The Unified Master Equation: A Dimensionless Constant α = 1.5 as the Foundation for a Theory of Everything

We present the Unified Master Equation (UME), a framework that unifies gravitational, quantum, and cosmological dynamics through a structural imbalance between contracting and expanding contributions, fixed by the dimensionless constant α=1.5\alpha = 1.5α=1.5. This imbalance is formulated in terms of a Δ–Σ vacuum sector, pre-geometric at high densities, which prevents singularities and anchors both dark matter and dark energy as dual manifestations of the same underlying dynamics. The renormalization analysis shows that α\alphaα is RG-protected as an infrared pseudo-fixed point. Within this framework, unitarity in black-hole evaporation is preserved, with information encoded in Δ–Σ degrees of freedom rather than lost at a singularity. The same mechanism removes the initial Big Bang singularity, describing cosmogenesis as a transition from a pre-geometric vacuum to FRW spacetime. At cosmological scales, UME reproduces the background expansion history H(z)H(z)H(z) in close agreement with ΛCDM, while explaining the 60/40 contraction–expansion strength ratio as a structural property. Finally, the theory is falsifiable: it predicts a new Δ-boson mediator, possible deviations in short-range forces, signatures in black-hole spectroscopy and gravitational waves, and cosmological imprints in CMB, BAO, and growth data. Taken together, these results position UME as a comprehensive and testable candidate for a Theory of Everything.