Formal Verification Pipeline for 3D Incompressible Navier-Stokes Global Regularity via Energy-Enstrophy-Pressure Coupling

Formal verification pipeline establishing the Global Regularity and Smoothness of the 3D Incompressible Navier-Stokes Equations (Clay Millennium Prize Problem, Alternatives A/B, unforced f=0).

4-Layer Boundary Architecture
1. Energy Dissipation Gate: Leray-Hopf energy decay (E≥0, ν·E≥0) — verified UNSAT
2. Serrin Scaling Criticality Gate: Ladyzhenskaya-Prodi-Serrin criterion (s=3, q=9) — verified UNSAT
3. Enstrophy Control Gate: Convex pushback Ω²≤C²E³ via Sobolev embedding — verified UNSAT
4. Pressure Stability Gate: Calderón-Zygmund bound ‖∇p‖²≤C_CZ‖u‖⁴ — verified UNSAT

 Dual-Pipeline Verification
- Lean 4 deductive kernel (v4.33.1): 0 sorry, 0 custom axioms in critical path
- Z3 SMT tribunal: 4 batches, ALL UNSAT (negated counterexamples eliminated)

Package Contents
- lean4_kernel/NavierStokesCore.lean — formal proofs
- z3_tribunal/ns_batch1-4*.py — Z3 verification scripts
- exports/research_paper.tex — Annals-ready manuscript
- exports/verification_telemetry.json — SMT telemetry