Minimal Phase–M Framework: A C6-Based Algebraic Reformulation of M-Theory without Dimensional Inflation

Abstract We propose a minimal reformulation of M-theory based on the phase algebra C6, defined by j6=−1j^6 = -1j6=−1, which naturally separates four visible and three hidden phase channels. This structure reproduces the essential geometric and dynamical elements of eleven-dimensional supergravity—including gravitational curvature, flux quantization, and supersymmetric closure—without requiring the 128/128 degree-of-freedom balance or explicit dimensional extension. The topological 3-form Θ=Tr(Φ dΦ∧dΦ)\Theta = \mathrm{Tr}(\Phi\, d\Phi \wedge d\Phi)Θ=Tr(ΦdΦ∧dΦ) plays the role of an effective C∧F∧FC \wedge F \wedge FC∧F∧F term, generating a quantized vacuum energy density Λeff\Lambda_{\mathrm{eff}}Λeff that matches the Freund–Rubin mechanism in a four-dimensional compactified form. A phase-based supersymmetry condition ∑vis∣Φi∣2=∑hid∣Φa∣2\sum_{\mathrm{vis}} |\Phi_i|^2 = \sum_{\mathrm{hid}} |\Phi_a|^2∑vis∣Φi∣2=∑hid∣Φa∣2 replaces traditional component-counting balance, achieving closure through energy–phase equilibrium rather than explicit field duplication. This framework provides a compact, geometrically transparent realization of M-theory’s essential dynamics in a reduced 4+3 phase space, offering a route to gravity–quantum unification without dimensional inflation.