We present the consolidated version of the TRUE framework (Théorie Redistributive Universelle Évolutive), which unifies the description of the universal regularities observed in quantum critical systems beyond the Landau Fermi-liquid paradigm. The fundamental invariant γ₀ = 0.13648 is derived analytically from the Koszul–Fisher curvature equation on the information phase space, with no free parameters. We introduce the spectral scaling law R_raw(τ) = τ · γ₀, 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 μ_B B. Validation is performed on six independent material classes, with deviations systematically below 5 %. 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 topological diagnostic tool. Three blind predictions are formulated for as-yet untested systems.
We present the consolidated version of the TRUE framework (Théorie Redistributive Universelle Évolutive), which unifies the description of the universal regularities observed in quantum critical systems beyond the Landau Fermi-liquid paradigm. The fundamental invariant γ₀ = 0.13648 is derived analytically from the Koszul–Fisher curvature equation on the information phase space, with no free parameters. We introduce the spectral scaling law R_raw(τ) = τ · γ₀, 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 μ_B B. Validation is performed on six independent material classes, with deviations systematically below 5 %. 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 topological diagnostic tool. Three blind predictions are formulated for as-yet untested systems.
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.
Nous présentons la version consolidée du cadre TRUE (Théorie Redistributive Universelle Évolutive), qui unifie la description des régularités universelles observées dans les systèmes critiques quantiques en dehors du paradigme du liquide de Fermi. L'invariant fondamental γ₀ = 0,13648 est dérivé analytiquement de l'équation de courbure de Koszul-Fisher sur l'espace des phases d'information, sans aucun paramètre libre. Nous introduisons la loi d'échelle spectrale R_brut(τ) = τ · γ₀, où τ est la dimension spectrale effective du système, mesurée par la trace du tenseur de dissipation spectrale. Nous démontrons l'équivalence physique entre le rapport de champs critiques et le rapport d'énergies critiques via l'énergie Zeeman E = g μ_B B. La validation est effectuée sur six classes de matériaux indépendants, avec des écarts systématiquement inférieurs à 5 %. Nous proposons une classification rigoureuse des systèmes en deux catégories : les systèmes prédictifs (τ calculable a priori) et les systèmes complexes (réseaux frustrés), où l'invariant devient un outil de diagnostic topologique. Trois prédictions à l'aveugle sont formulées pour des systèmes non encore testés.
To test the predictive power of the TRUE framework (Théorie Redistributive Universelle Évolutive) and its geometric invariant \gamma_0 = 0.13648, we formulate a set of a priori numerical predictions for three quantum critical systems not yet characterized within this formalism: the Planckian viscosity of the ^6\text{Li} Fermi gas in the unitary regime, the transition ratio of the \alpha\text{-RuCl}_3 spin liquid under field, and the critical energy ratio of the metamagnet \text{Sr}_3\text{Ru}_2\text{O}_7. All numerical values are locked with no free parameters and are accompanied by their spectral dimension \tau, providing a direct experimental verification protocol for the community.
We develop a mathematically rigorous and experimentally testable framework for the classification of physical regimes based on the modular structure of quantum states. The central object of the theory is the modular generator K = −log ρ, which provides a unified language for spectral, geometric, and information-theoretic diagnostics. We introduce a universal instrument panel (MSRO: Modular–Spectral RG Observables) that integrates spectral quantiles, commutator-based response functions, partition-based locality diagnostics, and information-geometric structures. A key requirement of the framework is strong portability: the same diagnostic protocol applies across multiple domains—including open quantum systems, information geometry, entanglement-based models, and RG-like flows—without domain-specific retuning. The main result of the work is the derivation of a universal and experimentally testable scaling law for the modular response signal: ν(λ) ∼ 1 log λ, which characterizes critical regimes in a wide class of quantum systems. We prove that this scaling emerges from spectral asymptotics of the modular operator and establish a strict equivalence between spectral, geometric, and information-theoretic descriptions of criticality: ν ↔ k(q) ↔ I(λ) ↔ K ↔ R ↔ Δ. The framework is supported by functional analytic results (including Fr´echet differentiability of log ρ), operator inequalities (Golden–Thompson, monotonicity of relative entropy), and stability estimates. We further provide a concrete experimental protocol for quantum simulators, including statistical error bounds and Fisher information constraints, making the prediction directly testable. Beyond regime classification, the results suggest a new perspective on criticality as a geometric phenomenon associated with vanishing modular curvature. The approach opens pathways toward large-N limits, quantum field extensions, and the discovery of new classes of non-standard critical behavior.
Afin d'éprouver la capacité prédictive du cadre TRUE (Théorie Redistributive Universelle Évolutive) et de son invariant géométrique \gamma_0 = 0.13648, nous formulons un ensemble de prédictions numériques a priori pour trois systèmes critiques quantiques non encore caractérisés dans ce formalisme : la viscosité planckienne du gaz de Fermi ^6\text{Li} au régime unitaire, le rapport de transition du liquide de spin \alpha\text{-RuCl}_3 sous champ, et le rapport d'énergie critique du métamagnétique \text{Sr}_3\text{Ru}_2\text{O}_7. Toutes les valeurs numériques sont verrouillées sans paramètre libre et assorties de leur dimension spectrale \tau, offrant un protocole de vérification expérimentale directe à la communauté.
We report the discovery of a new class of critical phenomena in open quantum systems that is not governed by divergence of correlation length. In contrast to the standard paradigm, where criticality is identified by ξ → ∞, we demonstrate the existence of regimes characterized by: Δ → 0, Γ > 0, ξ = O(1), where Δ is the partition gap and Γ is the switching rate of optimal decompositions. We show that such systems exhibit a universal modular scaling law: ν(λ) ∼ 1 log λ, derived from the spectral structure of the modular generator K = −log ρ. This scaling defines a new diagnostic observable independent of spatial correlations. We formulate a hard, experimentally testable prediction: Ξ(λ) = ν(λ) · log λ → 1, which provides a falsifiable signature of modular criticality accessible in quantum simulators. The results establish a new notion of criticality rooted in spectral redistribution, commutator dynamics, and information geometry, rather than correlation length. This reveals a previously unrecognized universality class applicable to open quantum systems, non-equilibrium dynamics, and information-theoretic regimes.