The Renormalization of Gravity via 8-Spinor Gauge Symmetry: A Topologically Protected Unification

We present a rigorous resolution to the century-long discordance between General Relativity and Quantum Field Theory through formalization of the Partanen-Tulkki Unified Gravity Framework. The framework abandons metric-fundamentalism in favor of a Space-Time Dimension Field (I_g) generated by four independent U(1) gauge symmetries. We demonstrate that gravity emerges as a gauge interaction within an 8-dimensional spinor manifold, and establish that this formulation yields a dimensionless gravitational coupling constant—a necessary condition for perturbative renormalizability that resolves the intractable Goroff-Sagnotti divergence. We establish a novel isomorphism between the I_g field and Penrose's Infinity Twistor, confirming that global quantum structure projects onto local classical geometry via a principal fiber bundle, providing topological protection for the renormalization group flow. The framework unifies gravity with the mass-polariton theory of light, bridging Einstein's geometry with Feynman's fields through a single coherent mathematical structure.