{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:E4LN4VR2UYQO3WIG4SLFLFD5HX","short_pith_number":"pith:E4LN4VR2","schema_version":"1.0","canonical_sha256":"2716de563aa620edd906e49655947d3dda318fcb89c50429d00e900631610765","source":{"kind":"arxiv","id":"1811.04805","version":1},"attestation_state":"computed","paper":{"title":"Invariant measures for typical continuous maps on manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Eleonora Catsigeras (IMERL), Serge Troubetzkoy (I2M)","submitted_at":"2018-11-09T14:44:05Z","abstract_excerpt":"We study the invariant measures of typical $C^0$ maps on compact connected manifolds with or without boundary, and also of typical homeomorphisms. We prove that the weak$^*$ closure of the set of ergodic measurescoincides with the weak$^*$ closure of the set of measures supported on periodic orbits and also coincides withthe set of pseudo-physical measures.  Furthermore, we show that this set has empty interior in the set of invariant measures."},"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":"1811.04805","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-11-09T14:44:05Z","cross_cats_sorted":[],"title_canon_sha256":"bb712b2139a777a8a638313704ed2f2c4ac53d0dc420656e000b8ac4da70406c","abstract_canon_sha256":"eb4cd5df38b25904b6fc9b4144dec28f954a94e37df31d7ce55ae537b9fac2dc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:30:53.924360Z","signature_b64":"N8YTDozEWrH8N2YXHVBbA1JeqQ4ZlFwBO4QByBYiGX+wrdrX2r7TLyOVDp+2ilsEUbRK2bZpJVf129ms9/WZBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2716de563aa620edd906e49655947d3dda318fcb89c50429d00e900631610765","last_reissued_at":"2026-07-05T00:30:53.923877Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:30:53.923877Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Invariant measures for typical continuous maps on manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Eleonora Catsigeras (IMERL), Serge Troubetzkoy (I2M)","submitted_at":"2018-11-09T14:44:05Z","abstract_excerpt":"We study the invariant measures of typical $C^0$ maps on compact connected manifolds with or without boundary, and also of typical homeomorphisms. We prove that the weak$^*$ closure of the set of ergodic measurescoincides with the weak$^*$ closure of the set of measures supported on periodic orbits and also coincides withthe set of pseudo-physical measures.  Furthermore, we show that this set has empty interior in the set of invariant measures."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.04805","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/1811.04805/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":"1811.04805","created_at":"2026-07-05T00:30:53.923934+00:00"},{"alias_kind":"arxiv_version","alias_value":"1811.04805v1","created_at":"2026-07-05T00:30:53.923934+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.04805","created_at":"2026-07-05T00:30:53.923934+00:00"},{"alias_kind":"pith_short_12","alias_value":"E4LN4VR2UYQO","created_at":"2026-07-05T00:30:53.923934+00:00"},{"alias_kind":"pith_short_16","alias_value":"E4LN4VR2UYQO3WIG","created_at":"2026-07-05T00:30:53.923934+00:00"},{"alias_kind":"pith_short_8","alias_value":"E4LN4VR2","created_at":"2026-07-05T00:30:53.923934+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"1907.08755","citing_title":"Physical-like Measures Coincide with Invariant Measures Supported on Chain Recurrent Classes","ref_index":19,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/E4LN4VR2UYQO3WIG4SLFLFD5HX","json":"https://pith.science/pith/E4LN4VR2UYQO3WIG4SLFLFD5HX.json","graph_json":"https://pith.science/api/pith-number/E4LN4VR2UYQO3WIG4SLFLFD5HX/graph.json","events_json":"https://pith.science/api/pith-number/E4LN4VR2UYQO3WIG4SLFLFD5HX/events.json","paper":"https://pith.science/paper/E4LN4VR2"},"agent_actions":{"view_html":"https://pith.science/pith/E4LN4VR2UYQO3WIG4SLFLFD5HX","download_json":"https://pith.science/pith/E4LN4VR2UYQO3WIG4SLFLFD5HX.json","view_paper":"https://pith.science/paper/E4LN4VR2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1811.04805&json=true","fetch_graph":"https://pith.science/api/pith-number/E4LN4VR2UYQO3WIG4SLFLFD5HX/graph.json","fetch_events":"https://pith.science/api/pith-number/E4LN4VR2UYQO3WIG4SLFLFD5HX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/E4LN4VR2UYQO3WIG4SLFLFD5HX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/E4LN4VR2UYQO3WIG4SLFLFD5HX/action/storage_attestation","attest_author":"https://pith.science/pith/E4LN4VR2UYQO3WIG4SLFLFD5HX/action/author_attestation","sign_citation":"https://pith.science/pith/E4LN4VR2UYQO3WIG4SLFLFD5HX/action/citation_signature","submit_replication":"https://pith.science/pith/E4LN4VR2UYQO3WIG4SLFLFD5HX/action/replication_record"}},"created_at":"2026-07-05T00:30:53.923934+00:00","updated_at":"2026-07-05T00:30:53.923934+00:00"}