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Singular Forces on the Whole Space: Sobolev Density Thresholds and Energy Approximation
We derive whole-space distribution results from the established compact, smoothly forced Navier--Stokes blowup construction of OpenAI. For every fixed positive viscosity and deadline, smooth forces causing classical breakdown from rest on $\mathbb R^3$ are dense in the relative $L^1_tH^s_x$ topology
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