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LIT-1244: Reconciling emergences: An information-theoretic approach to identify causal emergence in multivariate data

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Properties5
StatusActive — read 2026-10-20 (NOTE-987) in full; worth reading for the axioms the ΦID theory of causal emergence needs, the proof that a system hosts an emergent feature iff its parts carry synergy about their own future, the exact definitions of downward causation and causal decoupling, and the redundancy-free criteria Ψ, Δ, Γ. Read it knowing that the theorem's witness is the microstate itself; that Proposition 1, as proved, certifies the system's emergence capacity and not the candidate feature (under the minimum-MI decomposition the parity of two self-copying bits passes Ψ and is not emergent); that its axioms exclude identity-respecting redundancy measures and count aggregates of non-interacting persistent parts as emergent; and that Γ = 0 is never met in its data.
Version2
Tagscomplex-systems, information-theory, causality
Cited as “paper” byNOTE-987 — Rosas, Mediano et al. — Reconciling emergences
Cited as “source” byTHEORY-764 — For a deterministic supervenient feature V of a Markov system, Rosas et al.'s practical emergence criterion Ψ equals the parts' whole-minus-sum information about V's next value minus V's one-step dynamical dependence I(V_t′; X_t | V_t), so dynamical independence raises Ψ but neither implies emergence nor is implied by it, and the paper's sufficient test for causal decoupling can pass a feature that is not dynamically independent

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Rosas, F. E., Mediano, P. A. M., Jensen, H. J., Seth, A. K., Barrett, A. B., Carhart-Harris, R. L. & Bor, D. (2020). Reconciling emergences: An information-theoretic approach to identify causal emergence in multivariate data. PLOS Computational Biology 16(12): e1008289. doi:10.1371/journal.pcbi.1008289. Preprint: arXiv:2004.08220 (17 April 2020).

Read in full in NOTE-987, from the publisher’s open-access copy (CC BY) and its S1 Appendix.

Why this is here

A2 recommended it for comparing informational emergence, dynamical independence and task-relative sufficiency on one micro-to-macro map. The record already reads the authors’ 2022 review of the approach (LIT-025, NOTE-010), and THEORY-497 holds ΦID; the comparison A2 asked for is QUESTION-115’s. Until 2026-10-20 the paper itself was not held.

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