The Anti-Congruent Bridge: From Verticity to Navier–Stokes via Curvature-Controlled Dissipation — A Scope-Disciplined Geometric Certification Framework

This paper completes a trilogy. Paper 1 (Verticity, doi:10.5281/zenodo.18731593) supplies an admissibility architecture for axis-threshold governance claims under shock. Paper 2 (Dragons, doi:10.5281/zenodo.18740729) provides a capsule-grade, provenance-gated empirical instantiation under those rules. Paper 3 (this paper) is the geometric bridge: it isolates the implication that any domain reduction yielding a reversible diffusion with an explicit Bakry–Émery curvature lower bound inherits both a certified dissipation inequality and an exponential relaxation certificate, with explicit falsifiers. The paper supplies: the Anti-Congruent Control Template (ACT) as a reusable compiler kernel; a dual-layer validation protocol (geometric gate + semantic/leakage gate); a domain-route checklist (items A–F); a typed leakage interface for approximate reductions; a bridge failure taxonomy with four operational falsifiers; an import/export law; a Misreadings block; a certificate schema with lockable fields; Route-Blockers as first-class negative outputs; a Fork Manifest for anti-phantom disclosure; refusal conditions; worked certificate instantiations for the Ornstein–Uhlenbeck process, the Falconer pinned-measure route, and the Navier–Stokes skeleton; and a machine-readable COGNITENGINE-compatible appendix. This paper does not certify Navier–Stokes regularity. It certifies the geometric implication layer and provides the scaffolding for downstream manuscripts to invoke it correctly.