Phase–M Theory and the Algebraic Compactification of Reality

Abstract We present a minimal and self-consistent version of the Phase–M framework based on the C6 phase algebra (j⁶ = −1), offering an algebraic reinterpretation of M-theory in which hidden spatial dimensions arise as closed phase channels rather than compactified topological spaces. This reformulation unifies the dynamics of spinor fields, cosmological expansion, and vacuum tension under a single covariant phase–geometric law. Three core sections follow: (i) the Phase–Dirac operator and its coupling to particle fields, (ii) comparative cosmography and a phase–tension interpretation of cosmological observables, and (iii) simplified phase–wave solutions illustrating example universes, black holes, and expansion scenarios.