{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:6OCHWADAYML6AOBGV2IGXFAHID","short_pith_number":"pith:6OCHWADA","schema_version":"1.0","canonical_sha256":"f3847b0060c317e03826ae906b940740ce044b6619524b4c4ed8870b29fdf3cb","source":{"kind":"arxiv","id":"2606.05245","version":1},"attestation_state":"computed","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 "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2606.05245","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2026-06-03T11:23:57Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"d29a06f2a6d1f800a5b5308f3122f1871f1a497d72bd9a55b4ab5d7518d8b78f","abstract_canon_sha256":"0800a94772cc0f0be30a30956cd9bf71f12415a5abe2143f3cc6c600f92f259a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-05T00:13:50.343644Z","signature_b64":"voGv7qUCzb8kTDJuJ5KpCUK6Hb7Z84lA844gntocbNB0e/LYU5CQlGhIBbTkjCHrvOFGQjwav+gOk3fR04QRCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f3847b0060c317e03826ae906b940740ce044b6619524b4c4ed8870b29fdf3cb","last_reissued_at":"2026-06-05T00:13:50.343141Z","signature_status":"signed_v1","first_computed_at":"2026-06-05T00:13:50.343141Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2606.05245","created_at":"2026-06-05T00:13:50.343219+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.05245v1","created_at":"2026-06-05T00:13:50.343219+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.05245","created_at":"2026-06-05T00:13:50.343219+00:00"},{"alias_kind":"pith_short_12","alias_value":"6OCHWADAYML6","created_at":"2026-06-05T00:13:50.343219+00:00"},{"alias_kind":"pith_short_16","alias_value":"6OCHWADAYML6AOBG","created_at":"2026-06-05T00:13:50.343219+00:00"},{"alias_kind":"pith_short_8","alias_value":"6OCHWADA","created_at":"2026-06-05T00:13:50.343219+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6OCHWADAYML6AOBGV2IGXFAHID","json":"https://pith.science/pith/6OCHWADAYML6AOBGV2IGXFAHID.json","graph_json":"https://pith.science/api/pith-number/6OCHWADAYML6AOBGV2IGXFAHID/graph.json","events_json":"https://pith.science/api/pith-number/6OCHWADAYML6AOBGV2IGXFAHID/events.json","paper":"https://pith.science/paper/6OCHWADA"},"agent_actions":{"view_html":"https://pith.science/pith/6OCHWADAYML6AOBGV2IGXFAHID","download_json":"https://pith.science/pith/6OCHWADAYML6AOBGV2IGXFAHID.json","view_paper":"https://pith.science/paper/6OCHWADA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.05245&json=true","fetch_graph":"https://pith.science/api/pith-number/6OCHWADAYML6AOBGV2IGXFAHID/graph.json","fetch_events":"https://pith.science/api/pith-number/6OCHWADAYML6AOBGV2IGXFAHID/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6OCHWADAYML6AOBGV2IGXFAHID/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6OCHWADAYML6AOBGV2IGXFAHID/action/storage_attestation","attest_author":"https://pith.science/pith/6OCHWADAYML6AOBGV2IGXFAHID/action/author_attestation","sign_citation":"https://pith.science/pith/6OCHWADAYML6AOBGV2IGXFAHID/action/citation_signature","submit_replication":"https://pith.science/pith/6OCHWADAYML6AOBGV2IGXFAHID/action/replication_record"}},"created_at":"2026-06-05T00:13:50.343219+00:00","updated_at":"2026-06-05T00:13:50.343219+00:00"}