Topological Dimensional Inversion: Spacetime as a Nested Constraint of the 0D Quantum Vacuum

Standard models of dimensional topology construct spacetime additively from the bottom up (e.g., 0D points integrating into 3D volumes). However, when applying General Relativity to the quantum regime, this additive geometric framework inherently produces non-renormalizable infinite divergences and unresolvable singularities. To resolve these paradoxes, this paper proposes a Topological Dimensional Inversion model, postulating that spacetime dimensions emerge top-down. Specifically, we define any emergent dimension D(n) not as an additive spatial expansion, but as a mathematically constrained phase-space subset of the preceding dimension D(n-1) {D(n) subset of D(n-1)}.

Applying the large-N limit of the IKKT Matrix Model, we formalize the 0D quantum vacuum as the absolute, unconstrained macro-state of infinite algebraic probability. We demonstrate that spontaneous symmetry breaking of this 0D state generates a 1D Goldstone mode (frequency/tension), which algorithmically restricts into a 2D Holographic Tensor Network (MERA). Finally, utilizing the Ryu-Takayanagi formula and the Bekenstein Bound, we prove that 3D volume, mass, and gravity are emergent, localized entropic constraints strictly bounded by the 2D Conformal Field Theory (CFT) phase space. By framing macroscopic inertia and spatial depth as severe restrictions of degrees of freedom rather than fundamental expansions, this top-down topological formalism eliminates infinite density singularities and offers a novel, bounded pathway toward quantum gravity.