We prove that the extremum stack Πₙ of a discrete sequence u₀: ₍ ∈ GL^n+1 is a minimal sufficient statistic for the class R of all computable, causal, rate-independent functionals, in the sense of Kolmogorov complexity. Specifically, we establish: K (Πₙ) − O (1) ≤ KR (u₀: ₍) ≤ K (Πₙ) + O (1), where KR (u₀: ₍) is the length of the shortest program answering every query in R, and the O (1) overhead is independent of both the sequence length n and the stack depth k. Sufficiency follows from the classical wiping property of the Preisach hysteresis operator. Minimality is established via a finite indicator family whose rate-independence is verified explicitly. Any compression of a hysteresis-driven stream that preserves the full class R must therefore retain at least K (Πₙ) − O (1) bits; the stack-based compression algorithm implied by the result carries a Kolmogorov optimality guarantee absent from standard time-series compression methods. Submitted to Information Processing Letters (Elsevier).
Piotr Frydrych (Sat,) studied this question.