Definition: XI-E's polynomial microcausal domain, copied

${\mathcal{F}}_{\mathrm{mc},\mathrm{pol}}$ consists of finite graded polynomials $F(\Phi )={\sum }_n⟨u_n,{\Phi }^{\otimes n}⟩$ on ambient configurations on $M={\mathbb{R}}^4$, with compact, graded symmetric distributional kernels $u_n$ on $M^n$ satisfying

where ${\tilde{V}}_{+},{\tilde{V}}_{-}$ are the closed future and past causal covector cones with zero included, and the total zero covector is never a wavefront point. Field indices are finite and do not change the criterion. Admission is kernel inclusion in ${\mathcal{F}}_{\mathrm{mc},\mathrm{pol}}$ followed by restriction to ${\mathcal{C}}_{\mathrm{sol}}$: $Q_H(F)=[F{|}_{{\mathcal{C}}_{\mathrm{sol}}}]\in {\mathcal{E}}_H$. Slab functionals are viewed on $M$ through their slab restriction; for the inherited symbols the ramp is flat at $t=0$, so no boundary conormal appears.