A Smooth Quartic-Core Regular Black Hole: Exact Static Solution with a Validation Program

We present an exact static, spherically symmetric regular black-hole background with lapse A_sc(r) = 1 − R_s r² / (r⁴ + a⁴)^(3/4) and a = γ R_s. The metric is asymptotically Schwarzschild and real analytic in local Cartesian coordinates at the center, where the curvature is finite and the leading geometry is de Sitter-like. We reconstruct a purely magnetic nonlinear-electrodynamics (NED) source and verify the Einstein-matter equations, central regularity, horizon threshold, and circular-null-orbit structure. The source has finite central density and radial pressure p_r = −ρ. Its reconstructed weak-field law is L ∝ F^(7/4), which limits a universal microscopic interpretation but does not invalidate the exact static solution. Its characteristic combination L_F + 2F L_FF is negative for 0 < r < (6/5)^(1/4) a, excluding this minimal reconstruction as a globally hyperbolic matter completion. This dynamical limitation does not invalidate the regular static geometry. We distinguish these established results from a validation program covering rotation, coupled perturbations, causal structure, observational inference, formation, and semiclassical backreaction. The open calculations are specified through governing equations and acceptance criteria, not presented as completed tests. The result is an exact regular background with an explicit effective source and a delimited program for assessing dynamical completions.