Comment by gus_massa

You (sorta) can! https://en.wikipedia.org/wiki/Lattice_QCD

The trick is (as the sibling comments explain) that it involves an exponential number of calculations, so it's extremely slow unless you are interested only in very small systems.

Going more technical, the problem with systems with the strong force is that they are too difficult to calculate, so the only method to get results is to add a fake lattice and try solving the system there. It works better than expected and it includes all the forces we know, well except gravity , and it includes the fake grid. So it's only an approximation.

> Could a competent software engineer, even without knowing the fundamental origins of things like particle masses or the fine-structure constant, capture all known fundamental interactions in code?

Nobody know where that numbers come from, so they are just like 20 or 30 numbers in the header of the file. There is some research to try to reduce the number, but I nobody knows if it's possible.