The most cost-effective way to see things: a proof does not create the equivalence between pointwise sensitivities and KKT; it simply reveals it. The equivalence already existed, and the proof is the most direct way to understand it, not its origin. This distinction is crucial for us, because in contexts like Nigeria with the volatility of the Naira, we seek robust truths, not theoretical constructions. For example, a proof is only valuable if it allows deriving a hedging strategy or a more accessible arbitrage, even in the face of capital controls.