Definition: Coherent contact space

Let ${\mathcal{D}}_{\le N}=\mathrm{span}\{{\partial }^{\gamma }\delta :|\gamma |\le N\}$. After Theorem thm:M2, and using XVI-L, thm:L5,

(using Theorem thm:M2, hence Theorem thm:wpA-Sbv; raw labelled slots $14321$). Coordinates are $C_{N,b,\gamma }$ with $b\in {\mathcal{B}}_N$ and $|\gamma |\le N$. The regression-preserving subspace ${\mathcal{C}}_{\mathrm{reg}}=\{\Delta {\mathfrak{R}}_{\mathrm{L}}{|}_{{\mathcal{V}}_{\mathrm{K}}}=0\}$ consists of the coordinates with $N\ge 3$; it has dimension $3150$.