Vacuum Permeability and Schur Fractions: Parameter-Free Predictions from Electroweak Couplings to QCD Confinement

We propose 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. Adopting Schur fractions f(R)G = 1/d2R, derived unconditionally from the Peter–Weyl decomposition of compact gauge groups, and modelling the Reynolds projector P̂G as a Krein filter, we demonstrate that quantum-purity loss is geometrically quantised by the vacuum. The formalism predicts exact algebraic identities without adjustable parameters: the tau-lepton axial coupling |gτA| = 1/4, a 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. These algebraic predictions 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.