Proposed Solution

We propose Hamiltonian-SMT, the first MARL framework to replace “guess-and-check” evolution with verified Policy Impulses. By modeling the population as a discrete Hamiltonian system, we enforce physical and logical conservation laws:

System Energy (E): Formally represents Social Welfare (Global Reward).

Momentum (P): Formally represents Behavioral Diversity.

Impulse (∆W): A weight update verified by Lean 4 to be Lipschitz-continuous and energy-preserving.