Structural Principle of Entanglement Core Framework

Abstract

The 6.0 release of the PSE — Structural Principle of Entanglement represents the fully stabilized and final formulation of the theory, following the complete consolidation of its fundamental ontological chain: 𝑺 ⟶ 𝑫𝑺(𝒇) ⟶ 𝑪𝒇 ⟶ 𝑫s(𝒆) ⟶ 𝑪𝒆 ⟶𝒟physical. The transitions between the levels of the ontological chain are carried out by the operators 𝔇, Δ, Fλ, Gλ, and Φ, each with a specific structural role defined in the formalization of the PSE. In this structure, the chain is no longer referenced to the metric as its final object, but to the projection map Φ, which formalizes the transition from the pregeometric emergent domain to the physical domain. All physical quantities — metric, fields, geometric invariants, energetic and dynamical quantities — arise as compressed images of the emergent structure. Φ is not an ontological operator: it expresses the level of emergent structural complexity at which physical quantities become definable. Version 6.0 introduces a significantly expanded conceptual framework, now including: a precise theoretical positioning of the PSE within contemporary ontological approaches to quantum theory, a clarified physical interpretation of emergent quantities and their non‑fundamental status, a more comprehensive general introduction, outlining motivations, structure, and implications of the theory, a refined distinction between emergent structural objects and physical quantities, ensuring that the physical domain is understood as a deterministic projection of the emergent complexity of S, not as an ontological layer. The release definitively consolidates: the general conceptual framework of the PSE and its emergent chain, the rigorous mathematical formalization of the emergent domain, the definition of the fundamental operators 𝔇, Δ, Fλ, Gλ, and Φ, the proof of the functional uniqueness of the projection Φ, the deterministic derivation of the metric and emergent fields as components of Φ, the physical corollaries concerning curvature, derived tensor fields, and emergent stability. The release includes four documents: Conceptual framework (IT) — complete exposition of the theoretical structure, ontological assumptions, emergent chain, theoretical positioning, and physical interpretation. Mathematical formalization (IT) — definitions, operators, Theorems, Corollaries, stability and functional determination. Conceptual framework (EN) — rigorous English version intended for international dissemination. Mathematical formalization (EN) — rigorous English version intended for international dissemination. Version 6.0 is declared conceptually final: the theoretical structure is complete, coherent, and ready for future integration with applied physical models. This work was developed with the support of artificial intelligence. Author: Andrea Toricelli (independent researcher)Email: a.toricelli@hotmail.it