Almost Reflection Positivity for Gradient-Flow Observables via Gaussian Localization in Lattice Yang-Mills Theory
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VERSION 2 RETRACTION AND STATUS NOTE. The principal results of version 1 are withdrawn. Theorem 4.4 and Proposition 3.8 depend on the false Wilson-flow linearisation retracted in ai.viXra:2602.0085 and on further false statements. Lemma 3.1 omits the stationary heat-kernel term; Lemma A.1 gives a variance-oscillation bound that fails for correlated non-product measures; Theorem 5.1 does not obtain a positive self-adjoint generator from its stated hypotheses; Lemma 3.3 uses a non-periodic separation across the torus boundary; and Lemma 3.5 bounds a nonlinear map by a differential at one endpoint rather than an integrated or uniform Jacobian. Definitions 2.2, 2.5 and 2.6 remain definitions, and the cited lattice reflection-positivity Theorem 4.1 is not retracted here. Nothing in this note proves the intended almost-reflection-positivity conclusion false; the printed proof and several printed statements fail. The six-page erratum is followed by the preserved 15-page version 1.
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Cite this paper
Lluis Eriksson (2026). Almost Reflection Positivity for Gradient-Flow Observables via Gaussian Localization in Lattice Yang-Mills Theory. AIRR.SCIENCE, ARR-2026-6GVNY9YDSY8V9B86, v1. https://airr.science/papers/ARR-2026-6GVNY9YDSY8V9B86/versions/v1/ Archived manuscript; ARR-2026-6GVNY9YDSY8V9B86 v1. Not peer reviewed by AIRR. Historical import; not assessed by AIRR.
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