The LEV–TSE Emergence Framework: A Structural Principle for Non-Additive Systems

This repository contains the full publication of the LEV–TSE Emergence Framework, a structural principle describing the emergence of global properties in stronglycoupled, non-additive systems. The framework introduces the relation: E = (ρL³) γ² + Σ Interpretation note (clarification). In this framework, E denotes an emergent regime capacity (a global structural property), not physical energy measured in joules. Accordingly, ρ denotes structural constraint density (not an energy density in J/m³). where: ρ = structural densityL³ = coherence volumeγ = coherence factorΣ = irreducible residual (structural non-closure) Unlike classical physical equations, this relation does not describe the conservationor redistribution of predefined quantities. It formalizes the structural conditionsunder which global regimes arise in organized systems. The work develops: Formal mathematical properties Ontological consequences Cosmological interpretation Cognitive interpretation Structural falsifiability criteria Formal axioms (appendices) The framework applies to systems characterized by: Strong coupling Structural coherence Historical dependence Regime persistence Non-additive behavior This deposit includes both English and French versions of the complete framework, together with cryptographic hashes for integrity verification. This work does not propose a closed physical theory. It proposes a structuralconstraint on what additive and closed-form models can, in principle, explain. Acknowledgement: The author thanks Marie-Hélène Tremblay for a conceptual suggestion regarding the notation and framing of the residual term Σ. The author remains solely responsible for the content, structure, and claims. Note to readers (status): This record is a working theoretical framework (preprint) and is not peer-reviewed. The LEV–TSE equation is proposed as a structural meta-law intended to guide operationalization and empirical testing. Version updates will (i) define measurable proxies for ρ, L³, and γ, (ii) specify estimation procedures for Σ under refinement, and (iii) provide toy models/simulations to test regime transitions and superadditivity. Claims labeled as “theorem/lemma” in early drafts are to be treated as axioms/propositions until formal proofs are supplied. Version 1. 1 — Changes / Errata Clarified that E denotes an emergent regime capacity (not physical energy in joules). Clarified that ρ denotes structural constraint density (not energy density J/m³). Standardized equation formatting: E = (ρL³) γ² + Σ. No change to axioms, scope, or overall framework claims; this update is a clarification and notation stabilization. This work does not propose a closed physical theory. It proposes a structural constraint on what additive and closed-form models can, in principle, explain. Acknowledgement: The author thanks Marie-Hélène Tremblay for a conceptual suggestion regarding the notation and framing of the residual term Σ. The author remains solely responsible for the content, structure, and claims. Note to readers (status): This record is a working theoretical framework (preprint) and is not peer-reviewed. The LEV–TSE equation is proposed as a structural meta-law intended to guide operationalization and empirical testing. Version updates will (i) define measurable proxies for ρ, L³, and γ, (ii) specify estimation procedures for Σ under refinement, and (iii) provide toy models/simulations to test regime transitions and superadditivity. Claims labeled as “theorem/lemma” in early drafts are to be treated as axioms/propositions until formal proofs are supplied. Version 1. 1 — Modifications / Errata (FR) Clarification: E désigne une capacité émergente de régime (et non l’énergie physique mesurée en joules). Clarification: ρ désigne une densité de contraintes structurales (et non une densité énergétique en J/m³). Standardisation de la notation: E = (ρL³) γ² + Σ. Aucun changement des axiomes, du périmètre, ni des affirmations principales ; cette mise à jour stabilise l’interprétation et la notation. File integrity (SHA-256) / Intégrité des fichiers (SHA-256) LEV-TSEEmergenceFrameworkENᵥ1. 1. pdf: b4b34bf1f507a5a66c28b42fda3b4cd8681c272c682e6b4302ece5b44b23dcbe LEV-TSEEmergenceFrameworkFRᵥ1. 1. pdf: b246cbbefcc008850a3230560b793044531d0a9d414284365cc5942c5267c750