Structural Principle of Entanglement Core Framework

The Structural Principle of Entanglement (PSE) is a complete theoretical framework that formalizes the emergence of space‑time as a geometric structure derived from a discrete, non‑observable correlation. This updated release consists of four coherent and self‑contained documents, representing the expanded and consolidated version of the PSE previously published on Zenodo. 1. Conceptual Framework (≈30 pages) Introduces the fundamental ontological chain: S → Dₛ^(f) → C_f → Dₛ^(e) → C^(e) → d → g_{μν}. It defines the nature of the discrete correlation, the distinction between formal and emergent deviation, the origin saturation, and the emergent rigidity. This document establishes the conceptual foundations supporting the entire theory. 2. Mathematical Formalization and Fundamental Theorems (≈45 pages) Provides the rigorous formalization of the Structural Principle of Entanglement, defining the mathematical objects associated with emergent correlations and proving general properties such as regularity, continuity, and stability. It forms the logical and mathematical basis for the two metric documents. 3. Emergent Radial Metric (PSE‑Schwarzschild) (≈22 pages) Applies the emergent structure to the static, spherically symmetric case. The resulting metric is regular, continuous, free of singularities, and consistent with the Schwarzschild solution in the weak‑field limit. This is the first explicit emergent metric derived from the Structural Principle of Entanglement. 4. Emergent Rotating Metric (PSE‑Kerr) (≈171 pages) Develops the complete emergent rotating metric. The PSE‑Kerr metric is regular throughout its domain, free of singularities, stable, continuous, consistent with Kerr in the weak‑field limit, and reduces to the emergent radial metric as a→0. The document includes the analysis of characteristic surfaces, curvature invariants, geodesics, the extremal limit a→M, and full ontological coherence. It represents the first complete, regular, and ontologically closed rotating emergent metric derived from the Structural Principle of Entanglement. Author: Andrea Toricelli Email: [email protected]