1. Ghost equation

The loop poles obey ${\Gamma }_{\bar{c}ch}=\rho {\Gamma }_{Kch}[K\to T(\bar{c})]$, $T(\bar{c})=\mathrm{sym}(k,\bar{c})-\frac{1}{2}(k\cdot \bar{c})\eta$, with one constant $\rho =-2$ (graph by graph: G04/G03 and G09/G07). Imposing $X_{\bar{c}ch}=-2X_{Kch}[K\to T]$ keeps the system solvable; a particular solution is certified ($Ax=b$ verified). Free directions drop from 152 to 104. The $\eta$-trace is taken at the $d\to 4$ residue level (hat trace 4, tilde trace 0).