Unified Evolution Equation: A Master Equation for Open Quantum, Gauge, and Gravitational Systems

At-a-Glance For the first time, a single operator equation simultaneously solves three Millennium-class problems— 1.Four-dimensional Yang–Mills mass gap 2.Three-dimensional Navier–Stokes finite-time blow-up counterexample 3.Cosmological constant (vacuum-energy) cancellation mechanism—while fully preserving gauge, gravitational, and thermodynamic consistency.Key Highlights (10-Second Summary) ・Mass Gap Proof: Analytic demonstration of a strictly positive lower bound in the spectrum of 4D SU(N) Yang–Mills theory.・NS Blow-Up Counterexample: Explicit construction of a finite-time singularity in the γ → 0 limit of 3D Navier–Stokes.・Vacuum-Energy Cancellation: One-line derivation of “ρ_vac + ρ_Φ = 0” from RG fixed-point β=0 conditions, reproducing observations more precisely than ΛCDM.・Unified Framework: A single CPTP master equation merging reversible quantum dynamics (Dirac–Yang–Mills–gravity) with irreversibility (Lindblad + zero-area resonance kernel).What’s UEE? (What’s New) The Unified Evolution Equation (UEE) is a single operator-valued master equation encompassing reversible, dissipative, and scale-dependent effects in one:・Reversible Sector: A rigorously defined Dirac-type operator implementing vierbein gravity, Standard-Model interactions, and a fractal RG operator.・Dissipative Sector: A zero-order Lindblad generator plus a zero-area resonance kernel that preserves essential self-adjointness, CPTP structure, and entropy monotonicity.