymptotic for each fixed k and supplied the lower-bound direction. The four-set asymptotic, local threshold and finite FC(4,9) value remained unresolved in the cited account.
AI involvement
Models mainly developed the FC(4,9) classification and jointly developed the charging inequality and core-petal weights with Mingchang Liu. Liu set and refined the problem and supplied the later all-k extension.
The manuscript attribution assigns the finite classification mainly to models and the central four-set charging method to joint human/model work. The all-k extension is kept separately human-credited.
Importance
Resolves the four-uniform case and supplies an exact finite classification.
Limitations
Published exact certificates and exhaustive code check FC(4,9)=16. No completed check of the full four-set asymptotic proof is documented; the later all-k argument is outside the finite certificate’s scope.
Technical verification
The V1 source reports exact certificates and exhaustive computation for FC(4,9)=16. That machine check is confined to the finite classification; no completed rigorous review of the general nine-petal or asymptotic argument is documented, and V2's all-k extension is outside the V1 certificate scope.
Independent checking
Exact finite certificates and exhaustive search cover FC(4,9)=16.
- Checker
- Liu's published V1 verification program and finite certificates
- Scope
- Finite FC(4,9)=16 classification, including the fifteen-block negative certificate and exhaustive upper bound
- Basis
- Reported by the linked checker
Human understanding
Liu's account identifies the 3:1 core-petal weights, charging inequality and extremal forcing as the four-set mechanism and credits his proof development; no central part is reported unexplained.
Correction and publication history
Resolves the four-uniform case and supplies an exact finite classification.
Read this published revision