What was already known
Adriaensen and coauthors gave the general bound HG_P(G)≤|V(G)|+χ(G)−1 but did not settle this endpoint for K5−e.
AI involvement
GPT-5.6 Pro developed the central F₂³ construction and Hall proof in a project directed by Matthew Protti, who selected the target and accepted responsibility for the release.
The source identifies the model-assisted central construction and proof, while Protti directed and scoped the work.
Importance
Determines one previously open finite case of the K_n−e problem.
Limitations
The construction does not resolve the general K_n−e family. Independent human mathematical review was pending at the frozen release.
Technical verification
The release reports exact regeneration of the compact certificate, a residual matching, a separate game checker and exhaustive coverage of all 8,400 proper eight-colourings. These are source-reported machine checks of this finite theorem.
Formal checking
Exact finite certificate regeneration and exhaustive game check
- Checker
- verify_k5e_fano_hall.py, direct game checker and independent matching/CNF checks
- Scope
- Winning eight-colour strategy for K5−e and all 8,400 proper colourings
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The author directs and evaluates the research, but the source does not document his own explanation of the F_2^3 construction. Few is the evidence default.
Correction and publication history
Determines one previously open finite case of the K_n−e problem.
Read this published revision