EVOLUTIONARY UNIVERSAL REDISTRIBUTIVE THEORY (TRUE) – SPECTRAL INVARIANT γ₀ = 0.13648 AND SCALING LAW FOR QUANTUM CRITICAL SYSTEMS

Abstract

We present the consolidated and corrected version of the TRUE framework (Evolutionary Universal Redistributive Theory), which unifies the description of universal regularities observed in quantum critical systems outside the Fermi liquid paradigm. The fundamental invariant γ₀ = 0.13648 is analytically derived from the Koszul-Fisher curvature constraint on the symplectic manifold of information phases, without any free parameters. We introduce the spectral scaling law R_{\text{raw}}(\tau) = \tau \cdot \gamma_0 , where τ is the effective spectral dimension of the system, measured by the trace of the spectral dissipation tensor. We demonstrate the physical equivalence between the ratio of critical fields and the ratio of critical energies via the Zeeman energy E = g \mu_B B . Validation is performed on six independent classes of materials, with deviations systematically below 5% (with the exception of MATBG, whose deviation is 9.4% within the standard scaling law framework, which will be discussed). We propose a rigorous classification of systems into two categories: predictive systems (τ computable a priori) and complex systems (frustrated lattices), where the invariant becomes a tool for topological diagnostics. Three blind predictions are formulated for as yet untested systems. A note on the constant ξ is added.