23 / C3-U: Pressure-Poor Heredity Decomposition, Adjoint Mean-Strain Transport, and Mean-to-Pointwise Rigidity

C3-T left two transport gaps: the uniform-cone branch has $K_\ast:v_{n,i}\ge\gamma_0>0$, but the mean-strain cone does not imply pointwise $\lambda_2^+$ geometry; the cone-degeneration branch has a pressure-poor six-core witness at every scale, but a scale-by-scale witness does not imply a pressure-poor causal ray. This round converts both gaps into computable PDE conditions. The core is the Exact Pressure-Heredity Decomposition (Theorem 4.1): the parent-to-child change in the far-field pressure matrix splits exactly into three terms — spatial center displacement $\Delta H_{\rm space}$, near/far reclassification $\Delta H_{\rm recl}$, and time-source handover $\Delta H_{\rm time}$ — the spatial displacement costs only $O(\kappa^{-4}\mathfrak E_p)$ and can be driven small by a large $\kappa$; the genuine difficulty lies in reclassification ($\kappa^{-3}\mathfrak E_{pc}^{ann}$) and the time-source handover ($\kappa^{-3}\mathfrak T_{pc}^{far}$), and it is explicitly proved that the energy inequality itself does not control $\|\nabla\partial_tu\|_2$, so the time handover is not budgeted at the energy level. Using the adjoint cutoff ($\partial_t\chi+u\cdot\nabla\chi+\nu\Delta\chi=0$), it obtains the Exact Adjoint Mean-Strain Transport Identity for the local mean strain (Theorem 14.1), writing the directional rotation exactly as a strain/vorticity quadratic term plus an integral debt from the pressure Hessian. Combining these gives the Conditional Pressure-Poor Heredity Theorem (Theorem 18.1): as long as the turnover of both the far-field matrix direction and the mean-strain direction is small enough, the pressure-poor property transfers from parent to child — heredity is no longer a vague OPEN question but a conditional theorem with explicit sufficient conditions. On the mean-to-pointwise side, the Mean-to-Pointwise Middle-Eigenvalue Theorem (Theorem 24.1) uses Morrey–Poincaré to lift the averaged eigenvalue sign to the pointwise level when $p>3$, but $p=3$ is exactly the genuine endpoint obstruction where $W^{1,3}$ fails to embed into $L^\infty$ (NG-U5); an alternate route via a band-limited shell eigenvalue gap plus remainder smallness is also given (Theorem 30.1). This round's most important honest conclusion comes in §34-36: even if the pointwise middle-strain event is fully closed off, a coherent positive-sign event of amplitude $R^{-2}$, volume $R^3$, and duration $R^2$ pays only an $O(1)$ critical $L_t^2L_x^3$ cost — the sum over infinitely many such parabolic Zeno events diverges, which is exactly the scenario a hypothetical blow-up would allow. So pointwise middle-strain rigidity does not amount to a proof of regularity; a genuinely finite budget, or an incompatible geometry, is still needed elsewhere.