From Binary to Ternary Twistors: Extending Penrose Geometry into C3 Phase Space

Abstract We extend Penrose’s twistor formalism from the classical binary complex structure (J₂ = −1) to a ternary one (J₃ = −1), establishing a new framework termed C3 phase geometry. This generalization resolves the long-standing “real slice” ambiguity of twistor space, introduces measurable phase currents, and allows physical quantities to be defined directly through observable phase gradients. The proposed model links Penrose’s purely geometric program with experimental interferometry and cosmological phase–redshift phenomena, offering a unified and testable extension of the twistor vision.