24 / C3-V: Turnover Packing, the Pressure-Heredity Failure Trichotomy, and Strain-Fluctuation Escape

C3-U split pressure-poor heredity into three terms — spatial displacement, reclassification, and time handover — and gave an exact adjoint transport identity for the local mean strain. This round asks the real question: can these turnover/fluctuation debts stay large across infinitely many viscous ancestry generations? The core is the Endpoint Pressure-Turnover Bound (Theorem 3.1): the time-source handover in fact admits an endpoint enstrophy bound that does not require $\partial_tf$ to be integrable, which yields the Bounded-Enstrophy Far-Pressure Direction Stability (Theorem 10.1) — as long as the parent/child rescaled enstrophy is bounded and the far-field matrix is nondegenerate, the far-field pressure direction itself can be transported stably for a sufficiently large $\kappa$, no longer a vague OPEN question. So if pressure-poor heredity genuinely fails on this branch, the blame must shift to the rotation of the local mean-strain direction (Theorem 14.1: Pressure-Efficiency Recovery Requires Mean-Rotation Toll). Mean rotation further splits into two carriers — quadratic strain/vorticity-term rotation and local pressure-Hessian rotation (the dichotomy of Theorem 16). The quadratic-term rotation obeys Weighted Quadratic-Turnover Packing (Theorem 18.1): $\sum_nR_n\mathfrak R_n^Q\le C\|u_0\|_2^2/\nu^2$ — but this is $R$-weighted, not unweighted-finite; under geometric-series scaling $R_n=2^{-n}R_0$ one has $\sum R_n<\infty$, so every generation can still spend an $O(1)$ normalized rotation without violating the kinetic-energy dissipation budget at all. This gives this round's most important result, the Turnover Zeno No-Go (§20): finite kinetic-energy dissipation does not imply finite total mean-direction variation — energy alone cannot force directional convergence, and energy-only Pressure-Poor Heredity is formally ruled a NO-GO (§43). On the other side, mean-to-pointwise failure is compressed, via the Fluctuation–Intermittency Identity (Theorem 31.1), into a single exact algebraic equality, yielding the Strain-Fluctuation Escape Dichotomy (Theorem 32.1): a large Morrey obstruction must be carried by either a higher-derivative stock $\mathfrak H_R$ or a shrinking, intermittent active volume $\phi_{p,R}\to0$ — not by unstructured "large fluctuation." The only branch in this round to genuinely exhibit a rate obstruction is the Persistent Cone-Degeneration Packing Theorem (Theorem 24.1): if common far-field pressure support must persist over a fixed fraction of the viscous window, then $\sum_nR_n\kappa_n^2\gamma_n^{-2/3}<\infty$ — the first result on the turnover route to connect a geometric decay rate directly to the global energy budget, requiring the cone-margin decay exponent $\alpha<3/2$.