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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 p","title":"The Extremum Stack is a Minimal Sufficient Statistic for Rate-Independent Functionals: A Kolmogorov Complexity Characterisation","url":"https://arxiv.org/abs/2605.18885","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.18885v1 Announce Type: cross \nAbstract: 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 p","title":"The Extremum Stack is a Minimal Sufficient Statistic for Rate-Independent Functionals: A Kolmogorov Complexity Characterisation","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-05-20T04:43:44Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2605.18885"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:f63bf7d59eddb19e45ea974cf82d17fcf7e166403a2cdcc2b64bf0d1234cf27ae88e29ce278abfcba3350864bdfbe05cff8a1eaa1b477f9b9705445cdb970908","signer":"crovia.substrate","subject":{"observed_at":"2026-05-20T04:43:44Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2605.18885"},"tsa":{"authority":"crovia.substrate.bootstrap","rfc3161_token":"{\"kind\":\"crovia.bootstrap.tsa\",\"source_jsonl\":\"/opt/crovia/spider/data/news/vendor_press_v1.jsonl\",\"source_seal_merkle_root\":\"spider_vendor_press_v1\",\"upgrade_path\":\"Sessione H \\u2014 OpenTimestamps weekly anchor\"}"},"zk_mode":"clear","zk_proof":null},"ledger":{"leaf_hash":"2c5685f83514bcd1dd4850082b88221ca91f97af28a246f4192714b42014921a","leaf_index":145036,"ledger_path":"/opt/crovia/substrate/axiom_ledger.jsonl"},"merkle_proof":{"hash_alg":"sha256","leaf_prefix":"0x00","node_prefix":"0x01","odd_leaf_rule":"duplicate_last","path":[{"sibling":"23f82d46c5791cd40cd73676948e8cf75541ab2d7e13d7b884ee3bb6efd04df6","side":"right"},{"sibling":"3899bd6bb4df695ae480e8fdc91a8b4b07dabe6592e08a3593185f0d8badd0ef","side":"right"},{"sibling":"ecb962d147f08877974f8edefa2c541ac47c96d29dc47c75ad781072a382c877","side":"left"},{"sibling":"361ee222d2362a8c044f1a0de2899cc2df420c8b70a5995e49f2259eddf52187","side":"left"},{"sibling":"148b11a5ac76a6dd703868823dfa462ac7e41cdc1a5aada9ce2c9a103eb39f09","side":"right"},{"sibling":"0ab1cbf9ea1c7bc2998254a1b9ed1ffec18ac6f82d1467ebc2dcb67301c9ac1e","side":"right"},{"sibling":"3c054fc9610e75398c84d6602026026e93d4cc85db18f6da86b0e99184718c59","side":"right"},{"sibling":"3047d0cbdc103ff93a1a073ea940e12ff062595dae419513748ed63fbcb3359c","side":"left"},{"sibling":"9db04d2181fb869f16a5baf7dcfe999cc93a7e9beef8493d0cc71f57470fe5e1","side":"right"},{"sibling":"1526885f19d1fadf6955cf519dbc4e62d593a4bba99d741e8c301740a7068233","side":"left"},{"sibling":"e3a7d5c07f161682d61bd453ffc02ecdf87cfeda70f986d6650017f9d2d6b265","side":"left"},{"sibling":"edbc49f08e5b92291934c05c9e6efd270a6b0698d8d2fa474006366027dfe098","side":"right"},{"sibling":"3e4df6e7457cecbf36f350375e72dcab336a3984422e4c406ef809e4e2944e96","side":"left"},{"sibling":"8f4c0fbe56b6c010fbb8c782ebcd478079bb3f991d8704e2534209a075d9163c","side":"left"},{"sibling":"be08fedc4e72a6fb56606f66812fae7317e09690b9acb18385f4ab117a981238","side":"right"},{"sibling":"0534329a7475dc9df51998c83c16892126679dade0fa34182f21e869599386c7","side":"right"},{"sibling":"2d24720928ead0e7670650eb55f558c4f20e4c18df376f47ba72cfa8cf0ed344","side":"right"},{"sibling":"d841ad93efda0869e5eb97678f348f03f5caab4353e05ff4bf18f47fb945b822","side":"left"}]},"schema":"crovia.axiom_proof.v1","seal":{"first_collector_run_id":"","first_receipt_hash":"","jsonl_path":"/opt/crovia/substrate/axiom_ledger.jsonl","key_id":"430895f101d38164","last_collector_run_id":"","last_receipt_hash":"","leaf_count":147301,"merkle_root":"08903d7159c3b38eeeeafc09eab15139ea417f1d94f02f1fbc87296b37db840a","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260521T183701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-05-21T18:37:33Z","sig_algorithm":"ed25519","signature":"905f2924632dfa2970c8690285f5b5d4a1d891d0e0ef1cbc404ebec2fd937215ac768e16f0a9f28b18977a55ae0bfd226db6833ae7ef588729054117d2da7303","signer_version":"1.1.0"},"trust_root":{"key_id":"430895f101d38164","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","signature_algorithm":"ed25519","url":"/registry/canon/TRUST_ROOT.md"},"verifier":{"spec":"/registry/canon/AXIOM_RECEIPT_v1.md","url":"/v/axm_0c1d344ffad8c285709b42a4fbfaf2aa674f4863e8f510fd0764652fa9b38c1d"}}