[
  {
    "id": "ARR-2026-0S1R9TEN1580VT82-v1",
    "type": "article",
    "title": "DLR-Uniform Log-Sobolev Inequality and Mass Gap for Lattice Yang—Mills at Weak Coupling: a Conditional and Windowed Reduction",
    "author": [
      {
        "literal": "Lluis Eriksson"
      }
    ],
    "issued": {
      "date-parts": [
        [
          2026,
          2,
          12
        ]
      ]
    },
    "publisher": "AIRR.SCIENCE",
    "archive": "AIRR.SCIENCE",
    "archive_location": "ARR-2026-0S1R9TEN1580VT82",
    "version": "v1",
    "genre": "Archived manuscript",
    "URL": "https://airr.science/papers/ARR-2026-0S1R9TEN1580VT82/versions/v1/",
    "note": "Archived manuscript; ARR-2026-0S1R9TEN1580VT82 v1. Not peer reviewed by AIRR. Historical import; not assessed by AIRR.",
    "abstract": "We study the passage from the uniform log-Sobolev inequality (LSI) on periodic tori, developed in the companion series, to a DLR-uniform LSI for the conditional Gibbs specification of SU(N_c) lattice Yang-Mills in d >= 3 at weak coupling (beta >= beta_0), and from there to a mass gap via Stroock-Zegarlinski and Osterwalder-Seiler reflection positivity. Version 2 corrects the logical status of the main results after a quantitative audit (companion numerical suite included; Appendix A). (i) The fiber assembly (Lemma 3.5) assumes the block Dobrushin condition delta < 1, which v1's own Remark 3.6 left unverified; the printed influence bound c_ij <= tanh(beta n_bd/2) tends to 1 as beta -> infinity and yields delta < 1 only for beta <~ 10^(-2) (d=3) or beta <~ 10^(-3) (d=4) — the opposite of the weak-coupling regime. A rotor exhibit shows the genuine worst-case block influence also tends to 1, so no worst-case criterion can close the gap: the condition is now the explicit hypothesis (H-DOB-blk), and v1's claim of removing the Dobrushin-type Assumption 6.3 of [14] is withdrawn — the present paper reduces that assumption to (H-DOB-blk). (ii) The quantitative absorption in Proposition 4.3 inherits hypothesis (H-P0) of ai.viXra:2602.0052(v2): under the polylog penalty floor p0(g) >= c_0 |log g|^(1+epsilon_0) the required inequality e^(-c p0(g_k)) <= C L_RG^(-(d-1)k) fails already at k = O(1). (iii) The proof assumes g_k <= gamma_0 for all k <= n_max ~ log_LRG diam(Lambda'); with the corrected asymptotic-freedom flow of the series erratum this holds only on the volume window log_LRG diam(Lambda') <= k*(beta), i.e. diam(Lambda') <= e^(C/g^2+O(1)). Theorems 1.1-1.2 are therefore restated as windowed and conditional on (H-DOB-blk) and (H-P0). What survives unconditionally — and is validated numerically — is the boundary-uniformity mechanism itself: the per-plaquette oscillation and gradient bounds (Lemma 3.1; sharp for N_c=2), the \"frozen = slow\" reduction (Lemma 3.2), the refined dynamical large-field event, the energy-penalty identity ||U-1||_HS^2 = 2N_c(1 - Re tr U / N_c), the TV <= tanh(osc/4) lemma with its two-point equality case, and the Bakry-Emery constant N_c/4 in the = -2 tr(XY) convention. The contribution of the paper is thus retagged: a boundary-uniform reduction of the DLR-LSI and the mass gap to (H-DOB-blk)+(H-P0) within the volume window — not an unconditional mass gap."
  }
]