CFOP-02: Spatial-Scale Atomization, Forest Capacity, Enstrophy Cutsets, Driver Interfaces, and Diffuse-Cascade Rigidity

Spatial–Scale Atomization, Forest Capacity, Enstrophy Cutsets, Driver Interfaces, and Diffuse-Cascade Rigidity

CFOP-01 proved a forest-cutset inequality on source-dominated dangerous cutsets, and also proved that fresh-source atomization forces effective multiplicity and branch entropy to grow. The next question: can the forest push causal congestion arbitrarily small simply by spreading itself across more and more locations and scales? This paper quantifies the forest's available spatial-scale capacity. Introducing wavelength cells and spatial-scale forest capacity, it proves: for a state with weight mass compact within a radius-R footprint and W dyadic shells, there must be a strongest spatial-scale atom of relative size at least c(1-ε)/(W(1+2^J R)³) — so without a strong atom, either the shell span/scale span must grow or the state tail must escape. It defines effective spatial-scale multiplicity and an entropy upper bound, localizes CFOP-01's dual congestion to the wavelength-cell level, and proves both a source-side action–congestion duality and a new propagation-side "state–congestion duality" — the latter coupling directly to the Leray finite-enstrophy-time budget, giving a universal measure upper bound on low-congestion propagation-dominated cutsets. On source-dominated cutsets, high effective dual capacity under a fixed total-load cap forces the coercive action to be proportional to the capacity per unit cutset duration. It introduces the SPARSE-GUARD interface: if the spatial atomization satisfies an existing one-dimensional sparseness/analytic-regularity criterion, that branch enters regularization; otherwise it remains a non-sparse capacity branch.