[JeetuSK0808]

Adds a new constant in the Ramsey family: C_17b = lim R(3,k) log k / k^2, which is Erdős problem #165.

Current bounds are 1/2 <= C_17b <= 1. The lower bound is from Hefty, Horn, King and Pfender (arXiv:2510.19718), the upper bound from Shearer (1983). The page records the history on both sides (Ajtai–Komlós–Szemerédi, Kim, Bohman–Keevash, Fiz Pontiveros–Griffiths–Morris, Campos–Jenssen–Michelen–Sahasrabudhe) and links the small-k computational bounds (Radziszowski's survey, Coniglio et al. 2026, and my circulant certificate for R(3,33) >= 241 on Zenodo).

I left the existing [17] row label alone to avoid conflicting with #223. Happy to relabel it 17a if you prefer.

Claude Code was used to draft the page. The bounds were checked against the arXiv abstracts and the Erdős problems page.

🤖 Generated with Claude Code

[carlostoledo1891]

An independent re-decision of R(3,33) ≥ 241 (your circulant certificate, linked from this page)

@JeetuSK0808, alongside the graphon replays on #255, #277 and #279: we re-decided R(3,33) ≥ 241 from the deposit (zip sha256 a17548de…) with our own code, never running yours. We rebuilt the graph from the connection set D in the README: x ~ y iff y − x ∈ ±D on Z_240, giving 3,840 edges, equal to the certificate's edge list. It has no triangle.

It also has no independent set of size 33. The graph is circulant, so any such set can be translated onto one through vertex 0. The multipliers 1, 13, 37, 71, 169, 203, 227 and 239, each checked as an automorphism, fix 0 and split its non-neighbours into 31 orbits. Our orbital branch-and-bound searched the 31 pieces this leaves: 2,572 units, 2.9·10⁹ nodes, 9 minutes on 8 laptop threads, and found none. A second path that shares no code with the first (one CNF per cube, kissat with DRAT proofs, every UNSAT checked by drat-trim) closed 22 of the 31 cubes; the nine largest stayed open at a 20-minute cap. So the verdict rests on the first path, which is held to a Python reference root by root on 78 smaller instances.

Record: carlostoledo1891/cert-machine @ f4ee2715, certs/ramsey-ledger.json (the "outside" row), instruments/ramsey/orbital.c + orbital.py, corpus/ramsey/runs/R_3_33_ge_241.*.