{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1992:YNVKSUB454YLGMX232XONBBPWD","short_pith_number":"pith:YNVKSUB4","schema_version":"1.0","canonical_sha256":"c36aa9503cef30b332fadeaee6842fb0c31239282e99700bbda94603ad1e1a38","source":{"kind":"arxiv","id":"math/9201300","version":1},"attestation_state":"computed","paper":{"title":"The existence of sigma-finite invariant measures, applications to real one-dimensional dynamics","license":"","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Marco Martens","submitted_at":"1992-01-15T00:00:00Z","abstract_excerpt":"A general construction for $\\sigma-$finite absolutely continuous invariant measure will be presented. It will be shown that the local bounded distortion of the Radon-Nykodym derivatives of $f^n_*(\\lambda)$ will imply the existence of a $\\sigma-$finite invariant measure for the map $f$ which is absolutely continuous with respect to $\\lambda$, a measure on the phase space describing the sets of measure zero. Furthermore we will discuss sufficient conditions for the existence of $\\sigma-$finite invariant absolutely continuous measures for real 1-dimensional dynamical systems."},"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/9201300","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.DS","submitted_at":"1992-01-15T00:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"fa9aba8501bf7d59a04752a66dc488edb5462d10d7ec15d72a60de95b2adbcf4","abstract_canon_sha256":"425809ebf0ab3d871988af3d92dcd976796e27bb4d9986b8e5a2ad6bd635204c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:53.034861Z","signature_b64":"WyKVYDnlPKYtNR8rs9NyOB6gjTxCdBtmt/U7WieuIKictqhbcK5C5ooQRYnKlDA1MiY0Q4Cjj/N3HQfpR/dFBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c36aa9503cef30b332fadeaee6842fb0c31239282e99700bbda94603ad1e1a38","last_reissued_at":"2026-05-18T01:05:53.034355Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:53.034355Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The existence of sigma-finite invariant measures, applications to real one-dimensional dynamics","license":"","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Marco Martens","submitted_at":"1992-01-15T00:00:00Z","abstract_excerpt":"A general construction for $\\sigma-$finite absolutely continuous invariant measure will be presented. It will be shown that the local bounded distortion of the Radon-Nykodym derivatives of $f^n_*(\\lambda)$ will imply the existence of a $\\sigma-$finite invariant measure for the map $f$ which is absolutely continuous with respect to $\\lambda$, a measure on the phase space describing the sets of measure zero. Furthermore we will discuss sufficient conditions for the existence of $\\sigma-$finite invariant absolutely continuous measures for real 1-dimensional dynamical systems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9201300","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/9201300","created_at":"2026-05-18T01:05:53.034418+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/9201300v1","created_at":"2026-05-18T01:05:53.034418+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9201300","created_at":"2026-05-18T01:05:53.034418+00:00"},{"alias_kind":"pith_short_12","alias_value":"YNVKSUB454YL","created_at":"2026-05-18T12:25:47.102015+00:00"},{"alias_kind":"pith_short_16","alias_value":"YNVKSUB454YLGMX2","created_at":"2026-05-18T12:25:47.102015+00:00"},{"alias_kind":"pith_short_8","alias_value":"YNVKSUB4","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/YNVKSUB454YLGMX232XONBBPWD","json":"https://pith.science/pith/YNVKSUB454YLGMX232XONBBPWD.json","graph_json":"https://pith.science/api/pith-number/YNVKSUB454YLGMX232XONBBPWD/graph.json","events_json":"https://pith.science/api/pith-number/YNVKSUB454YLGMX232XONBBPWD/events.json","paper":"https://pith.science/paper/YNVKSUB4"},"agent_actions":{"view_html":"https://pith.science/pith/YNVKSUB454YLGMX232XONBBPWD","download_json":"https://pith.science/pith/YNVKSUB454YLGMX232XONBBPWD.json","view_paper":"https://pith.science/paper/YNVKSUB4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/9201300&json=true","fetch_graph":"https://pith.science/api/pith-number/YNVKSUB454YLGMX232XONBBPWD/graph.json","fetch_events":"https://pith.science/api/pith-number/YNVKSUB454YLGMX232XONBBPWD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YNVKSUB454YLGMX232XONBBPWD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YNVKSUB454YLGMX232XONBBPWD/action/storage_attestation","attest_author":"https://pith.science/pith/YNVKSUB454YLGMX232XONBBPWD/action/author_attestation","sign_citation":"https://pith.science/pith/YNVKSUB454YLGMX232XONBBPWD/action/citation_signature","submit_replication":"https://pith.science/pith/YNVKSUB454YLGMX232XONBBPWD/action/replication_record"}},"created_at":"2026-05-18T01:05:53.034418+00:00","updated_at":"2026-05-18T01:05:53.034418+00:00"}