Extended action and master square

The cubic density and Euler source are quoted from XII-C, not re-proved: ${\ell }_3=-2(r_3+b_1{r}_2+b_2{r}_1)$ and ${\mathrm{Euler}}_h({\ell }_3)=J_3$. The operators $A=2G_{\mathrm{lin}}$, $Q_{\nu }$, $N_{0,\nu }$, and the ramp defect are likewise quoted. Gate 4 records an exact-arithmetic sampling of unrestricted retained jets. That sampling is corroboration. It is not a universal-identity certificate.