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 symmetry-based framework that unifies gravitational, quantum, and cosmological dynamics through a single structural constant: α = 1.5. This asymmetry between expansion and contraction emerges from a pre-geometric Δ–Σ vacuum and is treated not as a free parameter, but as a measurable, RG-stabilized quantity—anchored empirically in the range 1.47–1.53. From this foundation, we derive structurally a wide set of observables across scales and sectors: the cosmological expansion function H(z), the fine-structure constant α_EM, the electron–proton mass ratio, the proton radius anomaly, the anomalous magnetic moments (g−2) of e⁻ and µ, neutrino masses, and the strong CP suppression—with α=1.5 as the sole structural input, complemented by known physical scales (e.g., M_Pl, m_e) for RG flow. The framework also reproduces the deceleration parameter q₀ ≈ –0.40 and the ΛCDM-compatible expansion history without requiring Ω_m or Ω_Λ as input. A novel contribution is the hierarchical mapping of α = 1.5 into ubiquitous 3/2 scalings in quantum and statistical systems—from partition functions and fermion gases to QCD plasma and gravitational dynamics. This “dimensional echo” is formalized as a causal tree from the Δ–Σ stem to RG-stable branches and observable leaves. UME also makes falsifiable predictions: a Δ-sector mediator admixture at 125 GEV, and a Δ-boson resonance near 0,9 TeV, directly testable with existing LHC data, deviations in short-range gravity, and signatures in gravitational wave spectra. Together, these results position UME as a mathematically explicit and testable unification scheme—with roots in symmetry, branches in known physics, and leaves in observable precision. At the RG-stable point α = 1.5, Ward-balanced Δ–Σ dynamics enforce Zt = Zx, deriving the universal light cone (v* = c) as a structural prediction rather than a postulate. This provides a fundamental conceptual bridge between pre-geometric vacuum structure and Lorentz invariance. This work establishes a structural connection between the universal light cone and the thermodynamic arrow of time. Within the Unified Master Equation (UME), Ward balance at the RG-stable fixed point α = 1.5 enforces the relation Z_t = Z_x, yielding v* = c as a structural consequence. The same Δ–Σ vacuum asymmetry produces an irreversible information flow (dI/dt > 0), providing a fundamental origin of time orientation without assuming a low-entropy initial state. This result unifies causal structure and temporal direction under a single principle.