Self-improving federated agent networks keep training after deployment by collecting new trajectories with the current policy and feeding them back into later rounds. This closed loop makes unlearning harder than a one-time model repair. When a data owner requests deletion, the target data may have already shaped later retained trajectories, so retraining or model-side unlearning can leave an influence echo that returns as the network continues to operate. We show that this echo survives retained-data retraining, grows with the amount of forget-shaped retained data, and can be traced from deployment, collection, and aggregation records. To address this problem, we propose MUTE, a Muting Unlearned Trajectories' Echoes method for reliable deletion in self-improving federated agent networks. MUTE estimates downstream influence from a lightweight server ledger, removes the current residue through a forget-retain update, contains high-influence retained trajectories through quarantine or down-weighting, and audits later behavior to schedule additional erasure under an uplink budget. Experiments on LIBERO with two vision-language-action backbones, three deletion granularities, and a physical Jetson-based edge testbed show that MUTE keeps behavioral leakage and influence regeneration low while preserving task utility and using much less communication than full retraining.
The Internet taught us that the value of a network depends on \emph{how} its nodes connect: broadcast stars scale as $V\!\propto\!N$ (Sarnoff), fully-connected meshes as $N^2$ (Metcalfe), and group-forming networks as $2^{N}$ (Reed). We ask the analogous question for networks of AI agents. We model the net value of connection as a function of coordination-group size, derive from it the properties an optimal collaboration protocol must have, and introduce ANet Patu-1 -- a self-organizing consensus protocol in which the network continuously re-forms its own coalitions, adaptively riding the upper envelope of all three regimes at $O(1)$ parallel consensus rounds. To measure value without opinion-grading, we score an emergent protocol by formally specifying it and deriving its complexity, the way distributed algorithms are analyzed. Two results follow. (i)~Emergence -- a crowd of the \emph{cheapest} model, when heterogeneous, starts weak but its collective value compounds with $N$ and \emph{overtakes} a crowd of a far \emph{stronger} model that is homogeneous: a crossover that marks a scaling law for collaboration rather than for scale. (ii)~Reflexivity -- a heterogeneous network, given only its own problem and no design hints, converges on ANet Patu-1 itself, reconstructing the high-dimensional law that governs its own connective value.