Remark: Conditional σ -images

With $\tilde{K}$, 71 of 194 nonzero $F$ images and 8 of 33 $G$ images lie in $N$, and those images satisfy the ghost equation. Twelve $F$ generators fail through the antifield-type piece alone when the $\bar{c}$ partner and the $E$ channel are missing. A $(\lambda ,\mu )$ scan is only a diagnostic: no single normalisation works for every generator. Failures occur with and without trace monomials, so the $\eta$-trace hypothesis is not the sole cause. On the evanescent sector of the $h\cdot h\cdot c$ row, the row operators do not compose to zero with this $\sigma$. A candidate cause is the four-dimensional momentum rule $T(p,\cdot )=0$ for hat components, under which $s_0\hat{h}=0$. That cause is open.