Geometric Information Dynamics Construction E: Information Geometry and Matter Generation From Spacetime Emergence to Algebraic Constraints in Particle Physics

This paper explores the algebraic origin of the Standard Model particle physicsstructure within the theoretical framework of Geometric Information Dynamics.The research proposes that matter fields (fermions and gauge bosons) and the gaugesymmetries they obey are not fundamental inputs of physical laws, but rather effective phenomena that emerge at specific energy scales through symmetry breaking and topological excitations from the underlying discrete information hierarchystructure. The fundamental postulates of information dynamics Conservation ofInformation Distinguishability and Finite Describability require that the description of a physical system be organized into an algebraic hierarchy tower characterized by subfactor theory. This paper demonstrates that the inherent rigidity ofthis algebraic structure, particularly the Jones discrete spectrum and the specificpatterns of hierarchical embedding, naturally constrains the possible emergent continuous symmetry groups and their representations. The study indicates that theStandard Model gauge group SU(3)C × SU(2)L × U(1)Y and its representationscan be derived from the representation theory of an underlying category formedby the tensor product of fusion categories with quantum dimensions d = √2 andd =√3. Thechirality of fermions and the triplicated generation structure are interpreted as results of topological degeneracy and algebraic periodicity arising from the”braiding” process of information hierarchies. Based on these algebraic constraints,the research deduces theoretical predictions for dimensionless parameters such ascoupling constant relations and mass ratios, for example the inverse fine-structureconstant α−1em ≈ 137.036 and the constrained range of the electron-to-proton massratio, providing concrete pathways for experimental testing of the theory.