{
  "abstract": "We study how far a fixed Ramsey upper bound can be improved by descending through blue neighborhoods in one vertex set while keeping a second set fixed. A weighted inequality in the two set sizes determines when the descent can stop. For the source bound specified here, the infimum diagonal exponent over all finite derivations lies in $[1.305,\\,1.307]$. A finite derivation gives $R(k,k)\\le3.69507^k$ for all sufficiently large $k$; a concave polygon proves the lower bound for every finite depth. We also characterize the infimum as a greatest fixed point and show that every larger exponent has a finite derivation valid uniformly for nearby clique-size ratios.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14525",
  "author_total": 2,
  "authors": [
    {
      "name": "Zhipeng Lu"
    },
    {
      "name": "Sichen Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0sn465ysjf0nz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14525",
  "fulltext_url": null,
  "id": "0sn465ysjf0nz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14525",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7213333626",
  "pdf_url": "https://arxiv.org/pdf/2609.14525",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0sn465ysjf0nz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.14525",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14525"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Retained-Set Descent for Diagonal Ramsey Numbers",
  "title_text": "Retained-Set Descent for Diagonal Ramsey Numbers",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/0sn465ysjf0nz",
  "venue": "arXiv",
  "versions": []
}