Admission

X-E's admission lemma for its single tree is the $n=2$ case of the same argument, with $\Theta$ treated as a composite field; the three-slot case needed for ${\mathsf{T}}_{\mathrm{self}}$ is what X-E named and did not construct. The sum-zero form is sharper than X-E's chain argument and needs no case distinction between diagonal and off-diagonal parts of $\mathrm{WF}({{\mathsf{E}}_0}^{\mathrm{R}})$.