The Scale Duality Model in Twistor Space (SDM): Complete and Extended Framework

Abstract We propose the Scale Duality Model (SDM), a geometric framework based on twistor space and orbifold topology, aimed at unifying the fundamental aspects of spacetime, mass, charge, and quantum behavior without invoking external fields such as the Higgs field. In SDM, physical properties emerge from the resonant configurations of Planck-scale orbifolds embedded in twistor geometry. The model introduces a topological field T(x), whose solitonic excitations (vortexes) define the structure of matter and spacetime. We provide a complete mathematical formalism and discuss key observational implications, including alternatives to dark matter and dark energy.