Manuscript XIII-C@1 · XIII-C.tex · section · e6556893

Collision inventory

C1: complete incidence inventory for the selected pair › Collision inventory · lines 677–709

The two new edges join $y$ to the selected observable locations. They create a unique combinatorial cycle in the observable tree. The following table lists the cycle vertices; its connected collision subsets are the $Δ_{I}$ used in $C_{part}$ .

Branch	Selected observable locations	Cycle vertices
$B_{1}$	$(u, v)$ or $(v, v)$	${y, u, v}$ or ${y, v}$
$B_{2}$	$(u, u)$	${y, u}$
$B_{3}$	$(u, v)$ or $(v, v)$	${y, u, x, v}$ or ${y, v}$
$B_{4}$	$(u, x)$ or $(v, x)$	${y, u, x}$ or ${y, v, x}$
$B_{5}$	$(u, x)$ or $(v, x)$	${y, u, x}$ or ${y, v, u, x}$
$B_{6}$	$(u, x)$	${y, u, x}$
$B_{7}$	$(u, x)$ or $(v, x)$	${y, u, x}$ or ${y, v, x}$
$B_{8}$	$(v, x)$	${y, v, u, x}$
$B_{9}$	$(v, u)$	${y, v, u}$
$B_{10}$	$(v, v)$ or $(v, x)$	${y, v}$ or ${y, v, u, x}$
$B_{11}$	$(v, v)$ or $(v, u)$	${y, v}$ or ${y, v, u}$

Repeated locations still carry separately labelled field slots. The scalar-sourced parallel collision is one row, not a model for all the mixed-species triangles and four-vertex cycles.