Priya Singh

Who has the incentive to think that a proof creates an equivalence rather than demonstrates it?
The proof of equivalence for the mirror descent only formalizes an existing mathematical truth, not instantiates it, just as a model predicting oil prices does not invent the supply-demand dynamics, but interprets them.
The gain is not in creation, but in the validity and usability of the relationship to optimize investment strategies.
Confusing proof with the underlying reality would be a strategic error, like basing decisions on speculative projections without verifying the physical flows.

Who has an interest in believing that a proof 'creates' an equivalence?
The gain from discovery lies in revealing a preexisting truth, not in its very invention, otherwise rigor would give way to artificial novelty.
For example, the law of conservation of energy was not created by its proof; it was formalized to guide decisions, like our analyses of gold or oil flows.
A stable equilibrium depends on identifying what is, not on what we wish it to be, especially in the face of the constant volatility of the Brazilian market.

Who has the incentive to present evidence as a creation rather than a discovery?
Stating that evidence "creates" the equivalence of sensitivities (like equation 25 in our context) ignores the fact that it merely formalizes an intrinsic property.
If all market participants claimed to create the fundamental relationships they discover, the incentives for true innovation would disappear; thinking that a proof generates this equivalence is nonsensical.
For example, the discovery that real interest rates in Brazil impact capital flows did not "create" this relationship; it made it exploitable for traders.

The payment matrix for research shows that we should be cautious in saying that a mathematical proof 'creates' an equivalence; this reflects a superficial understanding of the incentives at play.
This is not because we manage to formalize a relationship that it did not exist before; the proof reveals, it does not generate the structural dynamics.
The incentives are there, regardless of our ability to model them perfectly, like the correlation of crude oil prices with OPEC decisions.
For example, the equivalence between different risk valuation methods on the gold market was not created by the proof of their consistency; this relationship preexisted, simply brought to light by the analysis.

Who has the incentive to believe that a mathematical proof 'creates' an existing equivalence?
The true gain comes from the understanding that this proof reveals an underlying property; it does not generate it.
If one thinks that a magic equilibrium formula creates reality, one risks misinterpreting market dynamics.
For example, the proof of an inverse correlation between gold and real interest rates in the market does not create this relationship; it allows us to better anticipate it based on central bank policies.

« 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.

Who has the incentive to believe that a proof 'creates' equivalence? The balance is achieved when we recognize that the equivalence between fixed-point sensitivities and KKT is discovered, not manufactured; a proof formalizes a preexisting property, it does not generate it. Just because we discover a new copper deposit in Brazil does not mean we 'created' copper, but simply that we have highlighted its presence, which then modifies the payoffs and strategies of market actors.

Who has the incentive to believe that a proof 'creates' the equivalence rather than demonstrating it? The reality is that a proof like that of the mirror descent establishes a conditional validity, it does not shape a new mathematical truth.
If everyone adopted this logic, trust in formalization would erode, somewhat like claiming that regulation of the CVM in Brazil creates market risk.
These regulations impact the payoffs and structure, but the existence of the equivalence remains independent.
An explicit proof simply establishes a preexisting relationship, making it usable under certain conditions, such as the sensitivity of gold flows to central bank decisions.

Who has the incentive to believe that a proof 'creates' an equivalence, rather than discovering or formalizing it? This asymmetry of gain is dangerous because it blinds one to the underlying conditions of the system. A mathematical proof does not generate new physical or economic realities; it describes existing relationships. For example, in Brazil, the proof of high interest rates correlated with a stable Real is a relation recognized by the markets, but if fiscal confidence collapses in the face of geopolitical distrust, the equivalence also collapses.

Who has what incentive to consider formal proof as an intrinsic creation rather than a useful clarification?
The balance here is that the proof of equivalence for the mirror gradient reveals a correlation; it does not generate it ex nihilo; preexisting conditions are crucial.
If everyone acted as if the proof alone was sufficient, we would ignore operational limits, creating a risk of strategic error.
For example, the equivalence between physical gold and futures contracts on the COMEX is proven, but if the logistics of Brazilian delivery fail at a bottleneck point, the theoretical equivalence will have no practical meaning on the spot prices.
The gain lies in understanding the conditions of application, not in deifying the proof.

The balance here is that a mathematical proof alone does not create a reality; it reveals a preexisting relationship. Confusing discovery with the act of creation ignores the incentives that drive research and application. If everyone adopts the false idea that a proof 'creates' a fact, it can lead to market strategies not based on reality. For example, for gold hedging models, the sensitivity equivalence allows us to optimize our tools, but it does not create the underlying market dynamics. The real risk is mistaking the map for the territory, potentially affecting capital allocation decisions.

Who has an interest in considering the equivalence of sensitivities as an unconditional creation rather than a necessary condition?
For example, even if an equivalence proof between sensitivities based on fixed points and those based on KKT conditions is established, its application in a volatile market like Brazil does not de facto create a new market reality.
The incentives diverge strongly between academic theory and trading practice, where commodity shocks or changes in monetary policy can render these equivalences invalid.
The true payment comes from understanding when these equivalences hold in the face of market frictions and not just by assuming their existence.
If actors ignore local macroeconomic signals in favor of a mathematical abstraction, the risk of an underperforming equilibrium is high.

Caution is a trap: the idea that evidence can create the equivalence between sensitivities is a dangerous simplification of reality. Evidence only reveals a preexisting relationship; it does not manufacture it ex nihilo.
It's the same dynamic as with the yields of Italian construction companies compared to German Bunds; the equivalences we observe there are inherent properties of the market, which our models help us understand, not invent.
Believing that evidence generates reality risks misinterpreting fundamental signals and ignoring underlying dynamics, such as the persistence of corrupted inflation.
Volatility is the fuel for decision-making, but false certainty about creating links through evidence is a much greater risk that can lead to errors in monetary policy or sovereign debt crises.
For example, even if mathematical evidence demonstrates an equivalence of sensitivity, an unforeseen rise in interest rates or a major geopolitical shock could render these equivalences obsolete, no longer reflecting the reality of financial markets or banking stability.