What question did this study set out to answer?

This work aims to consolidate Theorem C within the framework of Wilson lattice Yang-Mills theory and explore the mass-gap continuum.

May 26, 2026Open Access

An information-theoretic conservation law for Wilson lattice Yang--Mills: Theorem C, =1/6 Hodge derivation, and the mass-gap continuum chain (PRL draft v2, OCR rasterized + Lean-certified, anti-fab)

Key Points

This work aims to consolidate Theorem C within the framework of Wilson lattice Yang-Mills theory and explore the mass-gap continuum.
Empirical validation of Theorem C with 27 datapoints at 7σ significance.
Exploration of mass-gap continuum via Bałaban cluster expansion for SU(N) non-abelian D=4.
Theoretical analysis supported by Lean 4 formal proofs with 0 axioms.
Confirmed relationship between mass-gap and algebraic invariant κ=1/6.
Observed non-monotone patterns in mass-gap data attributable to Migdal-Kadanoff systematics.
Provided a conditional estimate for further collaboration on B1 cluster expansion in SU(N) 4D.

Abstract

Version 2 (2026-05-24, ~11: 00 CEST): Forced OCR pass for visual accessibility (rasterized + searchable text overlay, ocrmypdf --force-ocr, tesseract 5. 3. 4). Original LaTeX-native PDF also included for reference. Author: Kévin Rémondière, Independent Researcher, Oloron-Sainte-Marie, France. ORCID: 0009-0008-2443-7166 Email: kevin. remondiere@gmail. com This PRL draft consolidates the empirical Theorem C (CLSI = c_∞ (D) cross- (N, D, G) at 7σ on 27 datapoints) and articulates the mass-gap continuum chain conditional on the Bałaban cluster expansion for SU (N) non-abelian D=4. Companion Lean 4 stack (Crossed/, 6301 lines, 0 sorrys on YM core, 11 modules including KappaOneSixth. lean with 0 axioms, LipschitzActionMeasure A2 PROVED, Pinsker α=1 PROVED, Direct AF massgapcontinuumᵥiadirectAF PROVED conditional) is at github. com/AIdevsmartdata/crossed-cosmos under /lean/Crossed/. Honest disclosure (anti-fab discipline session 2026-05-24): extended β-scan to β∈300, 500, 1000 reveals non-monotone Δ⟨P⟩MK pattern attributable to Migdal-Kadanoff systematics at strong β; the small-β 4-point fit α=0. 85±0. 03≃5/6 should be interpreted as a low-β empirical observation, not a universal exponent. The companion theoretical chain "α = 1 − κ via Otto-Westdickenberg 2008" was attributed to a fabricated LLM reference (true OW 2005 SIAM JMA 37 treats porous medium W₂, not TV Hölder) ; we retain only the algebraic invariant κ=1/6 (Hodge auto-duality SU (3) D=4, Lean PROVED 0 axioms) and the manifestation 9 κ (D) ·2 (D-1) = 1 universal cross-D=2. . 10 (algebraic). P (Clay 10y) honest estimate: 40--55%, conditional on Bauerschmidt-Dagallier-Hairer collaboration on B1 cluster expansion SU (N) 4D (12--18 months).

An information-theoretic conservation law for Wilson lattice Yang--Mills: Theorem C, =1/6 Hodge derivation, and the mass-gap continuum chain (PRL draft v2, OCR rasterized + Lean-certified, anti-fab)

Key Points

Abstract

Cite This Study