← NS-X72 / X72-43 · Double-Divergence-Free Stress and Wave-Cone Gauge

NS-X72 · X72-43 NO-GO 2026-08

X72-43: Double-Divergence-Free Stress and Wave-Cone Gauge

Picks up Round 42's compression of the nonlocal obstruction into the double-divergence-free trace-free stress W_T (∂_i∂_j(W_T)_{ij}=0, STOP-C46), and tests directly whether this differential constraint alone can supply compensating regularity. Proves that the divdiv operator is constant-rank and cocanceling, but that its wave cone is full, so no quadratic Hardy/null-Lagrangian-type gain exists; constructing an explicit potential representation via a symcurl+devgrad gauge likewise gives no automatic endpoint gain — the generic constrained transfer remains nonzero and consumes a full derivative: divdiv constraint alone is too weak. STOP-C47 (Full-Wave-Cone/Vorticity-Realizability Gap) therefore points to what should really be used — the nonlinear realizability of W=ω⊗ω-1/3|ω|²I together with ∇·ω=0 — leaving the next round to examine actual vorticity triples.

This round's status: NO-GO — 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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