UNIVERSAL PHASE RELAXATION AND SPECTRAL DIMENSION IN QUANTUM CRITICAL SYSTEMS: THE TRUE FRAMEWORK

We present a unified theoretical framework, termed TRUE (Théorie Redistributive Universelle Évolutive), to describe the universal regularities observed in quantum critical systems beyond the Fermi liquid paradigm. We introduce a universal invariant \gamma_0 = 0.13648, derived analytically from the Koszul-Fisher curvature constraint on the symplectic manifold of critical phases, without recourse to any empirical fitting. The effective spectral dimension \tau of the dissipation phase space is defined as the invariant trace of the spectral dissipation tensor. We show that the 0\text{D} \to 1\text{D} crossover (unitary Kondo regime) leads to \tau = \sqrt{2}, whose combination with the curvature constraint yields the characteristic equation x^2 - x + \frac{\sqrt{2}}{12} = 0, whose roots are exactly \gamma_0 = 0.13648 and 1 - \gamma_0 = 0.86352. Quantitative validation is performed on five independent classes of materials (strange metals, iron pnictides, magic-angle graphene, Bechgaard salts, InAs nanowires), with deviations below 5% from the predicted invariant. We discuss the validity conditions of the framework, notably the spatial coherence extension condition \xi > 0, and propose a covariant tensor formalism anchored in Koszul-Souriau information geometry.