← NS_O / 27 / C3-Y: Derivative-Chain / Intermittency Tradeoff, Direct-vs-Chain Gap Closure, and Joint-Concentration Routing
The final round of the C3 series opens with a Source Audit Correction (§0): re-anchoring the external theorem to its formal journal version — Grujić & Xu, Asymptotic Criticality of the Navier–Stokes Regularity Problem, Journal of Mathematical Fluid Mechanics 26, Article 53 (2024-07-27) — explicitly listing the theorem numbers cited (3.5 the direct criterion, 3.7 the energy a priori, 3.8/3.9 the ascending/descending chain, 3.14 chain-assisted). It re-derives three scales: the energy-a-priori scale $R_{\rm apr}^{(k)}\sim A_k^{-1/(k+3/2)}$, the direct finite-$k$ regularity scale $R_{\rm dir}^{(k)}\sim A_k^{-3/2/(k+3/2)}$, and the chain-assisted scale $R_{\rm chain}^{(k)}\sim A_k^{-1/(k+1)}$, with $R_{\rm dir}
Relationship to the rest of the series, stated as closely as possible in the document's own words, not my interpretation.
“ancestry-local φ ⇏ uniform-local Φ — the missing link is globalization and time-gate recurrence, not just 'is it intermittent enough'.” — quoted from the paper's own Sections 19 and 47.
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