Axial Gravitational Stability of the Six-Throat Core and Positive Global Wave Continuation on the Periodic Completion

We establish axial gravitational stability of the exact spherical six throat core and positive wave continuation on its periodic global completion. The source free odd parity gravitational operator admits an exact positive factorization for every harmonic index from two upward, excluding exponentially growing axial modes in the spherical core even though the local potential contains six deep negative wells On the complete periodic geometry, an independently defined factorized continuation operator also has a strictly positive spectrum. High frequency radial gravitational characteristics close on the same finite global circuit with return time 15.6 times the fundamental length divided by the speed of light. The perturbative wave sector therefore remains regular and nonterminal throughout the periodic completion without requiring a singular or infinite endpoint.