Conjecture on strict separating systems of parameters for explicit varieties

Let $W\subseteq K^m$ be an explicit variety. A strict separating e.s.o.p. is a strict separating homogeneous system of parameters for the coordinate ring $K[W]$; for a weakly explicit positive variety, a strict separating positive weak e.s.o.p. is defined analogously. Strict separating e.s.o.p. conjecture.

(a) The coordinate ring $K[W]$ of any explicit variety has a strict separating e.s.o.p.

(b) The coordinate ring $K[W]$ of a weakly explicit positive variety $W$ has a strict separating positive weak e.s.o.p.

For $W=\Delta[\operatorname{det},m]$, part (a) would imply black-box derandomization of symbolic determinant identity testing; the source gives no resolution.