An explicit obstruction to unchanged free-shell descent

Let ${\mathcal{I}}_{\mathrm{eq}}\subset {\mathcal{F}}_{\mathrm{ml}}$ be the graded ideal generated by compact smearings of (eq:freeeq). Let ${\mathcal{I}}_{\mathrm{sol}}$ be the ideal of functionals vanishing on all smooth free solutions, interpreted with finite Grassmann coefficient algebras. Then

No equality between these ideals is needed.