20 / C3-R: Multi-Core Packing, Pressure-Horizon Congestion, and the Five-Dimensional Strain-Convexity Debt

C3-Q compressed the survivor into three mutually non-interchangeable interfaces — operator escape, ancestry-core geometry, and the far-field pressure matrix — and proved that operator escape and far-field pressure have no simple contradiction. This round instead asks: if the singular debt is not concentrated in a single core but spread across multiple same-scale spatial cores, how do finite energy, rescaled enstrophy, and the pressure horizon jointly constrain the multi-core geometry? The core is the Frontier Multi-Core Energy Packing Theorem (Theorem 6.1): using pointwise amplitude persistence (an annular Bernstein argument), it proves every near-saturated core carries at least $O(R)$ energy; summing over disjoint ball packings then yields the core-count bound $m_R\lesssim R^{-1}$ — a counterintuitive inverse-scaling packing law: not $O(R^{-3})$, because each critical high-frequency packet needs only $O(R)$ of ordinary kinetic energy, so critical objects can proliferate much faster than energy-density intuition suggests. Multi-Core Enstrophy Amplification (Theorem 9.1): the number of cores directly forces the rescaled enstrophy $\mathfrak E_R\gtrsim m_R\beta_\ast^2$. The document introduces the notion of a Certified Pressure Horizon (§13), explicitly distinguishing "certificate" from "actual physical coupling" — this is merely the decoupling radius guaranteed by a worst-case, generic estimate, not a true pressure-correlation length; densely packed core clusters must first be merged into a single pressure-source audit and cannot each independently claim decoupling (CERTIFICATE CONGESTION, not a PHYSICAL COUPLING THEOREM). This round's strongest new geometric result is the Common-Matrix Pressure Support Criterion (Theorem 28.1): a common far-field harmonic matrix supporting all cores positively exists if and only if the convex hull of the local mean-strain values does not contain the origin — since $\dim\operatorname{Sym}_0(3)=5$, Carathéodory's theorem directly yields the Six-Core Pressure Obstruction (Theorem/Corollary 30.1): as few as six cores already suffice to witness that "no single common far-field matrix can positively support all of them." But the document explicitly flags NG-R1: a 5-dimensional space does not mean at most five pressure sources — arbitrarily many far-field regions can still contribute matrices summing to the same $H_\ast$; finite dimension only constrains the composite geometry, linear dependence, and the common supporting half-space, not the number of sources. It also explicitly rules out directly applying Type-I terminal-singularity count bounds to this round's transient frontier cores (a type mismatch).