Counting paths through the graph coloring problem

Why does the quark system reveal all those new forces?

Because it is a three coloring and quark a can influence quark b directly or via quark c.  Multiple paths have to be equilibriated.

It is a prime problem, because if you had four quarks, and one three  step path can encloses a two step path, the math collapses.

This is also why you get a cubic when you do the three generations model, like Paul; and why it is useless to do the four generation problem, and beyond our ability to handle the five (until recently).

How does nature solve it? Adds a gluon, and the gluon can solve is approximately, within a bound error (Planck's).

Bitcoin blockchains has the gluon effect and is able to three and five color to some rough bound error. The error bound maintained by miner congestion fees which keep the exchange queue stable, and that can be proved to color the trade space to a bound error. TOE, don't lave home without it.