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

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 (C_LSI = 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 mass_gap_continuum_via_direct_AF 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).