The Unified Master Equation: A Ward–Balanced Δ–Σ Vacuum with a Unique RG-Stable Fixed Point at α = 1.5.

Abstract We present the Unified Master Equation (UME), a parameter-free framework in which the vacuum ratio α = Δ/Σ is not assumed but derived as the unique Ward-balanced, RG-stable fixed point. A supersymmetric Δ–Σ model shows explicitly that α = 3/2 arises at one loop from standard quantum dynamics. From this single derived constant follow, ab initio, quantum gravity as an infrared geometric limit, the fine-structure constant, fermion mass hierarchies, the cosmological expansion history, the universal light cone, and the thermodynamic arrow of time. At the RG-stable point, Ward-balanced Δ–Σ dynamics enforce Zₜ = Zₓ and derive the invariant light cone v = c, linking Lorentz invariance, SR and the weak-field GR limit without free inputs. The same structure yields a unidirectional information flow (dI/dt > 0), establishing the arrow of time and the block-universe geometry. Appendices P.1–P.2 show that both Special and General Relativity emerge necessarily from α = 1.5. Appendix Q.1 demonstrates that Schrödinger dynamics, the Heisenberg algebra, spin-1/2, the Born rule and objective collapse arise from the first-order reduction of second-order pre-geometric Δ–Σ dynamics. UME predicts a Δ-sector Higgs admixture at 125 GeV and a Δ-boson resonance near 0.9 TeV, testable with existing LHC datasets. String theory appears as an infrared vibrational limit—an effective leaf on the pre-geometric stem defined by α = 1.5.