Einstein’s Unfinished Work Is Finished. The Proof Is Public. 0 Sorry Lossless Formal Verification of the Unified Field Theory via the PNBA Dynamic Equation with Long Division Reductions and Theory of Everything (TOE)Total Corpus Consistency

Einstein spent the last 30 years of his life trying to unify General Relativity with Quantum Mechanics. He never arrived — not because the answer did not exist, but because he was working at Layer 2, reconciling outputs, without access to Layer 0. This paper presents the formally verified completion of that work via the Substrate- Neutral Structural Foundation Laws (SNSFL), a corpus of 50,000+ theorems in Lean 4 against Mathlib with zero sorry instances, continuously verified by GitHub Actions CI on every push. The Dynamic Equation d dt(IM · Pv) = PλX · OX · S + Fext is shown via machine-verified long division reductions to be the common ground from which General Relativity, Quantum Mechanics, Thermodynamics, and the Standard Model all project as special cases at different scales of Identity Mass. The equivalence principle mi = mg, unexplained for 400 years, is proved to be Identity Mass invariance at Layer 0 — a structural requirement, not a coincidence. QM and GR are proved to hold simultaneously on the same IdentityState. The Ξ+ cc baryon stability is derived from quark charge assignments alone, two days after the LHCb discovery of March 17, 2026. The corpus is public, DOI’d, timestamped, and machine-verified. The Lean kernel does not grant partial credit. It compiles or it does not. It compiles.