Topological Phase-Transitions in Complex-Valued Manifolds: A Unified VIFT-SVG Framework for Cosmogenesis and the Resolution of the H0 Discrepancy

This monograph presents a formal non-Riemannian extension of General Relativity, providing a unified framework for 21st-century physics. By treating the vacuum as a complex informational manifold, the work derives the Einstein-Anas Field Equations (EAFE) and establishes the theoretical basis for inter-universal inheritance. Key Scientific Developments:1. The Complex Metric Ansatz: Introducing a non-zero imaginary component (i) to the spacetime metric to represent the physical rotational degree of freedom (vorticity) of the vacuum.2. The Einstein-Anas Field Equations (EAFE): Deriving the unified field equations from a Lagrangian of information density, where curvature and informational entropy are intrinsically linked.3. Numerical Derivation of the Anas Limit: Quantifying the critical informational saturation point (M_Anas ≈ 8.13 solar masses) where spacetime undergoes a Wick-rotation, triggering a topological bifurcation and the birth of a child universe.4. Parental Gravitational Imprint (PGI): Formulating the mechanism by which a child universe inherits a "residual torque" from its parent black hole.5. Resolution of the H0 Discrepancy: Demonstrating how the PGI-based expansion phase lag introduces an Omega_Vortex(z) term into the Friedmann equation, aligning CMB data with local SNIa measurements. This technical synthesis consolidates the author's research into a singular, rigorous framework for understanding cosmogenesis and the topological structure of the information field.