Unified Evolution Equation

See also:

[Deriving the Area-Term Cancelling Operator]

• New Preprint URL: https://zenodo.org/records/15701805

• New Preprint DOI: 10.5281/zenodo.15701805

[Information Flux Theory]

• New Preprint URL: https://zenodo.org/records/15399114

• New Preprint DOI: 10.5281/zenodo.15399114

[Driving Principle of Life]

• New Preprint URL: https://zenodo.org/records/15621436

• New Preprint DOI: 10.5281/zenodo.15621436

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.

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https://zenodo.org/records/15316032/files/15316032.pdf

Change Log (ver 1.3): Minor Fix.