Input statement: XII-A and XI-B: carrier, free rule, uniqueness

${\mathcal{E}}_H=({\mathcal{F}}_{\mathrm{mc},\mathrm{pol}}[[\hslash ,\kappa ]],{\star }_H)/{\mathcal{N}}_{\mathrm{sol}}[[\hslash ,\kappa ]]$, with ${\mathcal{C}}_{\mathrm{sol}}=\{\square \gamma =0,P_m\varphi =0,\square c=\square \bar{c}=0,b=D\gamma \}$; ghosts in ${\mathcal{C}}_{\mathrm{sol}}$ are smooth ambient free solutions with arbitrary Cauchy data. The frozen free differential is $s_0\gamma =\mathcal{R}c$, $s_0\bar{c}=ib$, $s_0\varphi =s_{0}c=s_{0}b=0$, a nilpotent derivation of ${\star }_H$ descending to ${\mathcal{E}}_H$. A smooth solution of $\square u=0$ on the slab with zero Cauchy data on some $\{t=t_0\}$, $0\le t_0<T$, vanishes on $[t_0,T]\times {\mathbb{R}}^3$; the compact plateau residual intersection is $\{0\}$ XIIA,XIB,BGP.