Title Common and Profile-Dependent Consequences of Planck-Curvature Scale Setting in Exponential and Hayward-Type Regular Black Holes

This work investigates which consequences of regular black hole interiors follow from the curvature scale-setting condition itself and which remain dependent on the selected regularizing mass profile. The transition radius is fixed by imposing the invariant Schwarzschild curvature condition (Kₒ₂₇ (r ₂) = K ₏), where (K ₏= ₏^-4). This gives (r ₂ M^1/3), so the regularization scale is determined before the interior profile is chosen. The paper compares two controlled examples: an exponential regular black hole profile and a Hayward-type profile. Both models use the same exterior Schwarzschild mass, the same curvature threshold parameter, and the same curvature-derived transition radius, but differ in their radial interpolation between the regular center and the Schwarzschild exterior. The analysis separates common consequences of the curvature-derived scale from profile-dependent effects. The common results include the mass scaling of the transition radius, the absence of explicit asymptotic-mass dependence in the normalized curvature profile, the critical-mass scaling (M_^-1/4M ₏), the central curvature (K (0) =2 K ₏), and the Planck-scale large-mass limit of the inner horizon. The profile-dependent results include the critical numerical coefficients, detailed horizon radii, energy-condition transition surfaces, outer-horizon surface-gravity maxima, radial compactness, and the form of the exterior corrections. The supplementary material includes Python scripts, generated numerical data, validation logs, figures, and Lean 4 verification files supporting selected algebraic and formal components of the analysis.