Bounded Oscillatory Near-Core Dynamics in a Saturating-Scalar Black-Hole Interior: Numerical Evidence in Spherical Symmetry

This preprint presents the numerical companion to the analytic regular-interior framework paper. It studies an effective regularized black-hole interior in Einstein gravity minimally coupled to a scalar field with a saturating potential, and asks a single narrow question: whether the model admits a numerically resolved bounded oscillatory near-core regime consistent with explicit regularity diagnostics in a constraint-consistent 3+1 spherical evolution. Using polar-areal gauge and origin-safe algebraic diagnostics, the paper finds convergent evidence for a long-lived bounded oscillatory Regime III in coordinate time for a controlled amplitude family. The claim is intentionally limited to one effective closure, spherical symmetry, and the reliable simulation window; it does not establish global geodesic completeness, exterior matching, proper-time asymptotic stability, or perturbative stability beyond spherical symmetry.