Hierarchical Decoherence in Mixed Gauge Sectors: Geometric Quantization of Entanglement via the Holographic Vacuum Elasticity Framework

We present a parameter-free analytic framework for quantifying the structural decoherence rate of entangled quantum states subject to distinct gauge groups U(1), SU(2)L, and SU(3)c. The framework is the Holographic Vacuum Elasticity (HVE), governed by the Vacuum Suppression Law (VSL): Oobs = Oideal · exp(−χ · σ0G · W · Ω3 · fG), where the Schur fractions f(R)G = 1/dR2 are derived unconditionally from the Peter–Weyl decomposition of compact gauge groups, and the Reynolds projector P̂G acts as a Krein filter. The VSL predicts exact algebraic identities without adjustable parameters: the structural decoherence ratio of 2.25× between the fundamental and adjoint SU(2) representations, an inter-sector friction factor of 16× between SU(2) and SU(3) sectors, and a boosted-to-inclusive purity ratio of ≈ 1.78 for ZZ* relative to WZ production. Phenomenological post-dictions include the proton magnetic moment (0.047% error, Class II) and the Yang–Mills mass gap (0.35% error, Class I). These results are confronted with recently published quantum-tomography data from the ATLAS and CMS collaborations at the LHC (2024–2026), achieving consistent agreement across four distinct gauge sectors without any free parameter. All post-dictions are explicitly labelled as such; all preexisting experimental data are cited from published sources.