To solve consensus, the output complex must consist of distinct, disconnected components (one component where everyone decides 0, and another where everyone decides 1).
: A set of mutually compatible local states forms a simplex (a triangle, tetrahedron, or higher-dimensional equivalent). distributed computing through combinatorial topology pdf
He grabbed a napkin. "Combinatorial topology gives us the exact number. For 12 nodes and 3 failures, the minimum number of clusters we must allow is 4. That’s not a guess. That’s a homotopy invariant ." To solve consensus, the output complex must consist
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