{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:5RCIGVWRYKFT2DU3VN3WE3VLC5","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":"f758c09d3b41a060ee9015ba4ddd7351600c0b7eb8fe04086f2610ea5f1efa45","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-08-12T22:23:20Z","title_canon_sha256":"61a627b473ca6e70c0662d7647087af43465f0892d05a9a16d13ae21e661b2b9"},"schema_version":"1.0","source":{"id":"1908.04424","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.04424","created_at":"2026-07-04T23:55:13Z"},{"alias_kind":"arxiv_version","alias_value":"1908.04424v1","created_at":"2026-07-04T23:55:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.04424","created_at":"2026-07-04T23:55:13Z"},{"alias_kind":"pith_short_12","alias_value":"5RCIGVWRYKFT","created_at":"2026-07-04T23:55:13Z"},{"alias_kind":"pith_short_16","alias_value":"5RCIGVWRYKFT2DU3","created_at":"2026-07-04T23:55:13Z"},{"alias_kind":"pith_short_8","alias_value":"5RCIGVWR","created_at":"2026-07-04T23:55:13Z"}],"graph_snapshots":[{"event_id":"sha256:291c01d732e76ad0ee2dbc9f528f029dc7da6e247185c4639fd55adc532e0d1b","target":"graph","created_at":"2026-07-04T23:55:13Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.04424/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study small perturbations of a sectional hyperbolic set of a vector field on a compact manifold. Indeed, we obtain robustly finiteness of homoclinic classes on this scenary. Moreover, since attractor and repeller sets are particular cases of homoclinic classes, this result improve (A. M. L\\'opez B, Finiteness and existence of attractors and repellers on sectional hyperbolic sets, Discrete and Continuous Dynamical Systems-A 37).","authors_text":"A.E. Arbieto, A. M. L\\'opez B","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-08-12T22:23:20Z","title":"Finiteness of homoclinic classes on sectional hyperbolic sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.04424","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:a2c539ab80a02745b9c6be7e4dccdd83b66a77b165bf598489ca5dfbc7d8cf51","target":"record","created_at":"2026-07-04T23:55:13Z","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":"f758c09d3b41a060ee9015ba4ddd7351600c0b7eb8fe04086f2610ea5f1efa45","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-08-12T22:23:20Z","title_canon_sha256":"61a627b473ca6e70c0662d7647087af43465f0892d05a9a16d13ae21e661b2b9"},"schema_version":"1.0","source":{"id":"1908.04424","kind":"arxiv","version":1}},"canonical_sha256":"ec448356d1c28b3d0e9bab77626eab17720607223af06ce6d678797db0cbdf1b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ec448356d1c28b3d0e9bab77626eab17720607223af06ce6d678797db0cbdf1b","first_computed_at":"2026-07-04T23:55:13.666794Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:55:13.666794Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/1yRt79PoB9rIcKBJlg2bRPzZNU0Nru10WgltH9RF4+x1UJDgu3s8obNG0El42OuRroAUYBJaCqFx5yuRQgzDg==","signature_status":"signed_v1","signed_at":"2026-07-04T23:55:13.667143Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.04424","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a2c539ab80a02745b9c6be7e4dccdd83b66a77b165bf598489ca5dfbc7d8cf51","sha256:291c01d732e76ad0ee2dbc9f528f029dc7da6e247185c4639fd55adc532e0d1b"],"state_sha256":"6da1da478b5783dc03d7816b91ebfbd8d3b7dc4297bfe88732ae17b5ec8ccb32"}