Antichain-lattice indexing in PID is structurally insufficient to recover mutual information from information atoms for multivariate cases.
Rec- onciling emergences: An information-theoretic approach to identify causal emergence in multivariate data.PLoS computational biology, 16(12):e1008289
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Structural Impossibility of Antichain-Lattice Partial Information Decomposition
Antichain-lattice indexing in PID is structurally insufficient to recover mutual information from information atoms for multivariate cases.