by hands ("ad hoc") and what else should come from it if not what you put in?

The united field theory (TOE), many scientists work on now will DERIVE everything - the values of fundamental constants like c,h,G, charge quanta (electron charge), 3-dimensionality of space in Universe, masses of all elementary particles, strength of nuclear and other interactions, etc and possibly even symmetries themselves as a mathematical properties of something more fundamental (sypersymmetry? superspacetime? false vacuum?...).