The Geometric Theory of Matter: A Unified Topological Framework for Subatomic Particles as Spacetime Distortions

This preprint proposes the Geometric Theory of Matter (GTM), a unified framework treating elementary particles as stable topological structures (Hopfions) in a spacetime superfluid rather than dimensionless points. The theory addresses the singularity problem in quantum field theory by modeling particles as finite-core vortices with mass, spin, and charge emerging from geometric properties. Wave-particle duality is explained through deterministic hydrodynamic coupling between the particle (knot) and its field wake. Three falsifiable predictions are presented: toroidal electron structure at 10⁻²⁰ m scales, wake re-seeding mechanism for quantum tunneling, and measurable gravitational in-flow near massive bodies. Note: This paper presents the theoretical framework and conceptual structure. Full mathematical derivations are under development and will be presented in subsequent work.