Proposition: Lift of Δ I to W : refused

The record contains no dictionary between XIII-C's vertex labels ($y,u,v,\dots$ of the cycle-vertex table) and the coordinates $(a,b,z,y)$ of $W$. Hence no presentation-level map lifting ${\Delta }_I$ to $W$ can be given, and none is given. XIII-C's ${\mathcal{U}}_{\Gamma }$ is the open set on which the Hörmander sum condition holds for the graph product of the time-ordered line XIIICU; XIII-C states that ${\mathcal{U}}_{\Gamma }$ is not identified with the complement of the collision diagonals, and no sheet identifies ${\mathcal{U}}_{\Gamma }$ with $U_{\mathrm{can}}$, which belongs to a different product (the retarded-tree cross-line composition of XIV-I/XIV-J).

Proof. The record; Lemma lem:index fixes the only variable correspondence available in $W$ ($I$ at $a$, $J$ at $z$, cross-lines at $a$, $b$), which does not name $u$ or $v$.