The ΨO Model for the Functional Integrity of Singular Systems

This document formalizes the \Psi_O model, a theoretical framework for resolving spacetime singularities through quantum-mechanical regularization. Unlike classical General Relativity, where curvature diverges, this model introduces an Effective Field Theory (EFT) where the Kretschmann scalar is saturated at the Planck scale.Key Features of Version 1.1: • Curvature Saturation: Implements a mathematical regularization of physical curvature K_{eff}, ensuring a C^0-continuous metric throughout gravitational collapse.• Information Preservation: Preserves information-theoretic functional integrity and avoids the firewall paradox by maintaining maximum discrete information density.• Empirical Falsifiability: Proposes a definitive observational test via Gravitational Wave (GW) echo analysis, providing a specific time-delay scaling formula \Delta t_{echo} for interferometric verification.• Comparative Framework: Includes a falsification matrix comparing the \Psi_O model against General Relativity and the Firewall conjecture regarding singularity bounds and signal predictions.