{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:HPXU6JUZUXUNOCED4QFZWWQVRP","short_pith_number":"pith:HPXU6JUZ","schema_version":"1.0","canonical_sha256":"3bef4f2699a5e8d70883e40b9b5a158bf38c4e9d79ff62290b7c6a3aae0aa1c0","source":{"kind":"arxiv","id":"1512.03365","version":2},"attestation_state":"computed","paper":{"title":"The generalized recurrent set and strong chain recurrence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jim Wiseman","submitted_at":"2015-12-10T18:57:51Z","abstract_excerpt":"Fathi and Pageault have recently shown a connection between Auslander's generalized recurrent set $GR(f)$ and Easton's strong chain recurrent set. We study $GR(f)$ by examining that connection in more detail, as well as connections with other notions of recurrence. We give equivalent definitions that do not refer to a metric. In particular, we show that $GR(f^k)=GR(f)$ for any $k>0$, and give a characterization of maps for which the generalized recurrent set is different from the ordinary chain recurrent set."},"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":"1512.03365","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-12-10T18:57:51Z","cross_cats_sorted":[],"title_canon_sha256":"dc4eadd70f20fc836a6d7360ab74f8fda42504047242d50b41e78d13e339b92e","abstract_canon_sha256":"d67a09c38652c326d04c106a058853aee3c0539c031412e7ad17b9a7869e8e05"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:13.083256Z","signature_b64":"Ek01a0MZa0lud9HJ+dTcvi4iUtiC2dDdn4Nlv7o5Bc+VblXbHtTjqya+5Ddt2FrSIpkDJ4z8fmtHYsfOrNRlDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3bef4f2699a5e8d70883e40b9b5a158bf38c4e9d79ff62290b7c6a3aae0aa1c0","last_reissued_at":"2026-05-18T01:11:13.082752Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:13.082752Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The generalized recurrent set and strong chain recurrence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jim Wiseman","submitted_at":"2015-12-10T18:57:51Z","abstract_excerpt":"Fathi and Pageault have recently shown a connection between Auslander's generalized recurrent set $GR(f)$ and Easton's strong chain recurrent set. We study $GR(f)$ by examining that connection in more detail, as well as connections with other notions of recurrence. We give equivalent definitions that do not refer to a metric. In particular, we show that $GR(f^k)=GR(f)$ for any $k>0$, and give a characterization of maps for which the generalized recurrent set is different from the ordinary chain recurrent set."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.03365","kind":"arxiv","version":2},"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":"1512.03365","created_at":"2026-05-18T01:11:13.082841+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.03365v2","created_at":"2026-05-18T01:11:13.082841+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.03365","created_at":"2026-05-18T01:11:13.082841+00:00"},{"alias_kind":"pith_short_12","alias_value":"HPXU6JUZUXUN","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_16","alias_value":"HPXU6JUZUXUNOCED","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_8","alias_value":"HPXU6JUZ","created_at":"2026-05-18T12:29:25.134429+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/HPXU6JUZUXUNOCED4QFZWWQVRP","json":"https://pith.science/pith/HPXU6JUZUXUNOCED4QFZWWQVRP.json","graph_json":"https://pith.science/api/pith-number/HPXU6JUZUXUNOCED4QFZWWQVRP/graph.json","events_json":"https://pith.science/api/pith-number/HPXU6JUZUXUNOCED4QFZWWQVRP/events.json","paper":"https://pith.science/paper/HPXU6JUZ"},"agent_actions":{"view_html":"https://pith.science/pith/HPXU6JUZUXUNOCED4QFZWWQVRP","download_json":"https://pith.science/pith/HPXU6JUZUXUNOCED4QFZWWQVRP.json","view_paper":"https://pith.science/paper/HPXU6JUZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.03365&json=true","fetch_graph":"https://pith.science/api/pith-number/HPXU6JUZUXUNOCED4QFZWWQVRP/graph.json","fetch_events":"https://pith.science/api/pith-number/HPXU6JUZUXUNOCED4QFZWWQVRP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HPXU6JUZUXUNOCED4QFZWWQVRP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HPXU6JUZUXUNOCED4QFZWWQVRP/action/storage_attestation","attest_author":"https://pith.science/pith/HPXU6JUZUXUNOCED4QFZWWQVRP/action/author_attestation","sign_citation":"https://pith.science/pith/HPXU6JUZUXUNOCED4QFZWWQVRP/action/citation_signature","submit_replication":"https://pith.science/pith/HPXU6JUZUXUNOCED4QFZWWQVRP/action/replication_record"}},"created_at":"2026-05-18T01:11:13.082841+00:00","updated_at":"2026-05-18T01:11:13.082841+00:00"}