← NS-X72 / X72-42 · Piola–Vorticity Visible Stress

NS-X72 · X72-42 Proof 2026-08

X72-42: Piola–Vorticity Visible Stress

Picks up Round 41's compression of the nonlocal Piola defect into the scalar 𝔙_ω=1/12|ω|²+1/4ℛ_iℛ_j(ω_iω_j) (STOP-C45), identifies it as the Riesz-visible projection of the trace-free vorticity stress W=ω⊗ω-1/3|ω|²I, and establishes the visible/invisible orthogonal decomposition together with the Vorticity-Stress Visibility Pythagorean identity. Proves that under this projection the transport–Riesz commutator only performs a conservative transfer of visible/invisible energy, without creating total quartic stress energy, so total stress growth can only come from vorticity–strain alignment and diffusion; the genuine remaining nonlocal obstruction is whether the double-divergence-free invisible stress itself carries extra compensating regularity. STOP-C46 (Visible–Invisible Vorticity-Stress Transfer/Double-Divergence Compensation Gap) hands this problem to the next round.

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.

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