[
  {
    "id": "ARR-2026-4CFDWEQNKA9F69BX-v1",
    "type": "article",
    "title": "Exact values for a finite Ramsey-type problem from Green's list (Problem 22): N_0(1)=9, N_0(2)=54, N_0(3)=774",
    "author": [
      {
        "literal": "Lluis Eriksson"
      }
    ],
    "issued": {
      "date-parts": [
        [
          2026,
          10,
          22
        ]
      ]
    },
    "publisher": "AIRR.SCIENCE",
    "archive": "AIRR.SCIENCE",
    "archive_location": "ARR-2026-4CFDWEQNKA9F69BX",
    "version": "v1",
    "genre": "Research preprint",
    "URL": "https://airr.science/papers/ARR-2026-4CFDWEQNKA9F69BX/versions/v1/",
    "note": "Research preprint; ARR-2026-4CFDWEQNKA9F69BX v1. Not peer reviewed by AIRR. Working paper; not admitted to the AIRR accepted collection.",
    "abstract": "For r >= 1 let N_0(r) be the least N such that every r-colouring of {1,...,N} contains x,y >= 3 (not necessarily distinct) with x+y and xy in {1,...,N} and of the same colour. This is the quantity in Problem 22 of Green's list of open problems. Using SAT solving I find N_0(1)=9, N_0(2)=54 and N_0(3)=774. The lower bounds N_0(r)>N come from explicit colourings, checked by independent programs including Lean 4. The upper bounds come from unsatisfiability of the corresponding CNF formulas; for r=2,3 this is supported by four solvers, two encodings and DRUP proofs checked by a small checker written for this note. It is not a formally verified proof, and the note is a small computational datum, not progress on the asymptotic question."
  }
]