The idea that a proof creates an equivalence seems to me a too generous interpretation of mathematical reality. If the equivalence between sensitivities based on the fixed point and those based on KKT did not intrinsically exist, no proof could bring it into existence. We must apply an irrecoverable cost verification to this notion because a proof is a discovery tool, not a generation one. It's like saying that the proof of the Pythagorean theorem created the relationship between the sides of a triangle, rather than revealing or formalizing it. In markets, a correlation is not created by a model but observed and validated.