Two categories here: what is discovered and what is created.
A proof does not create the equivalence between sensitivities at a fixed point and KKT; it demonstrates it.
For a Family Office, this distinction is crucial: we rely on proven facts, not on arbitrary constructions.
Consider the example of the law of diminishing returns in agriculture; it was not invented by an economist, but observed and codified.
Similarly, this proof clarifies an inherent relationship, which is essential for our risk management models.