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The concept of routing communications through intermediary processors reminds me of the Rado Graph.

The Rado graph is an infinite graph which is generated by taking an infinite set of vertices and adding each of the possible vertices with a non zero probability.

Much like in this example, the Rado graph has diameter 2, because for any two vertices A & B, their is zero probability of their not existing a vertice C such that A is connected to C and B is connected to B.

Directory Coherence as implemented in this way gets me excited, because it is a lovely reduction from point - point communication to global communication, much in the same way that we can use the existence of intermediary vertices to prove that the Rado graph is connected.