What was already known
Abbott–Hanson gave S(k+2)>=9S(k)+4. Rowley's template method and later SAT-assisted templates improved other steps and yielded prior listed bounds S(8)>=5286 and S(13)>=2011290. Romain Ageron independently developed a closely related unpublished shifted-template approach, acknowledged by the authors.
AI involvement
The authors credit ChatGPT 5.5 Pro with the shifted-template idea. They refined it, found the explicit template and SAT construction, and derived the recurrence and numerical bounds.
The central shifted-template idea is expressly credited to ChatGPT; human refinement and search produced the final recurrence.
Importance
Strengthens the two-step Schur recurrence and two derived lower bounds.
Limitations
ChatGPT is credited with the shifted-template idea. The human authors found the final template, SAT search, proofs and numerical bounds. A closely related independent unpublished approach is acknowledged; no completed check procedure for the final recurrence is documented.
Technical verification
The paper provides an explicit template, proofs and a general statement that the idea was verified, but no identified checker and completed method for the final recurrence are documented. Reported is the evidence default; SAT search alone does not establish an exact certificate check.
Human understanding
The human authors present the conditions, multiplication and tail arguments, and explain how the displayed template gives the recurrence.
Correction and publication history
The model contributed the central template idea; the final recurrence and bounds were developed by the authors.
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