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

Abstract We present the Unified Master Equation (UME), a symmetry-based framework unifying quantum, gravitational, and cosmological dynamics through a single structural constant α = 1.5. This pre-geometric Δ–Σ vacuum asymmetry between contraction and expansion (the structural origin of dark matter and dark energy) is not an adjustable parameter but an RG-stabilized quantity empirically anchored near 1.5 (1,47-1,53). From it follow, ab initio, the fine-structure constant, mass ratios, g–2 anomalies, neutrino masses, and the cosmological expansion H(z) with q₀ ≈ 0.4, without free inputs. At the RG-stable point, Ward-balanced Δ–Σ dynamics enforce Zₜ = Zₓ, deriving the universal light cone (v* = c) as a structural prediction, linking GR, SR and Lorentz invariance to quantum field balance. The same mechanism yields a unidirectional information flow (dI/dt > 0), explaining the thermodynamic arrow of time. Appendices P.1–P.2 show that both Special and General Relativity emerge as necessary consequences of UME’s single structural constant α = 1.5. The Unified Master Equation (UME) continues to provide a pre-geometric foundation where Ward-balanced vacuum asymmetry governs the emergence of relativistic structure, quantum behavior, and cosmological dynamics. This update strengthens the connection between α = 1.5, the light-cone derivation, and the weak-field geometric limit that aligns with General Relativity. UME further predicts a Δ-sector Higgs admixture at 125 GeV and a Δ-boson resonance near 0.9 TeV, testable with existing LHC data. String theory emerges as the infrared limit of this structure, an effective vibrational leaf on the pre-geometric stem defined by α = 1.5. This work also formalizes the block universe as a derived result of the Ward-balanced Δ–Σ vacuum at α = 1.5. The invariant light cone (v* = c) and global equilibrium remove the need for universal simultaneity, defining spacetime as a static 4D manifold. Temporal experience emerges as a functorial selection by the observer (O) through the vacuum (Q) into the physical domain (S).