OpenAI reports: Off-diagonal Ramsey growth
The manuscript reports R(5,t) = t⁴/(log t)^(3+o(1)) as t tends to infinity.
Read original source Original manuscript · family 170github.com
Original report: 2026-10-06Off-diagonal Ramsey growth
Off-diagonal Ramsey numbers R(s,t) force a clique of size s in one edge color or size t in the other.
Progress records 1
Understand the problem ↓1 record · How we rate progress
Understanding the problem
Read the background
Off-diagonal Ramsey numbers R(s,t) force a clique of size s in one edge color or size t in the other. Fixing s and allowing t to grow creates an asymptotic question.
Read the claim in its exact mathematical setting. A manuscript is a research report; its presence in this catalog does not establish that the proof has been independently verified or that the historical novelty assessment is complete.
Why it matters
A focused research target whose precise scope can be followed separately from the general capability of an AI system.
What counts as progress
A sourced new theorem, construction, bound, algorithm, or formalization with its baseline and evidence stated.
What to watch for
- Check the formal statement, assumptions, and cited prior results against the claimed improvement.
- Keep author-reported checking, independent checking, and manuscript availability separate.
- Track revisions to the pinned source and any subsequent expert assessment.
Background review: 2026-10-11. Selected sources:
Website timeline
Publication dates and editorial changes.