The admissible set is not the collision complement

Let ${\mathcal{D}}_{\Gamma }$ be the relevant union of collision loci in a graph's vertex space. Define ${\mathcal{U}}_{\Gamma }$ to be the subset of its complement where the full graph product satisfies the distribution product criterion.

Every line is pulled back to the complete graph variables. The criterion excludes a selection of line wavefront covectors, with zero permitted for unused factors, whose sum vanishes at all vertices. It is not merely a test of the two cross-lines against each other.

On ${\mathcal{U}}_{\Gamma }$ the graph product is defined by the inherited product calculus. This does not establish equality

The following calculation identifies the retained failure of that proposed equality. No triangle cutoff is its starting point.