The ambient problem is unchanged

ambient problem is unchanged{ The flag $N_U\subset S_{\mathrm{resp}}\subset U$ has codimensions three and five, whose sum is eight.

This bookkeeping does not replace the target by a codimension-three or codimension-four numerical extension. Every reconstructed distribution still lives in the sixteen-dimensional common space with $z$ retained.

No transverse degree or extension threshold is assigned using this flag.}