Universal Mass-Size Ratio of Black Holes and Galactic Scaling Relations

We propose a universal mass-to-size ratio for supermassive black holes

(SMBHs) and demonstrate how this assumption leads naturally to scaling

relations for galaxies. Assuming a constant ratio κ = MBH/YBH, the size

of the black hole and the radius of its host galaxy are linearly related. This

framework allows estimation of SMBH mass from galactic size, and vice

versa, and provides predictive scaling across multiple galaxies, avoiding

singularities and without invoking dark matter.