Structural Principle of Entanglement (PSE)

Abstract

The Structural Principle of Entanglement (PSE) is a fully emergent theoretical framework in which physical quantities, geometry, and dynamical structures arise as compressed projections of a pregeometric domain. The theory is built on the non‑invertible ontological chain S → DS(f) → Cf → DS(e) → Ce → Ereg → Ereg(k) → Dphysical governed by the structural operators 𝔇, Δ, Fλ, Gλ, the regularization operator R, and the complexity thresholds Θ that determine when the emergent structure becomes physically representable through the projection map Φ. Version 6.5 introduces a refined conceptual exposition and a clearer presentation of the emergent hierarchy, preserving the mathematical formalization of previous releases. The framework includes the full treatment of emergent regularity, complexity thresholds, quantum maps, rigidity, and the functional uniqueness of the projection Φ. The release consists of four documents (IT/EN), covering both the conceptual structure and the complete mathematical formalization. The PSE is presented in its stabilized and coherent form, ready for scientific dissemination and future integration with applied physical models. Version 6.5.1 introduces exclusively targeted refinements in the mathematical formalization, while preserving the conceptual structure and the emergent framework of the theory. The updates concern notation clarity, consistency of the structural operators, and a more linear presentation of the emergent hierarchy, without altering the results or the fundamental ontological chain. This work was developed with the support of artificial intelligence. Author: Andrea ToricelliIndependent researchera.toricelli@hotmail.it My goal is to present this framework with maximum clarity and rigor, offering a constructive contribution to the scientific community.