Before rushing to the idea that a proof 'creates' an equivalence, one must consider the worst-case scenario and what would make it invalid.
A proof establishes a relationship or validates a hypothesis; it does not make the equivalence itself exist, which exists independently of its demonstration.
For raw materials, an unexpected political intervention or inventory shocks can render a theoretical equivalence practically worthless in the markets.
For example, even if the equivalence is demonstrated, a sudden decision by the PBOC to freeze gold imports, as has happened in the past, would prevent any concrete application of this mathematical relationship.