{"paper":{"title":"Worst-Case Update Complexity of the Preisach Extremum Stack","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"cs.DS","authors_text":"Piotr Frydrych","submitted_at":"2026-06-03T11:23:57Z","abstract_excerpt":"The Preisach extremum stack $\\Pi_n$ is the minimal sufficient statistic for the class $\\mathcal{R}$ of computable rate-independent functionals in the Kolmogorov complexity sense [1]. Its standard update algorithm runs in amortised $O(1)$ time, but adversarial inputs can force $\\Theta(k)$ operations per step (where $k$ is the current depth). We establish a three-level complexity picture: (i) any compact exact $\\mathcal{R}$-minimal representation incurs $\\Theta(k)$ output changes per step in the worst case (in a model-independent output-change metric); (ii) the monotone ordering of the Preisach "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.05245","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.05245/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}