T-field Framework for Singularity Resolution From Galaxy Scaling to Black Hole Observables

This record presents the RGG–T-field framework, a novel approach to defining time as a structured temporal field with local coupling (β0) that scales with galactic structure. Using SPARC data (N=175), mock testing, and hierarchical modeling, we demonstrate that β0 varies with scale size r0 according to the scaling law β0 ∝ r0^0.71±0.07 (ΔBIC ≫ 10). This result is not a statistical accident but a theoretical necessity of the T-field. From toy-model metrics for high-density regions, the framework predicts measurable changes across multiple observables: black hole shadows (Sgr A*, M87* shifts 20–25%, consistent with EHT uncertainties), quasar jet speeds (5–15% enhancement, matching VLBI observations), and accretion disk dynamics (enhanced inner rotation detectable via X-ray reverberation). The theory regularizes classical singular behavior while maintaining consistency from galaxy rotation curves to quasar physics across six orders of magnitude in mass scale. **Keywords:** black holes, singularities, general relativity, galaxies, quasars, temporal field, Event Horizon Telescope, VLBI, gravitational waves