Can you translate one economic model into another without losing answers?

Economists often solve the same optimization problem in multiple ways. This paper shows that when two dynamic programs are connected by an order isomorphism—a mathematical structure-preserving transformation—optimality properties carry from one to the other. Applied to real business cycle models, these translations improved numerical accuracy by 100x, while also proving that two seemingly different preference models (Kreps–Porteus and risk-sensitive) are mathematically identical.