Ultraviolet Stability of Wilson-Loop Expectations in 4D Lattice Yang-Mills Theory Via Multiscale Gradient-Flow Smoothing
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VERSION 2 RETRACTION AND ERRATUM. The principal results of version 1 are withdrawn. Lemma 3.6, Eq. (16), falsely identifies the Wilson-flow linearisation with a connected weighted scalar Laplacian plus a pointwise adjoint term. At the trivial configuration, gauge invariance forces the true Hessian to annihilate a pure-gauge subspace of dimension at least (|V|-1)(N^2-1), incompatible with the printed connected-Laplacian kernel; if the positive-weight graph is disconnected, the single stationary heat-kernel term used downstream is itself false. Consequently Lemma 3.8, Proposition 3.9, Theorem 3.11 and Theorem 1.1 are withdrawn. Lemma 2.2 and Proposition 1.3 remain intact. Lemma 3.2 is only recoverable as a separately specified scalar heat-kernel theorem; its original instantiation is withdrawn. Reflection positivity, Osterwalder-Schrader reconstruction, thermodynamic limit and mass gap remain open. The five-page erratum is followed by the preserved 21-page version 1.
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Cite this paper
Lluis Eriksson (2026). Ultraviolet Stability of Wilson-Loop Expectations in 4D Lattice Yang-Mills Theory Via Multiscale Gradient-Flow Smoothing. AIRR.SCIENCE, ARR-2026-5E8SDS6DM8826ABE, v1. https://airr.science/papers/ARR-2026-5E8SDS6DM8826ABE/versions/v1/ Archived manuscript; ARR-2026-5E8SDS6DM8826ABE v1. Not peer reviewed by AIRR. Historical import; not assessed by AIRR.
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