{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:XUNVMSUIT77UFKD6VUZRU3GK6Y","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"6b61e0244ac3833566068ff1182c93c334f3e0264e1d67c44d7b5023fd00d3d6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-10-16T02:29:05Z","title_canon_sha256":"ef1eb85e350b7be5d17ad9ef2cc821d0405357bb8b6c0919c1a197f14f5b7cde"},"schema_version":"1.0","source":{"id":"1010.3308","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.3308","created_at":"2026-05-18T04:39:09Z"},{"alias_kind":"arxiv_version","alias_value":"1010.3308v1","created_at":"2026-05-18T04:39:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.3308","created_at":"2026-05-18T04:39:09Z"},{"alias_kind":"pith_short_12","alias_value":"XUNVMSUIT77U","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"XUNVMSUIT77UFKD6","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"XUNVMSUI","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:f40fe0efd66701715171d3f7f148d359ca23c19f2d77cce30de8821e19120d4b","target":"graph","created_at":"2026-05-18T04:39:09Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We give a description of the $\\Cone$-interior ($\\Int^1(\\OrientSh)$) of the set of smooth vector fields on a smooth closed manifold that have the oriented shadowing property. A special class $\\Bb$ of vector fields that are not structurally stable is introduced. It is shown that the set $\\Int^1(\\OrientSh\\setminus\\Bb)$ coincides with the set of structurally stable vector fields. An example of a field of the class $\\Bb$ belonging to $\\Int^1(\\OrientSh)$ is given. Bibliography: 18 titles.","authors_text":"Sergei Yu. Pilyugin, Sergey Tikhomirov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-10-16T02:29:05Z","title":"Vector Fields with the Oriented Shadowing Property"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.3308","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:feef9ff7de340e6a387cd2c73d4d8528a50088535b2e68e141e2bd8603605ae6","target":"record","created_at":"2026-05-18T04:39:09Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"6b61e0244ac3833566068ff1182c93c334f3e0264e1d67c44d7b5023fd00d3d6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-10-16T02:29:05Z","title_canon_sha256":"ef1eb85e350b7be5d17ad9ef2cc821d0405357bb8b6c0919c1a197f14f5b7cde"},"schema_version":"1.0","source":{"id":"1010.3308","kind":"arxiv","version":1}},"canonical_sha256":"bd1b564a889fff42a87ead331a6ccaf608623986729ee8c40aaaf6dadee3d4cf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bd1b564a889fff42a87ead331a6ccaf608623986729ee8c40aaaf6dadee3d4cf","first_computed_at":"2026-05-18T04:39:09.531469Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:39:09.531469Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"25wSESzKMvOmPSD3GutGu31cXJoo8PjxlNDB/RkkA0vg2JYFfwyKU54xSOtp7bepqFFCLk69i5dzenUGlPmKBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:39:09.532096Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.3308","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:feef9ff7de340e6a387cd2c73d4d8528a50088535b2e68e141e2bd8603605ae6","sha256:f40fe0efd66701715171d3f7f148d359ca23c19f2d77cce30de8821e19120d4b"],"state_sha256":"56e53b88df2d6d89e1256d34dbe6fc68d85c2681a955a4288d90a5dccad15437"}