We prove that the extremum stack of a discrete sequence is a minimal sufficient statistic for the class of all computable, causal, rate-independent functionals, in the sense of Kolmogorov complexity. Specifically, we establish K(Pi_n) - O(1) <= K_R(u_{0:n}) <= K(Pi_n) + O(1), where K_R(u_{0:n}) is the length of the shortest program answering every query in the class 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(Pi_n) - O(1) bits; the stack-based compression algorithm implied by the result carries a Kolmogorov optimality guarantee that none of the standard time-series compression methods provide.

翻译：我们证明，在柯尔莫哥洛夫复杂性的意义下，离散序列的极值栈是全体可计算、因果、率无关泛函类的最小充分统计量。具体而言，我们建立了不等式 K(Pi_n) - O(1) <= K_R(u_{0:n}) <= K(Pi_n) + O(1)，其中 K_R(u_{0:n}) 是回答率无关泛函类 R 中每个查询的最短程序长度，而 O(1) 开销与序列长度 n 和栈深度 k 均无关。充分性源于经典普赖萨赫磁滞算子的擦除性质，而最小性通过一个显式验证了率无关性的有限指示函数族得以确认。因此，任何对磁滞驱动流进行压缩且保留完整泛函类 R 的方法，必须至少保留 K(Pi_n) - O(1) 比特信息；由该结果蕴含的基于栈的压缩算法具有柯尔莫哥洛夫最优性保证，这是任何标准时间序列压缩方法所不具备的。