Direct graded non-feedback and quotient response

The supplied R07–R09 descriptions report six even cubic classes, four odd classes before a Schouten quotient, and two afterwards SuppliedBot,CheungXVIR. Counts do not provide representatives or response maps.

Let ${\mathcal{P}}_q$ be local polynomial functionals homogeneous of field/antifield degree $q$, with any permitted relations required to preserve that grading. Let $P_2$ be homogeneous projection and $e:{\mathcal{P}}_2\to {\mathbb{K}}^{21}$ a declared quadratic coefficient map.