← NS-INRS / DCRP76/X72R59 · 2γ Stretch Resonance and Infinite Conveyor
Continuing from DCRP75's reduction of the independent turnover branch to a dynamic material-replacement/stretching branch, the candidate 'X-free escape route' requires pressure-curvature silence Π_P°=0 and periodic recurrence of the packet-centered kinetic-energy/enstrophy ratio Q_D°. This round works from D75's evolution equation (Q_D°)'=(2γ-σ_D)Q_D°-Π_P°/Z_D to derive that periodicity simultaneously forces two independent time-moment conditions — the material-averaged stretching rate must equal exactly 2γ, and the stretching modulation must be temporally orthogonal to the centered-packet scale — from which it further follows that any finite material-replacement cycle must carry a strictly >1 energy/enstrophy amplification factor e^{γκS₀}, so finite material cycles are excluded. At the same time, inward turnover requires the Euler observer to remain below DCRP61's neutral Floquet threshold, while the resonant material carrier must sit a fixed gap above that same threshold — the two cannot coexist within a finite cycle. The conclusion is that the sole surviving X-free equality route is forced into an infinite 2γ stretch-selection conveyor; if that conveyor stays coherently aligned, DCRP62 immediately forces its axial X72 pressure response to be strictly negative, leaving DCRP77 to test the tilt/pressure cost of crossing the threshold.
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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