[
  {
    "id": "ARR-2026-6RC0ZG5NW08AZ9WD-v1",
    "type": "article",
    "title": "Ultraviolet Stability for Four-Dimensional Lattice Yang-Mills Theory: Closing the Bałaban-Doob Circuit under Quantitative Blocking and Decoupling Hypotheses",
    "author": [
      {
        "literal": "Lluis Eriksson"
      }
    ],
    "issued": {
      "date-parts": [
        [
          2026,
          2,
          15
        ]
      ]
    },
    "publisher": "AIRR.SCIENCE",
    "archive": "AIRR.SCIENCE",
    "archive_location": "ARR-2026-6RC0ZG5NW08AZ9WD",
    "version": "v1",
    "genre": "Archived manuscript",
    "URL": "https://airr.science/papers/ARR-2026-6RC0ZG5NW08AZ9WD/versions/v1/",
    "note": "Archived manuscript; ARR-2026-6RC0ZG5NW08AZ9WD v1. Not peer reviewed by AIRR. Historical import; not assessed by AIRR.",
    "abstract": "We prove that the continuum limit of pure SU(N) lattice Yang-Mills theory in four Euclidean dimensions exists on the algebra of blocked observables at fixed finite volume, CONDITIONALLY on an explicit hypothesis ledger: a quantitative regularity hypothesis for the blocking map (squared-oscillation summability, Assumption A — equivalently (H-LIP^2), a strengthened form of the (H-LIP) contraction of 2602.0073 v2), the Dobrushin-type decoupling hypothesis (H-DEC/AT) of the sibling audits, and the audited statuses of the Balaban structural package. The argument assembles: (i) Balaban's renormalization group program (polymer representation, irrelevance bounds after beta-function extraction, UV stability of effective densities) — traceable per 2602.0069 v2, with the beta_LF dichotomy for the large-field part; (ii) a Doob-martingale covariance IDENTITY (exact for every measure) together with a conditional-oscillation influence bound — v1's claim that the oscillation control holds \"without product-measure hypotheses\" is withdrawn: v1's Remark 2.3 correctly rejected Efron-Stein for the non-product interpolating measures, but the Doob-oscillation Lemma 1.5 of v1 fails for the same reason (two-spin counterexample, 2602.0070 v2); the repair is (H-DEC); (iii) the RG-Cauchy summability framework of 2602.0073 v2, consumed with its full ledger (including (H-theta)/F-SQRT for the truncation errors). Under the ledger, the telescopic state sequence converges and the resulting state omega_L is gauge-invariant, Euclidean-covariant (hypercubic), and positive. Osterwalder-Schrader reconstruction, the thermodynamic limit, and the mass gap remain open, as in v1. All mechanical steps — the exact covariance identity, both counterexample adjudications, the Assumption A mechanics on explicit blocking maps (including a non-local sharpness example showing locality plus contraction are genuinely needed), and the corrected Proposition 6.1 arithmetic with its exact M 2^(-4k) scale cancellation — are machine-verified in a companion suite."
  }
]