ANet Patu-1: The Value of Connection in the Agent Network

The Internet taught us that the value of a network depends on how its nodes connect: broadcast stars scale as V!propto!N (Sarnoff), fully-connected meshes as N2 (Metcalfe), and group-forming networks as 2N (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 cheapest model, when heterogeneous, starts weak but its collective value compounds with N and overtakes a crowd of a far 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.