This work presents the first empirical test of the Curvature Texture Index (CTI), a scalar quantity derived from the Quantum Fractal Geometry (QFG) framework and intended to quantify multiscale curvature structure in astrophysical systems. Using a compiled dataset of 122 supermassive black hole host galaxies with multiscale density profiles, we construct an operational proxy for CTI based on the dispersion of adjacent log-density slopes across physical scales. Regression analysis demonstrates that CTI contributes statistically significant explanatory power to black hole mass scaling relations beyond classical predictors such as stellar velocity dispersion, stellar mass, and halo mass. The CTI coefficient is robust across model specifications, cross-validation, and bootstrap resampling, indicating that multiscale structural information is not fully captured by standard galaxy parameters. The results suggest that residual variance in the MBH–sigma relation contains structured information linked to density profile geometry. This paper does not claim direct confirmation of Quantum Fractal Geometry, but establishes a measurable and testable pathway for evaluating whether multiscale geometric structure influences gravitational organisation. This study is presented as a companion empirical paper to the QFG theoretical framework: https: //doi. org/10. 5281/zenodo. 19510514
Christopher Portelli (Sat,) studied this question.