The Phase–M Framework: A C6–Based Algebraic Reformulation of M–Theory

Abstract We present a minimal algebraic reformulation of M–theory based on the six-phase algebra C6 defined by j⁶ = −1. In this approach, the extra seven dimensions of M–theory acquire a concrete physical meaning: they are closed phase channels rather than compactified spatial coordinates. The model replaces geometric compactification with phase closure, achieving a unified treatment of energy conservation, dark energy, and supersymmetry through the intrinsic symmetries of a single cyclic field. A variational phase–Einstein action is introduced, yielding the effective cosmological constant Λ_eff directly from internal phase tension. The resulting theory preserves all predictive elements of M–theory while expressing them in a simpler algebraic language that naturally links quantum and cosmological domains.