Improved algebraic construction for off-diagonal Ramsey numbers
A finite-geometry construction supplied by a language model, then reworked by the authors, improves the explicit lower bound for off-diagonal Ramsey numbers.
- Lab
- Independent
- Model
- ChatGPT 5.6
- Field
- Mathematics
- Date
- 2026-08-25
- Human collaborators
- Ferdinand Ihringer, Sam Mattheus
What was found
The authors set out to use p-rank arguments on constructions in finite geometry to push the explicit lower bound for off-diagonal Ramsey numbers. The first construction, a graph on the points of a projective space with adjacency given by a trace condition, came from the model together with a bound on its clique number resting on algebraic geometry. The authors then developed and refined it into the published construction, which gives a bound of the form R(s,t) at least t to the power (1-o(1)) log s over log(log s + 1). The paper describes the underlying idea as a deterministic analogue of random sampling in finite-geometric settings.
Novelty check
Off-diagonal Ramsey lower bounds are a well-tracked ladder and the paper states the prior explicit bound it improves on, crediting Alon and Pudlak, and cites the recent off-diagonal literature it sits in. No registry carried this result at entry: it does not appear in vibemathed, MathDB, Palomar or ProofAtlas, and it reached this registry through a comment on the r/math weekly thread rather than through any catalogue. The construction is new; the p-rank framing it starts from is the authors' own and is credited as such.
Caveats and known objections
A preprint, unrefereed and not formalized. Autonomy graded ai-assisted, which is what the disclosure supports and no more: the authors state that they had the idea to use p-rank arguments as the starting point, that the first construction and a bound on its clique number were provided by ChatGPT 5.6, and that they subsequently developed, refined and independently verified all arguments and take full responsibility. The model supplied one object inside a human-chosen frame, and the published construction is not the one it returned. Worth recording that the disclosure is a clearly headed AI Declaration at the end of the introduction rather than a remark buried in the body, which is better practice than several other entries here.
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Entry history (1 event)
- AddedEntered the registry graded Author verified and AI-assisted.
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Graded author verified for verification and ai-assisted for autonomy. What these mean.
Cite this entry
whataifound.org. (2026). Improved algebraic construction for off-diagonal Ramsey numbers. whataifound.org: A Registry of AI Scientific and Mathematical Discoveries. https://whataifound.org/finding/2026-08-25-ramsey-algebraic-constructionBibTeX
@misc{whataifound-independent-2026-construction,
title = {Improved algebraic construction for off-diagonal Ramsey numbers},
author = {{whataifound.org}},
year = {2026},
howpublished = {whataifound.org: A Registry of AI Scientific and Mathematical Discoveries},
note = {Result by Independent. Verification: Author verified. Autonomy: AI-assisted.},
url = {https://whataifound.org/finding/2026-08-25-ramsey-algebraic-construction}
}