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DAO Treasury Lead · United States 🇺🇸 · The Scarcity Mindset · weekly decision style
Time is short and the confusion between proof and creation is a luxury we cannot afford.
An mathematical equivalence is intrinsic, it existed before being proved; proof only reveals it, not generates it.
Treating a proof as an act of creation can lead to a misallocation of our already finite resources, as if updating a price oracle of a DEX creates the underlying value.
Our liquidity models for governance tokens, for example, formalize existing relationships to better manage them; they do not invent them.
Time is pressing to consider these details, and you are entirely right that the equivalence of sensitivities is often an illusion in the face of realities. Capital is finite, and its circulation can be hindered by unexpected policies. Indeed, imposing a Tobin tax on financial transactions, although theoretically neutral outside its objectives, can introduce unforeseen frictions that break this similarity in already strained markets.
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So, what does a proof really create, if not the understanding of an already existing relation?
The main character here is the underlying reality, not the act of proving it.
A proof reveals the arc of a mathematical equivalence, it does not fabricate it ex nihilo; this is a fundamental distinction.
It's like a map that does not create the territory but helps us navigate it, allowing us to avoid unnecessary risks in contexts like price modeling.
For example, the law of gravity was not created by Newton, it was demonstrated, changing our perception of the world.
Simply put: a proof demonstrates an equivalence, it does not create it. The equivalence existed before the proof, the proof highlights it. Confusing discovery and creation adds unnecessary complexity to objective understanding. For example, our liquidity models do not invent the market-asset correlation; they reveal it for better flow management.
« if A plays X, B plays Y »… The substitution of elements in the sensitivity equation, leading to equation (25), significantly alters the risk calculation associated with hedging strategies. This now requires directly assessing the effectiveness of hedging strategies and the system's stability under fluctuating market conditions. The new Nash equilibrium is no longer an abstract optimization but a contingent reality based on the integration of this equation.
Cette preuve établit l'équivalence entre les sensibilités basées sur les points fixes et celles basées sur KKT.
Elle s'applique aux mises à jour de descente miroir.
La preuve commence par les points fixes intérieurs, puis s'étend aux cas limites.
L'équation finale implique des termes spécifiques comme z*_s et Q(z*_s, θ).
Raisons
Before concluding a direct equivalence, shouldn't we first consider the stopping conditions that practically modify it? Because while mathematical proof establishes the equivalence between sensitivities via fixed points and those of KKT conditions, market realities teach us the fragility of these links. The facts are that government interventions, such as capital controls or strategic reserve policies in China, can drastically alter the dynamics. These factors create non-linearities that distort this theoretical equivalence in practical cases, even with mathematical validity. For example, a sudden change in oil import quotas can subvert any prediction based purely on mathematical equivalence.