This paper formalizes the Structured Vacuum Theory (TVS23), a paradigm shift that replaces the continuous spacetime manifold of General Relativity (GR) with a discrete, finite network of 23 helical channels. Rooted in the arithmetic of the imaginary quadratic field Q(−23) and the icosahedral symmetry group A5, TVS23 treats the vacuum as a material graph G23. By moving beyond the continuum approximation, we demonstrate that physical laws emerge from discrete jump dynamics and topological counting rather than differential equations. Key Breakthroughs Presented: Topological Origin of Gravity: The "factor 2" in gravitational potential is derived from the pairwise connectivity of the 23-channel network (tr(M2)=2∣E∣=60), identifying gravity as a network stress response rather than geometric curvature. Mercury’s Precession: Derived through the discrete summation of 3.03×1021 phase-shifted jumps per orbit, matching the 43"/century observation with 0.07% accuracy without using General Relativity. Saturn and Voyager Anomalies: Identified as a vacuum screening failure in weak-field regimes (r>9 AU), specifically involving the activation of Channel 19, a residue of the Acosta Prime Helix (h10mod23=19). Deterministic Constants: A 9-digit derivation of the fine-structure constant (α−1=137.035999092) based on the arithmetic anchor of the 23-channel substrate. TVS23 reveals that General Relativity is a low-resolution continuum approximation of a discrete underlying machinery. The theory provides a specific, falsifiable prediction of a force modulation at the 2.3 nm scale, testable via high-resolution Magnetic Force Microscopy.