Quantum Geometrodynamics of Phase Synchronization (QGS): Resolving Singularities and the Information Paradox via Macroscopic Attractors

The intersection of General Relativity and Quantum Mechanics within the event horizon of a black hole yields well-documented pathologies, namely the emergence of infinite mass density singularities and the apparent destruction of quantum information. In this paper, we introduce a novel theoretical framework, Quantum Geometrodynamics of Phase Synchronization (QGS), which reframes gravitational collapse as a continuous topological phase transition rather than a geometric zero-volume point. By modeling the vacuum as a globally coupled, dynamic Hebbian network, we demonstrate analytically and numerically that spacetime curvature regularizes at the macroscopic limit (N → ∞). The gravitational singularity is replaced by a Perron-Frobenius macroscopic coherent state (R → 1), where topological tension dissipates exothermically, yielding a strict mathematical derivation of Hawking Radiation from first principles. Furthermore, local quantum information is irrevocably preserved in the topological winding numbers of a T⁶ manifold and the connection weights of the Hebbian vacuum tensor.