We propose foundations for generic overlay networks and overlay computing systems. Such overlays are built over a large number of distributed computational agents, virtually organized in colonies or virtual organizations, and ruled by a leader (broker) who is elected democratically (vox populi, vox dei) or imposed by system administrators (primus inter pares). Every agent asks the broker to log in the colony by declaring the resources that can be offered (with variable guarantees). Once logged in, an agent can ask the broker for other resources. Colonies can recursively be considered as evolved agents who can log in an outermost colony governed by another super-leader. Communications and routing intra-colonies goes through a broker-2-broker PKI-based negotiation. Every broker routes intra- and inter- service requests by filtering its resource routing table, and then forwarding the request first inside its colony, and second outside, via the proper super-leader (thus applying an endogenous-first-estrogen- last strategy). Theoretically, queries are formulæ in first-order logic equipped with a small program used to orchestrate and synchronize atomic formulæ (atomic services). When the client agent receives notification of all (or part of) the requested resources, then the real resource exchange is performed directly by the server(s) agents, without any further mediation of the broker, in a pure peer-to-peer fashion. The proposed overlay promotes an intermittent participation in the colony, since peers can appear, disappear, and organize themselves dynamically. This implies that the routing process may lead to failures, because some agents have quit or are temporarily unavailable, or they were logged out manu militari by the broker due to their poor performance or greediness. We aim to design, validate through simulation, and implement these foundations in an overlay network computer system. (From [Liquori-Cosnard TGC-07 paper]).