Collision sets and the displayed vertex

The connected subsets are those associated with XIII-C's cycle inventory. They live in the graph variables of that inventory. Nothing in Definition def:collisions identifies every graph variable with one of $a,b,z,y$. In particular, a formula for a collision in a graph with internal vertices is not automatically a formula for its lift or pushforward locus in $W$.

{Defines in the source. XIII-C.tex; eq:vertex; reported lines 416–421.}

The supplied interaction and stress are

Here $\eta =\mathrm{diag}(1,-1,-1,-1)$, consistently with the four supplied sheets. The vertex is a functional, not an Euler operator. Its mixed derivative will be computed algebraically in Patch J; no additional vertex from a non-input is used.