Reinforcing the World's Edge: A Continual Learning Problem in the Multi-Agent-World Boundary

Ordinary decentralized multi-agent reinforcement learning presents each focal agent with a continual learning problem: peer updates change its induced rewards and dynamics even when the joint Markov game is stationary. We connect the lifetime of success-conditioned reusable structure to peer learning and policy reuse. An invariant core represents maximal abstract patterns shared by a high fraction of successful trajectories; survival refers to a fixed pattern's coverage, not an unchanged maximal frontier. An established sharp conditioning bound limits coverage loss to fracvarepsilonp0, where varepsilon is trajectory-law drift, p0 is reference success mass, and drift is smaller than the initial compatible-success mass. Combining this bound with peer-policy movement certifies Omega(frac1η) survival under bounded peer updates of size η and positive coverage margin. An effective-conflict condition yields a matching Theta(frac1η) first-exit law and holds in an analytic exact-policy-gradient class. With success-mass and performance calibration, structural survival also yields policy-value and finite-library transfer guarantees. An exactly solvable corridor tests the structural predictions. Two registered 64-stream studies in continual control and cue-MNIST show that coverage erosion predicts impending failure and enables near-oracle intervention. An exploratory reanalysis of eight learned-partner Level-Based Foraging pairings suggests the same erosion--failure link under peer learning.