Information-Geometric Physics System I: Geometry and Spin Structure of the Single Oloid Manifold as the Origin of Leptonic Mass

Research Summary: IGPS I – Emergence of Leptonic Properties This work introduces the Information-Geometric Physics System (IGPS) to explain the origin of fundamental leptonic properties through the geometry of the Oloid manifold. Key Contributions: Geometric Modeling: Modeling fundamental particles as "closed information nodes" on an Oloid manifold under C2 continuity constraints. Mass Derivation: Deriving spectral mass from curvature integrals and normal bundle holonomy along the manifold's seam. Topological Spin: Proving that the SU(2) double-covering of the SO(3) seam moduli space naturally induces spin-1/2 structures. Fundamental Constant Beta: Identifying the universal geometric stiffness parameter β = 1/(sqrt(3)π) as the governing invariant for internal strain. Impact: The framework establishes a direct link between the fermion mass spectrum and the topology of informational manifolds, laying the groundwork for analyzing baryonic mass scaling and strong interactions in the IGPS series.