The Topological Transition of the Vacuum $0 \rightarrow \hat{U}(\pi) + \hat{I}$: Hamiltonian Foundation of the Zero-Energy Universe and Torsional Dynamics of the Horizon

Abstract 

The incompatibility between General Relativity and Quantum Field Theory has led modern cosmology to postulate ad hoc entities lacking direct empirical evidence: the graviton and the dark cosmological sector ($\Lambda$ and Dark Matter). In this work, we propose a unified geometric model in which spacetime acts as the dynamic polarization of a zero-energy vacuum. By reformulating Euler's fundamental identity through a topological operator, we demonstrate how the phase factor $e^{i\pi}=-1$ emerges dynamically within the Wheeler-DeWitt constraint to formalize the attractive curvature (negative gravitational potential). The gravitational collapse is modeled via the Einstein-Cartan-Sciama-Kibble (ECSK) theory within a Kerr metric: the spin-torsion coupling, combined with a primordial chiral anomaly driven by the Lense-Thirring effect, induces an isotropic bounce that eludes the singularity at the Cartan critical density ($\rho_C \sim 10^{45}\text{ kg/m}^3$). The model overcomes Hawking's information paradox by preserving unitarity on a multiversal scale (circumventing the Bekenstein bound) and provides strict empirically falsifiable constraints through parity violation in the CMB polarization (non-vanishing $TB$ and $EB$ modes) and by decoding the cosmological "Axis of Evil".