What was already known
The cited best general direct explicit off-diagonal Ramsey construction by Alon and Pudlák had exponent Ω(√(log s/loglog s)). Stronger results in other construction classes are not the direct comparison.
AI involvement
Ihringer and Mattheus chose the p-rank approach. ChatGPT 5.6 proposed the first trace graph and clique argument; the authors developed and verified the final ordered construction.
The model supplied a central initial trace graph and clique argument within the authors’ p-rank program; the stronger final graph is human-refined.
- Supporting source (arxiv.org) — v1 submission history through 18 October 2026
Importance
Supplied the central algebraic graph seed for an improved direct Ramsey construction.
Limitations
The published exponent in Theorem 1.3 belongs to the authors’ ordered refinement. The model dialogue and exact path from seed to refinement are unavailable; the authors report checking all arguments.
Technical verification
The authors state they independently verified all paper arguments, including the model graph in Remark 2.2 and their final construction.
Independent checking
independent author verification of all arguments. Model-suggested TG_{d,h} and refined Theorem 1.3
- Checker
- Ferdinand Ihringer and Sam Mattheus
- Scope
- ChatGPT 5.6 suggested the two-way trace graph TG_{d,h} of Remark 2.2 on projective points over F_(2^h). Ihringer and Mattheus bound its clique size by binom(d−2,ceil((d−2)/2)) and independence number by (d^h+1)². Their stronger one-way ordered graph and Theorem 1.3 are human-developed refinements.
- Basis
- Reported by the linked checker
Human understanding
The authors explain the trace graph, p-rank control, clique estimate and the ordered refinement.
Correction and publication history
The AI-suggested two-way trace graph is distinguished from the authors’ stronger ordered graph.
Read this published revision