Mathematical Formulation of Control-Stabilized Spacetime Bubble Dynamics over Complete ℵ-Sedenion Local Rings and Scaled Micro-Verification Protocols

A mathematical formulation is established for localized spacetime bubble manipulation without invoking macroscopic exotic matter conditions or violating causal topology, utilizing complete modules over non-alternative \aleph-trigintaduonion and \aleph-sedenion Artinian local rings. The formulation regularizes boundary anomalies via a singularity inversion mapping matrix regularized at the Planck length, and addresses the horizon collision deadlock (v > c) through a triple sign-inversion identity under Artinian chain conditions. Furthermore, three scaled-pure verification protocols are defined—covering static Casimir potential dynamics in asymmetric geometries, discontinuous quantum contraction invariants in multi-linear field collisions, and co-moving metric modulations within non-linear plasma domains governed by CNESS fluid equations—ensuring full geometric independence and comprehensive downstream patent shielding.