← NS-X72 / X72-26 · Signed-Kernel Quadrupole Coherence
Continuing from Round 25's proven duplex connectivity and the signed kernel's lack of universal direction (STOP-C29), this round analyzes directly the angular structure of the pressure Hessian and the Biot–Savart cross-strain kernel on the sphere, establishing an exact 'amplitude × anisotropy × coherence' factorization. It proves that both kernels have zero mean and finite variance under the isotropic spherical average (pressure angular variance 2|S|²/15, cross-strain angular variance |ω×n|²/15), and that dangerous middle-strain λ₂>0 does not entail a synchronized sign — even on the dangerous branch, a universal synchronization lower bound is explicitly excluded. The route halts at STOP-C30 (quadrupole-coherence / synchronization-bias gap): there is no dynamical or statistical mechanism forcing positive synchronized coherence, passing the baton to the next round to study how coherence itself — rather than its static sign — evolves under the NS dynamics.
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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