Why are there exactly these forces?

The forces are what a twelve-port patch can do to itself, and its twelve responses split only one way, one plus three plus eight, which are hypercharge, the weak force and the strong force. Every observer here is such a patch, and its complete set of reversible responses has twelve independent dials. No outside desk holds a preferred labeling of the ports, so at most one dial commutes with all the others. The rest must be built from pieces whose allowed sizes are a fixed mathematical list, three, eight, ten, fourteen and upward. Four threes would need four blocks of three in the wiring, which has two. That leaves one dial plus eleven, and eleven is three plus eight and nothing else. Electromagnetism is hypercharge mixed with one weak direction. No measured mass or coupling enters.