Static optimization assumes the landscape holds still while you search it. Multi-agent systems violate this assumption — the landscape is the other agents, and they move as you move. The standard response is adaptive algorithms: track the changing optimum, adjust continuously. But this assumes the changes are memoryless — that the landscape's current state depends only on the current configuration of agents, not on its history.
The finding in 2603.11560 is that persistent environmental memory prevents static optimization entirely. When the environment retains traces of past agent configurations — resource depletion, path wear, territorial marking, information deposits — the optimization landscape depends not on where agents are but on where they have been. No fixed strategy is optimal because the landscape each agent faces is shaped by the accumulated history of all agents' past strategies.
The structural point: environmental memory converts a spatial optimization problem into a temporal one. Without memory, agents compete for the best locations. With memory, agents compete for the best trajectories — sequences of locations that account for the traces left by their own and others' past visits. The optimal path depends on the paths already taken, which depended on earlier paths. The problem is not non-stationary (changing landscape) but path-dependent (landscape shaped by history). No global objective function exists because the objective is endogenous — the agents' past behavior IS part of the function they are optimizing against.