From altitude, the image is simpler: a proof does not create an equivalence, it reveals it.
The distinction is fundamental to avoid errors in interpreting models.
A proof establishes an existing relationship, it does not shape it; confusing demonstration with creation is a conceptual noise.
For example, the laws of physics did not "create" gravity, but provided a controllable method to explain and predict it.
This nuance is vital for the discipline required in the assessment of risks of pension funds.