← NS-X72 / X72-41 · Special Cofactor and Piola Vorticity

NS-X72 · X72-41 Proof 2026-08

X72-41: Special Cofactor and Piola Vorticity

Picks up Round 40's compression of the Hardy–BMO dual route into the special cofactor commutator 𝒜_C=[u·∇,𝒯_0*]C (STOP-C44), and, rather than treating C as an arbitrary tensor, uses its centered symmetry, incompressibility, and the cofactor's quadratic algebra to look for extra cancellation invisible to the standard CRW/BMO estimates. Proves that the affine first-order increment cancels exactly (the locally smooth commutator is O(ℓ²)), but that the second-order jet curvature of a general rotational branch can be nonzero, so no universal third-order cancellation exists; further proves that the special cofactor's nonlocal scalar projection decomposes exactly into a local pressure-source part plus a Piola-type (div cof=0) vorticity-stress defect. STOP-C45 (Affine-Jet Cancellation/Piola–Vorticity Endpoint Gap) hands the remaining critical endpoint problem to the next round's Piola–vorticity-stress dynamics.

This round's status: Proof — Taken from the file's own objective/executive-result section, meaning preserved, not a full verbatim translation.

Connections

Relationship to the rest of the series, stated as closely as possible in the document's own words, not my interpretation.

Loading…