In the exact-depth regime of context length r, the depth-r boundary process is the canonical finite-state Markov chain, smaller windows are deterministic truncations, coarser informative maps factor C^1-smoothly through it so rank cannot increase beyond r, and rank-drop criteria identify the exact m
Billingsley,Statistical Inference for Markov Processes, University of Chicago Press, Chicago
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Variable-Length Markov Chains on Finite Quivers: Boundary-Window Identifiability, Exact Depth, and Local Rank Comparison
In the exact-depth regime of context length r, the depth-r boundary process is the canonical finite-state Markov chain, smaller windows are deterministic truncations, coarser informative maps factor C^1-smoothly through it so rank cannot increase beyond r, and rank-drop criteria identify the exact m