Part 27: Falsifiability and Cross-Consistency of Dual–H₄ Geometry: Constraints from Cosmic Rays, Gamma Emission, Bulk Gravitational Modes, and Direct Detection

Origin Geometry (OG) proposes that effective spacetime may admit a dual-sector architecture consisting of a visible sector H₄ and an orthogonal sector φH₄ separated by an effective topological barrier. Within this framework, excitations pinned in φH₄ may manifest as effective dark matter, while phase-opposed excitations may generate antimatter-like components whose coupling to the visible sector is strongly suppressed. Previous works investigated electromagnetic suppression within the dark sector, WKB tunneling near regions of extreme curvature, positron leakage, and bulk gravitational-wave-like excitations. The present work introduces no additional physical mechanisms. Instead, it focuses on establishing falsifiability criteria and cross-consistency conditions for the entire Dual–H₄ framework. Constraints arising from cosmic-ray spectra, 511 keV gamma-ray emission, bulk excitations, black-hole distributions, and direct-detection experiments are incorporated into a unified dynamical structure. The objective is to transform OG from a conceptual geometric description into a framework that can be tested, constrained, and potentially falsified through observational data.