The 48 labelled matchings

For $j=1,\dots ,9$, label the two observable metric slots $i=1,2$ and the two interaction scalar slots $a=1,2$. The matchings

join the interaction metric to the selected observable metric and scalar slot $a$ to the single observable scalar. There are four for each branch.

For $j=10,11$, label the three observable scalar slots $i=1,2,3$. Select an unordered pair $i<k$ and one of its two bijections to the two interaction scalar slots:

There are six for each branch. Thus

Coincident slot locations do not erase the slot labels. Two metric cross-lines are absent because the interaction has only one metric slot; metric–scalar lines vanish for the frozen product data.