{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:6LFKYE64ZFLOONB6D3DPNQLE5N","short_pith_number":"pith:6LFKYE64","schema_version":"1.0","canonical_sha256":"f2caac13dcc956e7343e1ec6f6c164eb5031b8f2ef8b95178de2e0fb07391e81","source":{"kind":"arxiv","id":"1404.3545","version":2},"attestation_state":"computed","paper":{"title":"Oriented shadowing property and $\\Omega$-stability for vector fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Ming Li, Sergey B. Tikhomirov, Shaobo Gan","submitted_at":"2014-04-14T11:39:53Z","abstract_excerpt":"We call that a vector field has the oriented shadowing property if for any $\\varepsilon>0$ there is $d>0$ such that each $d$-pseudo orbit is $\\varepsilon$-oriented shadowed by some real orbit. In this paper, we show that the $C^1$-interior of the set of vector fields with the oriented shadowing property is contained in the set of vector fields with the $\\Omega$-stability."},"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":"1404.3545","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-04-14T11:39:53Z","cross_cats_sorted":[],"title_canon_sha256":"f1c5faa77336d90ec0babaf08bcf5513d4575f3c6e041d89c9e109324df1e3d8","abstract_canon_sha256":"9ff37d76825f9387e9467af76edcb84f0a89589038fee97a7bcb0ae742fd9883"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:31.435186Z","signature_b64":"uCA5vdqm9bfizBCjdvCWuNu8x/N/ibu5WfLJCtKq38Uv9Ji+SBnHZrRAYlQ7UitCpiGuo7LPBoaTVxPyoaUeAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f2caac13dcc956e7343e1ec6f6c164eb5031b8f2ef8b95178de2e0fb07391e81","last_reissued_at":"2026-05-18T02:45:31.434554Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:31.434554Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Oriented shadowing property and $\\Omega$-stability for vector fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Ming Li, Sergey B. Tikhomirov, Shaobo Gan","submitted_at":"2014-04-14T11:39:53Z","abstract_excerpt":"We call that a vector field has the oriented shadowing property if for any $\\varepsilon>0$ there is $d>0$ such that each $d$-pseudo orbit is $\\varepsilon$-oriented shadowed by some real orbit. In this paper, we show that the $C^1$-interior of the set of vector fields with the oriented shadowing property is contained in the set of vector fields with the $\\Omega$-stability."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.3545","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":"1404.3545","created_at":"2026-05-18T02:45:31.434670+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.3545v2","created_at":"2026-05-18T02:45:31.434670+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.3545","created_at":"2026-05-18T02:45:31.434670+00:00"},{"alias_kind":"pith_short_12","alias_value":"6LFKYE64ZFLO","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_16","alias_value":"6LFKYE64ZFLOONB6","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_8","alias_value":"6LFKYE64","created_at":"2026-05-18T12:28:16.859392+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/6LFKYE64ZFLOONB6D3DPNQLE5N","json":"https://pith.science/pith/6LFKYE64ZFLOONB6D3DPNQLE5N.json","graph_json":"https://pith.science/api/pith-number/6LFKYE64ZFLOONB6D3DPNQLE5N/graph.json","events_json":"https://pith.science/api/pith-number/6LFKYE64ZFLOONB6D3DPNQLE5N/events.json","paper":"https://pith.science/paper/6LFKYE64"},"agent_actions":{"view_html":"https://pith.science/pith/6LFKYE64ZFLOONB6D3DPNQLE5N","download_json":"https://pith.science/pith/6LFKYE64ZFLOONB6D3DPNQLE5N.json","view_paper":"https://pith.science/paper/6LFKYE64","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.3545&json=true","fetch_graph":"https://pith.science/api/pith-number/6LFKYE64ZFLOONB6D3DPNQLE5N/graph.json","fetch_events":"https://pith.science/api/pith-number/6LFKYE64ZFLOONB6D3DPNQLE5N/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6LFKYE64ZFLOONB6D3DPNQLE5N/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6LFKYE64ZFLOONB6D3DPNQLE5N/action/storage_attestation","attest_author":"https://pith.science/pith/6LFKYE64ZFLOONB6D3DPNQLE5N/action/author_attestation","sign_citation":"https://pith.science/pith/6LFKYE64ZFLOONB6D3DPNQLE5N/action/citation_signature","submit_replication":"https://pith.science/pith/6LFKYE64ZFLOONB6D3DPNQLE5N/action/replication_record"}},"created_at":"2026-05-18T02:45:31.434670+00:00","updated_at":"2026-05-18T02:45:31.434670+00:00"}