Descent through declared invisible directions

For $\mathfrak{C}=\mathbb{R}r$, this is a real quotient, even though the ambient distributions are complex. If source and target use the same nonzero residue $r$, descent requires $Pr\in \mathbb{R}r$. Failure of this inclusion is failure of descent for that specified quotient; it is not a proof that the original finite part fails to exist.

No multiplication is defined on these quotients.