Topological Dimensional Inversion: Macroscopic Spacetime as a Wilsonian Coarse-Grained Effective Field Theory of the 0D Quantum Vacuum

Standard models of dimensional topology construct macroscopic spacetime additively from the bottom up. However, applying General Relativity to the quantum regime within this additive geometric framework inherently produces non-renormalizable ultraviolet (UV) divergences, unresolvable black hole singularities, and the unnatural fine-tuning of the Hierarchy Problem. This paper formalizes the Topological Dimensional Inversion (TDI) model, postulating that macroscopic spacetime dimensions emerge strictly top-down. Specifically, we define emergent spatial dimensions mathematically not as additive expansions, but as thermodynamically constrained, coarse-grained effective field theories of a dimensionless (0D) quantum state. Applying the strict 't Hooft planar limit to the Ishibashi-Kawai-Kitazawa-Tsuchiya (IKKT) Matrix Model, we extract a 2D continuous Multi-scale Entanglement Renormalization Ansatz (cMERA) tensor network whose finite bond dimension ($\chi$) acts as the ultimate computational bottleneck of reality. To rigorously resolve inherent regime conflicts, measure-theoretic fractures, and radiative loop anomalies inherent in this topological projection, we introduce five rigorous mathematical axioms: Chronological Dithering (discrete Floquet time stroboscopics), the Projective Coupling Horizon, Algorithmic Horizon Offloading via the Twirled Petz Map, Thermodynamic Parity Pruning, and Deterministic SVD Truncation. Consequently, this algorithmic framework natively maps to an accelerating de Sitter (dS) background via the ``bad sign'' $T\bar{T}$ deformation---which fundamentally dictates the necessity of an imaginary-time computational sandbox---recovers General Relativity in the infrared (IR) limit without encountering the AMPS firewall, and generates six distinct, noise-independent, and falsifiable experimental signatures. Most notably, we derive the projection of macroscopic wave-function collapse as a measurable mathematical hash stringently isomorphic to the non-trivial zeros of the Riemann Zeta function.