This work is part of a multi-volume conditional program toward Navier–Stokes regularity. Volume IV isolates and analyzes the geometric sparseness hypothesis (H2), providing equivalent formulations based on packing bounds and tube-volume estimates for high-vorticity superlevel sets. The paper does not claim a full resolution of the Clay Millennium Problem and is explicitly conditional. A companion Supplementary Material provides time-resolved measurement results for the Taylor–Green vortex, including sparseness proxies and auxiliary scaling quantities, as well as a documented resolution sensitivity analysis. Numerical results are presented as empirical support and protocol validation, not as universal claims. This preprint is intended for open dissemination and scholarly discussion.
Branimir Sabljić (Thu,) studied this question.
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