← NS Zone · NS-CFOP

NS-CFOP

Navier–Stokes Causal Forest Obstruction Program · Cycle V · 3/3 built · global regularity OPEN

NS-CFOP continues from NS-ANP Cycle IV: relative to ANP's own definitions, ANP proved CN_Forest (an actual horizon causal forest exists), but atomic-level necessity (CN3) remains OPEN — the true pre-singular causal object may be a horizon-unbounded DAG/forest, not a single persistent lineage. CFOP therefore recasts the problem from "can every infinite path be blocked?" to "can the entire causal forest traverse every causal cutset without paying an impossible total dynamical cost?" Three rounds carry this forward: CFOP-01 proves a normalized causal-cutset capacity theorem and an action–congestion duality; CFOP-02 quantifies the forest's available spatial-scale capacity; CFOP-03 completes the Cycle V final audit.

CFOP-03's audit concludes that standard finite Navier–Stokes budgets cannot close the forest obstruction — the Leray enstrophy-time budget and the energy-class negative-Sobolev forcing budget are each summable per parabolic scale (O(R) and O(R^(4/3)) respectively), and neither alone can exclude an infinite geometric cascade. It formally defines the "Forest Coercive Budget Problem" and hands off to "NS-FCBP: Navier–Stokes Forest Coercive Budget Program." CFOP is the middle segment of this relay: NS-ANP (Cycle IV) → NS-CFOP (Cycle V) → NS-FCBP (Cycle VI) → NS-MORP (Cycle VII) → NS-DCRP.