This paper presents the Extended Zero Theory (EZT 4.5), a comprehensive theoretical framework that resolves gravitational singularities in General Relativity through the introduction of a fundamental structural constant 0_π = 1/π². The theory demonstrates that spacetime possesses an intrinsic geometric rigidity that prevents the collapse of matter into points of infinite density. The central innovation is the replacement of gravitational singularities with stable, finite-density structures called Pi-Cores. Key achievements include: - Complete derivation of a singularity-free spacetime metric - Quantum-gravity connection deriving Planck's constant from gravitational properties - Fractal cosmology solution to the 10⁶² scale hierarchy problem - Resolution of the information paradox through stable core remnants - Testable predictions including gravitational wave echoes The theory makes specific, testable predictions and establishes clear falsification criteria, making it a scientifically rigorous alternative to classical black hole physics.