I cannot judge whether any of the theory is "substantial proof." I can say there is no theory that is generally accepted by most theoreticians in the field. No one outside the field knows anything about the theories.
Cold fusion is an experimental finding. There is copious experimental proof that it is a nuclear effect, especially the heat produced per gram of material, and the tritium. It is yet to be explained theoretically, to the satisfaction of most people. Generally speaking, in science a theory is not "proof" of anything. Theories explain that which experiments prove.
