The Vakhitov–Kolokolov Slope on the Coherence Knot

This paper completes the stability analysis of neutrino coherence knots within the General Connectivity framework by providing an explicit numerical evaluation of the Vakhitov–Kolokolov slope, the quantity whose sign determines orbital stability. It first corrects a scaling‑sign error in the companion stability note, showing that a finite coherence knot cannot exist as a free Q‑ball and must be held together by the lattice confinement of the neutrino Aether. With the corrected scaling, the paper establishes the VK slope sign as a structural result using the Grillakis–Shatah–Strauss theorem and then evaluates the slope numerically through a controlled two‑collective‑coordinate model. The slope is found to be positive across the entire existence window, with a derived dimensionless interval s ∈ (6, ∞) and explicit sample values that can be verified by hand. The magnitude is reported as variational, while the sign and interval are the robust, derived content. The paper closes the numerical item left open in the companion stability analysis and identifies the full field‑theoretic spectral count as the next numerical task.