[
  {
    "id": "ARR-2026-7APPCT8GM198ERNP-v1",
    "type": "article",
    "title": "Spectral Gap and Thermodynamic Limit for SU(N) Lattice Yang-Mills Theory via Log-Sobolev Inequalities and Complete Analyticity",
    "author": [
      {
        "literal": "Lluis Eriksson"
      }
    ],
    "issued": {
      "date-parts": [
        [
          2026,
          2,
          18
        ]
      ]
    },
    "publisher": "AIRR.SCIENCE",
    "archive": "AIRR.SCIENCE",
    "archive_location": "ARR-2026-7APPCT8GM198ERNP",
    "version": "v1",
    "genre": "Archived manuscript",
    "URL": "https://airr.science/papers/ARR-2026-7APPCT8GM198ERNP/versions/v1/",
    "note": "Archived manuscript; ARR-2026-7APPCT8GM198ERNP v1. Not peer reviewed by AIRR. Historical import; not assessed by AIRR.",
    "abstract": "We present two parallel results for SU(N) pure gauge lattice Yang-Mills in four Euclidean dimensions, at fixed lattice spacing eta > 0 and weak coupling g0 <= g*, both conditional on a single shared input, the Dobrushin-Shlosman complete analyticity condition (H-CA): (A) a log-Sobolev inequality Ent(f^2) <= (2/rho) E(f,f) with rho > 0 independent of L, via Cesi's quasi-factorisation seeded by a Bakry-Emery/Holley-Stroock local LSI; and (B) a spectral gap m_gap >= m0 > 0 for the Osterwalder-Seiler Hamiltonian, via Dobrushin clustering and reflection positivity. The two outputs are logically parallel; neither implies the other here (the bridge lemma remains open, Remark 6.3). Version 2 corrects the status of the shared input: v1 declared (H-CA) verified from Balaban's infrastructure; per the audited chain (2602.0053/0054 v2) that route is conditional on (H-DOB-blk)+(H-P0) and valid only in the volume window L <= exp(C/g0^2). Accordingly all results are stated in two regimes: windowed (audit-backed conditional) and all-volume (under the strictly stronger bare hypothesis (H-CA)_infty, required for the thermodynamic limit, Theorem C). What is unconditional and machine-verified: the curvature computation Ric_SU(N) = N/4, the Holley-Stroock block-seed arithmetic, the variance/entropy decompositions and the failure of pointwise inheritance, the Dobrushin contraction machinery and its window arithmetic, the clustering => transfer-gap lemma on explicit operators, and the convergence of Cesi's geometric factor. All bounds remain explicit in N, g0, eta."
  }
]