← NS_O / 06 / C3-D: The Cutoff-Flux Sign Theorem, the Helical-Kernel Nonlocality Exponent, and the Class-II Logarithmic Reversal

NS · 06 / C3-D C3-D · Lambert W Critical Value 2026-08

06 / C3-D: The Cutoff-Flux Sign Theorem, the Helical-Kernel Nonlocality Exponent, and the Class-II Logarithmic Reversal

C3-C compressed nonlocal Class II down to "costly, but not ruled out." This round asks: what do these large, nearly cancelling high–high exchanges leave behind in the energy flux that genuinely crosses some fixed spectral cutoff $K$? Theorem 4.1 computes the Class II triad cutoff flux $\Phi_{\rm II}(K)$ piece by piece: it is negative (reverse) on $k

Outside the narrow window, the Class II flux is reverse everywhere; there is a Lambert-W critical value χ* ≈ 0.27846 below which the logarithmic-scale integrated flux must be negative under strong nonlocality. Class III/IV are uniformly forward across all intermediate cutoffs, but inherently carry O(χ) geometric suppression. An external scale-locality theorem cannot be borrowed to rule out nonlocal routes — only a research dichotomy is obtained (amplitude compensation vs. breakdown of the scaling assumption). — the bundle's own self-declared stage status, given as-is.

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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NS progress7 / 67
“nonlocal singular route ⟹ either amplitude compensation or scaling-law breakdown. This is a research dichotomy, not a regularity theorem.” — quoted from the paper's Section 23.

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