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 γ_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 τ of the dissipation phase space is defined as the invariant trace of the spectral dissipation tensor. We show that the 0D → 1D crossover (unitary Kondo regime) leads to τ = √2, whose combination with the curvature constraint yields the characteristic equation x^2 - x + {√2}{12} = 0, whose roots are exactly γ_0 = 0.13648 and 1 - γ_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 ξ > 0, and propose a covariant tensor formalism anchored in Koszul-Souriau information geometry.