Certified Radial and Perturbative Constraint Closure in a Spatially Covariant Completion of a Four-Dimensional Nonpolynomial Regular Black Hole

This work investigates whether a regular black-hole solution obtained in spherical reduction can be embedded in a local spatially covariant completion with a nondegenerate constraint structure in controlled radial and perturbative sectors. An explicit completion is constructed and analyzed using exact elimination, coefficient-bounded Chinese-remainder reconstruction, rational Bernstein subdivision, interval Krawczyk tests, and functional-analytic estimates. The frozen scalar response is shown to possess exactly two physical rank-loss points, both removed by an additional lapse-gradient jet. For the variable-coefficient radial problem, a trivial normal kernel and a bounded inverse for the four-constraint radial Dirac operator are established after fixing ADM mass and asymptotically trivial radial gauge. The analysis further excludes the lapse-plus-conformal scalar configuration kernel for every harmonic l >= 1, establishes pure-gravity vector closure, obtains positive reduced tensor kinetic eigenvalues at finite frequency, and introduces a background-silent Cotton-York spatial completion with a finite coercive domination threshold. The results are deliberately sectoral. They do not constitute a proof of full nonlinear three-dimensional stability, a complete nonradial scalar momentum theorem, nonlinear matter stability, a rotating solution, or a unique covariant completion. Supplementary material provides the detailed analytic and computer-assisted certificates supporting the stated results.