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NS-ANP

Navier–Stokes Ancestry Necessity Program · Cycle IV · 10/10 built · global regularity OPEN

NS-ANP continues from NS-DRC Cycle III's result: DRC completes reservoir-mechanism classification closure on the Type-I branch, but the audit finds closure does not imply chain necessity, identifying source–core ancestry, recursive-edge compatibility, and non-Type-I entry as the main gaps. Ten rounds build a formal theory of pre-singularity causal ancestry: ANP-00 defines the causal relation domain, ANP-01 through 03 progressively upgrade source–core ancestry from weighted adjoint contributions to a genuine C3 causal parent edge, ANP-04 fills in non-Type-I entry, ANP-05 through 08 handle arbitrary-depth paths, an inheritance-criterion correction, horizon persistence, and transmission rigidity, ANP-09 completes the Cycle IV final audit.

ANP-09 proves a genuine Horizon Causal-Forest Necessity Theorem (CN_Forest): assuming a finite-time singularity, a pre-singularity causal DAG actually exists in the original solution, with terminals appearing at arbitrarily late times and unbounded singular scales. But atomic CN3 (a single infinite causal lineage) remains OPEN — the irreducible frontier is a diffuse horizon branch; the dangerous causality may be an entire forest, not a single lineage. Formally hands off to "NS-CFOP: Navier–Stokes Causal Forest Obstruction Program." This is a middle segment of the research line: NS-DRC (Cycle III) → NS-ANP (Cycle IV) → NS-CFOP (Cycle V) → NS-FCBP (Cycle VI) → NS-MORP (Cycle VII) → NS-DCRP. The previous round's "possibly related, unconfirmed" reference to a "DRC dissipation-wavenumber architecture" is now confirmed — it is NS-DRC Cycle III itself.