Spherical Casimir Ownership and Scalar-Lift Obstruction: First-Class Lorentz Carriers for a Regular Black-Hole Geometry

We study the ownership of invariant mass and center-sensitive radial data in an explicit regular spherical black-hole geometry. A smooth mass-independent Poisson-sigma parent reproduces the complete positive-mass metric with mass carried by an intrinsic Casimir. The orbit-space dilaton has a nonzero odd center jet and cannot be an ordinary smooth SO(3)-invariant four-dimensional scalar; the same row is instead an intrinsic first-class Poisson-sigma Gauss constraint and admits a Cartan/Lorentz carrier interpretation. Under explicit hypotheses a constrained BFCG reference architecture protects the radial Lorentz-boost carrier. The later oxidation audit shows that the actual algebraic two-form auxiliaries are variationally eliminable and that the exceptional-flux term preserves primary kinetic rank by a smooth momentum translation. Full nonspherical Dirac closure is nevertheless not identifiable from the projected oxidation data alone because inequivalent four-dimensional parent-field completions have different canonical inventories. A complete two-degree-of-freedom theorem therefore requires one explicit covariant parent action. The paper establishes the spherical ownership theorem and completion boundary without claiming a completed four-dimensional theory.