Remark

The excluded set $\{a=b=z\}$ has codimension eight in $W$, as does $N={\tilde{\mathcal{N}}}_{\mathrm{att}}$ Grelease; no identification of the two is inferred. The theorem is a statement about the displayed internal expressions for arbitrary completions; it is not a statement about ${\mathcal{C}}_{\mathrm{cross}}{K}_{\mathrm{supp}}$ or about any product.