This work introduces the Og-set formalism and the associated concept of negative zero (−0) as a foundational mathematical and ontological structure underlying physical reality. The Og-framework establishes a deterministic numerical topology that governs quantum behavior, cosmological expansion, entropy dynamics, and gravitational interaction. Classical and quantum regimes are shown to emerge from intrinsic asymmetry in Og-interval relations, while metric distortions arise as consequences of Og-state constraints and informational curvature. In addition to formal axioms and mathematical constructions, the theory is grounded in a metaphysical interpretation of reality as a primordial numerical field, where physical laws originate from the structure of Og itself. This work bridges abstract formalism with philosophical reasoning and outlines physical implications, predictive features, and directions for computational and experimental evaluation.