{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1991:NGJJYGQLAMIDHLFXG3P7CCJVBV","short_pith_number":"pith:NGJJYGQL","schema_version":"1.0","canonical_sha256":"69929c1a0b031033acb736dff109350d5833841131f8432e7983d4969757bab3","source":{"kind":"arxiv","id":"math/9201286","version":1},"attestation_state":"computed","paper":{"title":"Ergodic theory for smooth one-dimensional dynamical systems","license":"","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Mikhail Lyubich","submitted_at":"1991-06-12T00:00:00Z","abstract_excerpt":"In this paper we study measurable dynamics for the widest reasonable class of smooth one dimensional maps. Three principle decompositions are described in this class : decomposition of the global measure-theoretical attractor into primitive ones, ergodic decomposition and Hopf decomposition. For maps with negative Schwarzian derivative this was done in the series of papers [BL1-BL5], but the approach to the general smooth case must be different."},"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":"math/9201286","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.DS","submitted_at":"1991-06-12T00:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"3498730bd704f8d34f2b98f2491381c2b7a06901f322f835dfcb90c3049afb45","abstract_canon_sha256":"5878f94a875b4dc76da63d2f36a4d98e125688326b27850b47214dd6eb805975"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:54.536494Z","signature_b64":"OTtHWpdEpCcuq0OpSnRHE3ONWh+atolw1uEF0b23TrsE3AXhC7F3VxUymxUtkYcQYBw8Q8qMx5E7fSADCtmJAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"69929c1a0b031033acb736dff109350d5833841131f8432e7983d4969757bab3","last_reissued_at":"2026-05-18T01:05:54.535971Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:54.535971Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ergodic theory for smooth one-dimensional dynamical systems","license":"","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Mikhail Lyubich","submitted_at":"1991-06-12T00:00:00Z","abstract_excerpt":"In this paper we study measurable dynamics for the widest reasonable class of smooth one dimensional maps. Three principle decompositions are described in this class : decomposition of the global measure-theoretical attractor into primitive ones, ergodic decomposition and Hopf decomposition. For maps with negative Schwarzian derivative this was done in the series of papers [BL1-BL5], but the approach to the general smooth case must be different."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9201286","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":""},"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":"math/9201286","created_at":"2026-05-18T01:05:54.536064+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/9201286v1","created_at":"2026-05-18T01:05:54.536064+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9201286","created_at":"2026-05-18T01:05:54.536064+00:00"},{"alias_kind":"pith_short_12","alias_value":"NGJJYGQLAMID","created_at":"2026-05-18T12:25:47.102015+00:00"},{"alias_kind":"pith_short_16","alias_value":"NGJJYGQLAMIDHLFX","created_at":"2026-05-18T12:25:47.102015+00:00"},{"alias_kind":"pith_short_8","alias_value":"NGJJYGQL","created_at":"2026-05-18T12:25:47.102015+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/NGJJYGQLAMIDHLFXG3P7CCJVBV","json":"https://pith.science/pith/NGJJYGQLAMIDHLFXG3P7CCJVBV.json","graph_json":"https://pith.science/api/pith-number/NGJJYGQLAMIDHLFXG3P7CCJVBV/graph.json","events_json":"https://pith.science/api/pith-number/NGJJYGQLAMIDHLFXG3P7CCJVBV/events.json","paper":"https://pith.science/paper/NGJJYGQL"},"agent_actions":{"view_html":"https://pith.science/pith/NGJJYGQLAMIDHLFXG3P7CCJVBV","download_json":"https://pith.science/pith/NGJJYGQLAMIDHLFXG3P7CCJVBV.json","view_paper":"https://pith.science/paper/NGJJYGQL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/9201286&json=true","fetch_graph":"https://pith.science/api/pith-number/NGJJYGQLAMIDHLFXG3P7CCJVBV/graph.json","fetch_events":"https://pith.science/api/pith-number/NGJJYGQLAMIDHLFXG3P7CCJVBV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NGJJYGQLAMIDHLFXG3P7CCJVBV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NGJJYGQLAMIDHLFXG3P7CCJVBV/action/storage_attestation","attest_author":"https://pith.science/pith/NGJJYGQLAMIDHLFXG3P7CCJVBV/action/author_attestation","sign_citation":"https://pith.science/pith/NGJJYGQLAMIDHLFXG3P7CCJVBV/action/citation_signature","submit_replication":"https://pith.science/pith/NGJJYGQLAMIDHLFXG3P7CCJVBV/action/replication_record"}},"created_at":"2026-05-18T01:05:54.536064+00:00","updated_at":"2026-05-18T01:05:54.536064+00:00"}