Establish frequency-dependent recovery of cooperation

Establish or refute whether rare cooperative lineages can recover from low frequency when \alpha\delta > 1 and E_{max} > \tilde{E}^*, particularly by accumulating residual energy through successful cooperator–cooperator interactions and thereby increasing their probability of controlling subsequent replication events under fully dynamic execution priorities.

Background

The Frequency-Dependent Rebound conjecture concerns populations in which defectors have become common and destructive interactions keep them at low energy. The proposed mechanism is that rare cooperators can gain residual energy during successful cooperator–cooperator encounters and later use that energy advantage to control replication events against defectors.

The supporting argument establishes only a positive-probability path under approximated, frozen execution priorities. The authors explicitly state that this reasoning does not prove rebound for the fully dynamic execution process, where energy and execution priorities are updated after each operation.