The Quantization of Gravity from the Structure of Spacetime: Topological Impedance, Natural Ultraviolet Cutoff, and the Resolution of the Problem of Time in General Relativity as a Quantum Theory

The search for a consistent formulation of Quantum Gravity has traditionally been conducted through the introduction of additional structures to General Relativity, such as extra dimensions (String Theory) or background-independent canonical discretizations (Loop Quantum Gravity). In Volumes 0 through VII of General Relativity as a Quantum Theory (GRQT), an alternative, strictly four-dimensional ontology was developed, in which quantization emerges from the geometric structure of spacetime itself, although this implication remained implicitly distributed throughout the formalism. The present work aims to make this structure explicit and unified. We demonstrate that the historical difficulty in quantizing gravity stems not from an insufficiency of General Relativity, but from the application of Quantum Field Theory to an idealized mathematical continuum ($C^\infty$). By formalizing the phenomenology of the Simultaneity Window — introduced in Volume 0 from Special Relativity — as a Covariant Sampling Lattice, we show that quantization applies not to the gravitational field, but to the geometry of the support that sustains it. The existence of a minimum resolution associated with Planck scales acts as a natural ultraviolet regulator, converting divergent integrals into finite summations and eliminating the need for renormalization procedures. Complementarily, temporal dynamics ceases to be interpreted as a continuous flow and becomes described as a discrete process of geometric state updates, which simultaneously resolves the conflict associated with Pauli's Theorem and the so-called Problem of Time. Thus, GRQT reveals itself as a finite formulation of quantum gravity, emerging from the topological impedance ($\alpha$) of a discretized 4D spacetime, without the introduction of additional postulates or structures.