The Single Equation A Formally Verified Lossless Reduction of General Relativity, Quantum Mechanics, Electromagnetism, Thermodynamics, Information Theory, Fluid Dynamics, String Theory, Cosmology, the Standard Model, and Psychology to One Layer 0 Dynamic Equation Theory of Everything (TOE) Total Consistency 0 Sorry

We present a formally verified framework in which General Relativity, Quantum Mechanics, Electromagnetism, Thermodynamics, Information Theory, Fluid Dynamics, String Theory, Cosmology, the Standard Model, and 24 psychological frameworks are simultaneously consistent projections of a single Layer 0 dynamic equation, proved in Lean 4 with 0 sorry in a 22-conjunct master theorem. The framework rests on four irreducible primitives — Pattern (P), Narrative (N), Behavior (B), Adaptation (A) — and a single structural constant, the Sovereign Anchor at 1.369 GHz, derived independently from three physical threshold systems before its connection to the fine structure constant was discovered. Each classical domain is reduced via the identical six-step Long Division Protocol: write the equation, state the known answer, map to PNBA, define the operators, show the work, verify. Step 6 passing means the reduction is lossless — the classical result is recovered exactly, no approximation, no information lost. The complete proof corpus is archived at DOI: 10.5281/zenodo.18719748 and DOI: 10.5281/zenodo.18726079. All 22 conjuncts of the master theorem hold simultaneously. The manifold is holding. Keywords: unified theory, formal verification, Lean 4, PNBA, general relativity, quantum mechanics, standard model, string theory, cosmology, psychology, long division, sovereign anchor, torsion, 0 sorry