Lemma: Lemma 8, actual-source support

Let $T=4$, $\epsilon =\frac{1}{2}$, and $U=(0.9,1.1)\times (-0.1,0.1{)}^3$. Let $S\in {C^{\infty }}_c(\mathbb{R};[0,1])$ with $\mathrm{supp}S=[2,3]$, not claimed inside $(2,3)$, and let the cutoff profile of the science volume produce $g=\sigma =1$ on a neighbourhood of $U$, with $U\subset \mathrm{Int}\{g=1\}\cap \{\epsilon <t<T\}$. For the massless special family with $\varphi =x^1$ and $v_f=\psi$,

globally on the slab, and ${\mathrm{supp}}_t(D_{\mathrm{div}}\alpha )\subset [2,3]$. On the open set where the cutoffs equal one,

Every advanced cone from a point of $U$ meets the source slab only inside that plateau set. The future cones from $U$ therefore see exactly that model source. The collar of the compact root equals one on the cones that are used, and the independent switch of XVI-J and XVI-K does not enter $t_D$. The local formulas on $U$,

follow from the actual compact construction by four-dimensional Huygens support of the advanced kernel, not from a polynomial surrogate. A numeric comparison of the actual source with the model source is corroboration only.