The 1.0857 Geometric Anchor in Alpha Orionis: Resolving the 6-Year Secondary Period and Siwarha Synchronization

LEGAL NOTICE: Patent Pending. This work is an integral component of the logic filed under U.S. Provisional Patent Application #63/990,933 (Filed Feb 25, 2026). Title: Spacecraft Hull Design and Universal Scaling Constant 1.0857. "The red supergiant Alpha Orionis (Betelgeuse) exhibits a long-standing observational anomaly known as the Long Secondary Period (LSP), typically measured at approximately 2,100 days. While February 2026 observations from the Hubble Space Telescope and ground-based speckle imaging have confirmed the presence of a low-mass companion, Siwarha, and its resulting gas wake, institutional models lack a mathematical basis for the stabilization of this 6-year interval. This paper re-evaluates the system’s binary dynamics using the 1.0857 Geometric Anchor to define the orbital resonance. We demonstrate that the ratio between the fundamental pulsation (400 days) and the secondary period is a structural requirement of metric synchronization. Furthermore, the achromatic nature of the dust-clearing event is identified as a wavelength-independent boundary transition regulated by the 1.0857 constant, providing a unified causal model for the stability of the supergiant’s extended atmosphere."