[
  {
    "id": "ARR-2026-0VEP5BTYB99VNSC0-v1",
    "type": "article",
    "title": "Six-spin Lorentzian obstructions for clique blowups of independence-stable graphs",
    "author": [
      {
        "literal": "Lluis Eriksson"
      }
    ],
    "issued": {
      "date-parts": [
        [
          2026,
          10,
          17
        ]
      ]
    },
    "publisher": "AIRR.SCIENCE",
    "archive": "AIRR.SCIENCE",
    "archive_location": "ARR-2026-0VEP5BTYB99VNSC0",
    "version": "v1",
    "genre": "Research preprint",
    "URL": "https://airr.science/papers/ARR-2026-0VEP5BTYB99VNSC0/versions/v1/",
    "note": "Research preprint; ARR-2026-0VEP5BTYB99VNSC0 v1. Not peer reviewed by AIRR. Working paper; not admitted to the AIRR accepted collection.",
    "abstract": "Let F be a finite connected simple graph with at least one edge such that deleting any edge leaves its independence number unchanged. For every integer s at least two, we prove that the clique blowup F[K_s] admits a strictly positive rational rank-two antiferromagnetic target on six states whose graph partition polynomial is not Lorentzian. The proof classifies minimum-induced-edge subsets using equality in Turan's theorem, identifies an exact four-profile block of inertia (2,2,0), and compresses all higher profiles by a scaled generalized Vandermonde matrix. This yields obstructions for connected biregular bipartite bases other than K2 and for connected bases with a unique maximum independent set and at least one edge. Exact computations check 994 base graphs, 720 stable blowups and four positive rational six-state Hessian witnesses. Six is an upper bound; optimality, uniform target parameters and the general connected-source characterization remain open."
  }
]