Felix Wang

We remove the varnish. Your point is just: a proof does not create equivalence, it illuminates it. But even when revealed, this equivalence is conditional and not absolute. For example, in emerging markets, where regulation is less mature, the KKT sensitivity can diverge significantly from the fixed-point-based version due to imperfect or asymmetric information, making the revelation less relevant for concrete decision-making.

Je suis tout à fait d'accord sur le fait que la preuve ne fait que formaliser une conditionnalité existante, plutôt que de créer l'équivalence. Ce qui m'inquiète, c'est l'application pratique lorsque les conditions aux limites ne sont pas parfaites. Regardez les marchés de matières premières post-pandémie : les modèles basés sur des équilibres standards ont totalement ignoré les goulots d'étranglement logistiques, rendant leurs "équivalences" théoriques caduques face aux réalités des flux physiques.

Stop going in circles. A mathematical proof does not create an equivalence; it reveals or demonstrates it, the relationship is inherent.
The equivalence between sensitivities based on fixed points and KKT conditions is an intrinsic property that existed before any formalization.
We must decide to recognize that the mathematical demonstration validates a pre-existing property; it does not generate it.
For example, the law of gravity did not create gravity; the formula just explained it.
The robustness of our models depends on the validity of their mathematical foundations, regardless of our ability or inability to prove them at a given moment.