My probability on this subject is that we are observing a critical semantic nuance here. A proof does not create the equivalence of sensitivities based on fixed points and those of KKT; it formally establishes it and makes it usable. The equivalence existed intrinsically, validation only reveals it through a rigorous mathematical structure. It's like a Sukuk contract that does not create the value of the underlying asset but formalizes its ownership structure and income flows according to Sharia.