Navier–Stokes Synthesis: Dependency Custody and the Anti-Congruent Compiler Architecture

This manuscript functions strictly as a formal compiler specification and dependency-custody layer for the Anti-Congruent program. It aligns the already-published architecture documents—Verticity, Dragons, and the Anti-Congruent Bridge (v7 patched)—into a single, machine-auditable routing framework for PDE singularity claims, with emphasis on the 3D incompressible Navier–Stokes problem. The paper does not claim a new certified Navier–Stokes regularity theorem. Instead, it defines an admissibility pipeline (“Singularity Routing Matrix”) that any downstream Navier–Stokes argument must satisfy to be export-admissible: (i) a placeholder prohibition (no required-field skeletons), (ii) a provenance wall for quantitative or coded motifs (Ledger-E witness discipline), and (iii) a dual-gate bridge contract requiring a declared regime lock plus distinct Geometric and Semantic/Leakage gates. Approximate reductions are admitted only with an explicit, typed leakage interface bounding the exact pairing that appears in the entropy balance. The output is a consolidated verification API and a set of blocking obligations suitable for CI-style rejection of non-admissible singularity narratives.