What was already known
Dean conjectured the corresponding divisible-cycle result for minimum degree at least k. Cases k=3,4 and all k≥6 were known; k=5 remained.
AI involvement
Elias Botsford authored and revised the proof. The paper credits generative AI, chiefly GPT-5.6 Sol, with the main results and also names Claude Opus 5, GLM 5.3 Flash and Danus; individual proof steps are not separately attributed.
The author explicitly attributes the main results primarily to generative AI; the exact roles of the listed systems and human repair are not separated.
Importance
If the full structural argument holds, the result closes the last case of Dean’s conjecture.
Limitations
Exact programs certify nine finite configuration propositions. They do not check the graph-to-state reductions or a revised exceptional-leaf step, and no complete human proof review is documented.
Technical verification
The archived v1.0.1 programs and certificates check nine finite propositions; the graph-to-state reductions, exceptional-leaf repair and remaining structural proof are mathematical arguments in the paper without a documented complete human or formal check.
Independent checking
exhaustive enumeration, independent object detection for some cases, witness and certificate checking
- Checker
- Botsford’s archived finite verifiers
- Scope
- nine stated finite configuration propositions in bipartite and triangle-free branches
- Basis
- Reported by the linked checker
Human understanding
Default for missing documented human explanation: the author presents a structural proof and repair, but the record does not establish a human account of the central mechanism independent of the primarily AI-generated results.
Correction and publication history
A revised k=5 divisible-cycle theorem with bounded computational certificates.
Read this published revision