The Finite Singularity: Resolving Black Hole Infinities with the Kimemia Depth Coordinate(Finite Singularities, Universal Ratios, and the Geometry of Spacetime)

We extend the Kimemia coordinate system developed in Paper 1 to black holes. For a Schwarzschild black hole, we derive the exterior depth function y(r) = r_s^2 divided by r (for r greater than or equal to r_s). Using the proper distance from the horizon, we define the Kimemia Potential and obtain the interior depth function. From this we prove that the singularity has finite depth y(0) = r_s times (1 + pi/2), approximately 2.5708 times the Schwarzschild radius. The Kimemia Photon Depth Ratio (photon sphere depth divided by horizon depth) equals 2/3, a universal constant. For rotating black holes we introduce the Kimemia Kerr Depth Function, and for charged black holes the Kimemia Reissner-Nordström Depth Function, which reveals infinite depth at the Cauchy horizon. All results are derived from first principles, with every quantity defined and every step shown.