CFOP-01: Diffuse Horizon Causality, Causal Cutsets, Action–Congestion Duality, and Forest Obstruction

Diffuse Horizon Causality, Causal Cutsets, Action–Congestion Duality, and Forest Obstruction

ANP Cycle IV proved CN_Forest (an actual horizon causal forest exists) relative to ANP's own definitions, but atomic-level necessity (CN3) remains OPEN — the true pre-singular causal object may be a horizon-unbounded DAG/forest, not a single persistent causal lineage. The obstruction problem must therefore be reformulated: no longer just "can every infinite path be blocked?" but "can the entire horizon causal forest traverse every causal cutset without paying an impossible total dynamical cost?" Using a revised terminal duality ledger, this paper proves a normalized causal-cutset capacity theorem: on every physical-time cutset before each dangerous terminal, the forward-propagation contribution plus the absolute-value nonlinear-source contribution is at least one; this extends to a weighted total over dangerous terminals. It defines a dual-witness congestion functional and proves an action–congestion duality inequality: when the total average propagation ratio is deficient by σ at some cutset, the shell-forced L² action times the forest's dual congestion is at least σ². It defines forward-source atomic multiplicity and branch entropy, proving that carrier-ratio collapse forces effective multiplicity and entropy to grow simultaneously. Over pairwise-disjoint fresh-update cutset windows, bounded congestion forces the coercive action to accumulate linearly — yielding a conditional forest-cutset obstruction principle under any finite global action budget.