A State-Resolved Framework for Coherence-Resonance-Structurization in Turbulent Flow

The paper asks whether a turbulent flow can preserve the capacity to organize even when particular structures disappear. The proposed sequence is that an available carrier develops organized phase relations, those relations become dynamically productive, productive interactions generate viable structures, and viable structures contribute to later organized capacity. Turbulent flows remain active even though individual vortices, streaks, filaments, and bursts continually deform, merge, fragment, and disappear. This manuscript develops a state-resolved framework for testing whether translation-invariant phase organization contributes to productive nonlinear transfer, viable coherent structure, and renewed organizational capacity. The framework separates initial carrier availability, organized phase capacity, realized resonance, viable structurization, renewed coherence, recoverable residue, conditional terminality, and epistemic residue. A normalized partition yields exact carrier accounting, while directed organizational currents, structured nulls, matched-amplitude reruns, positive-lag event tests, genealogy, successor networks, recoverability, and claim gates make the proposed pathway empirically decidable. The first substantive benchmark uses three-dimensional forced homogeneous isotropic turbulence and compares original, sham, phase-altered, and generic matched-cost branches with identical registered modal amplitudes at the intervention origin. The manuscript is a theoretical and computational-validation framework; numerical outcome claims remain pending benchmark execution. Keywords: turbulence; Fourier phase; triadic interaction; coherent structures; structurization; genealogy; regenerative networks; recoverability; structured nulls; matched-amplitude intervention; computational validation. This document distinguishes exact identities, operational definitions, accounting relations, estimators, constitutive and statistical models, hypotheses, and decision rules. Definition is not measurement; measurement is not mechanism; and an executable protocol is not a completed result. Figures and result tables are prospective until populated by registered computation.