The loops we end up with are of course cubic graphs, as they are 3-connected. Stray strands are not loops and therefore disregarded. When they join at each end, then this extends the loop into a foam. It will always be a cubic foam.
The useful properties of cubic foam is that there are a limited number of shapes possible.
They are also 3-coloring which means there is a clue here for ideas about three color behavior in particle physics.
Being able to generate cubic graphs from the counting number via the TPPT is great stuff. The idea now is how to classify the useful signal set from the new noise, and how to project them as interacting instances into two dimensions.
[PS] I looked into cubic graphs and found the 3-connected restriction to be quite restrictive and artificial. 6-connected implies chaining common c solutions, one assumes in n order, but it starts to look very artificial after a time. For the moment cubic or even 6-connected graphs are somewhat suspect.