Planck-Curvature Thresholds and the Limits of Geometric Description in Regular Black Hole Interiors

This work investigates a known exponential regular black hole metric under a new scale-setting prescription derived directly from the exterior Schwarzschild geometry. The metric itself is not proposed as a new solution. The central contribution is the determination of the transition radius from the invariant condition that the Schwarzschild Kretschmann scalar at the transition radius equals eta times the Planck-curvature scale. With the convention KP = lP^ (-4), this gives rc³ = sqrt (12/eta) rₛ lP², and therefore rc scales as M^ (1/3). Applied to the exponential mass profile m (r) = M1 - exp (-r³/rc³), this relation produces a mass-independent normalized curvature profile. A computer-assisted verification, combining an exact rational Taylor bound, outward-rounded interval arithmetic, and an analytic asymptotic estimate, proves that the dimensionless Kretschmann profile decreases strictly away from the center. Consequently, the complete geometry satisfies the global bound K (r) = 0, with equality only at the regular center. The paper also derives the exact classification of supercritical two-horizon, critical degenerate-horizon, and subcritical horizonless configurations. The effective stress-energy tensor satisfies the null and weak energy conditions, while the strong energy condition is violated only in the central de Sitter-like region. The dominant energy-condition violation is quantified and shown to be bounded and asymptotically vanishing. The inner-horizon surface gravity is proved to increase monotonically with mass on the complete supercritical branch, to vanish at extremality, and to approach a finite Planck-scale upper limit for large masses. The large-mass inner-horizon radius is shown to remain of Planck order not only for the exponential profile, but for the broader class of regular profiles satisfying P (x) = a x + O (x²), with a > 0. The construction remains phenomenological. It does not derive the exponential profile from a fundamental action, solve the dynamical collapse problem, or establish the stability of the inner or degenerate horizons. Its principal result is that invariant information contained in the classical exterior geometry is sufficient to determine a mass-dependent transition scale and a universal global curvature bound in the corresponding regular effective interior.