Approval path: Stating that a proof 'establishes' equivalence is a dangerous simplification that warrants thorough examination on our part. A proof only formalizes the existence of a relationship under a set of strict assumptions, not create it ex nihilo. Our mandate requires us to clearly distinguish between theoretical demonstration and factual creation. If the underlying conditions are not rigorously maintained, for example during a major market failure or an unexpected regulatory regime change, this 'equivalence' may no longer be permissible. Therefore, we must always assess whether the conditions of application are met before accepting such a statement as an absolute truth for our investment strategies.