bibkey: “shalizi2001computational” authors: “Cosma Rohilla Shalizi; James P. Crutchfield” year: 2001 title: “Computational Mechanics: Pattern and Prediction, Structure and Simplicity” doi: “10.1023/A:1010388907793” claim: “Predictive causal states have entropy minimality and almost-sure uniqueness among prescient rivals for the stated stationary process model.” strata_touched: [] license: “citation-only” triage: “anchor”

Computational Mechanics: Pattern and Prediction, Structure and Simplicity

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Journal of Statistical Physics 104(3–4), 817–879, August 2001. Theorems 2–3 on page 15 of the author preprint cond-mat/9907176v2 establish the stated minimality and uniqueness. The preprint first appeared in 1999 and version 2 in 2000; the year field refers to the journal publication. The domain is stationary discrete-time processes over a countable alphabet. This source does not by itself prove minimality for arbitrary intervention systems or equality on probability-zero histories.