 Even putting aside the contradictory assumptions used in different derivations, one should, in any event, note that one cannot try to justify the multifariousness of proofs by using an argument based on something like consilience, for it will not be consilience in anything like the standard form. (See the entry on  Scientific Discovery.)  This is not a case in which the same equations or relations or model, or values of quantities, are being derived for a given phenomenon based on studies of different types of interactions among different types of physical systems, as in the classic case of Perrin's calculation of Avogadro's number. This is rather a case in which different physical assumptions are made about the very same class of physical systems and interactions among them, and calculations and arguments made in very different physical and mathematical frameworks, with no clear relation among them. 