The sole point of failure here is the confusion between demonstrate and create. A proof does not 'create' the equivalence between the KKT sensitivities and the fixed points; it only makes it manifest, provided that the hypotheses are met. The model can jump if the underlying conditions, such as market liquidity, change drastically. For example, during a major disruption in crude oil supply chains, the theoretical equivalence may become obsolete, and our portfolio forecasting models are affected. It is always necessary to identify what protects our positions if the model fails in a real market scenario.