{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:MQPEEDXBS2DMVLM72QVHLHOW3D","short_pith_number":"pith:MQPEEDXB","schema_version":"1.0","canonical_sha256":"641e420ee19686caad9fd42a759dd6d8f73b8075625ab69de1a6e1dbc0ddcc79","source":{"kind":"arxiv","id":"1010.4937","version":2},"attestation_state":"computed","paper":{"title":"Diffeomorphisms with various $C^1$ stable properties","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Wenxiang Sun, Xueting Tian","submitted_at":"2010-10-24T07:22:36Z","abstract_excerpt":"Let $M$ be a smooth compact manifold and $\\Lambda$ be a compact invariant set. In this paper we prove that for every robustly transitive set $\\Lambda$, $f|_\\Lambda$ satisfies a $C^1-$generic-stable shadowable property (resp., $C^1-$generic-stable transitive specification property or $C^1-$generic-stable barycenter property) if and only if $\\Lambda$ is a hyperbolic basic set. In particular, $f|_\\Lambda$ satisfies a $C^1-$stable shadowable property (resp., $C^1-$stable transitive specification property or $C^1-$stable barycenter property) if and only if $\\Lambda$ is a hyperbolic basic set. Simil"},"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":"1010.4937","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.DS","submitted_at":"2010-10-24T07:22:36Z","cross_cats_sorted":[],"title_canon_sha256":"6c4f43ee505d6acdae3c2bb10a3da035dd3827d9b25482c2ed6b0bad5b326d09","abstract_canon_sha256":"e99179f771898765a3c0d9cb2fd250d80b79d1fac145fffdcb81aee9b4eac4e9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:04:43.742406Z","signature_b64":"Lz5OlmkJ0BJve1ZtnzxQ7CfXQweU9A5crvqUivr8FPoQcHQCR3F97uWvpyfVf0NYVJwQ6y2VqkV3vCWOZjlGBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"641e420ee19686caad9fd42a759dd6d8f73b8075625ab69de1a6e1dbc0ddcc79","last_reissued_at":"2026-05-18T04:04:43.741934Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:04:43.741934Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Diffeomorphisms with various $C^1$ stable properties","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Wenxiang Sun, Xueting Tian","submitted_at":"2010-10-24T07:22:36Z","abstract_excerpt":"Let $M$ be a smooth compact manifold and $\\Lambda$ be a compact invariant set. In this paper we prove that for every robustly transitive set $\\Lambda$, $f|_\\Lambda$ satisfies a $C^1-$generic-stable shadowable property (resp., $C^1-$generic-stable transitive specification property or $C^1-$generic-stable barycenter property) if and only if $\\Lambda$ is a hyperbolic basic set. In particular, $f|_\\Lambda$ satisfies a $C^1-$stable shadowable property (resp., $C^1-$stable transitive specification property or $C^1-$stable barycenter property) if and only if $\\Lambda$ is a hyperbolic basic set. Simil"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.4937","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":"1010.4937","created_at":"2026-05-18T04:04:43.742014+00:00"},{"alias_kind":"arxiv_version","alias_value":"1010.4937v2","created_at":"2026-05-18T04:04:43.742014+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.4937","created_at":"2026-05-18T04:04:43.742014+00:00"},{"alias_kind":"pith_short_12","alias_value":"MQPEEDXBS2DM","created_at":"2026-05-18T12:26:10.704358+00:00"},{"alias_kind":"pith_short_16","alias_value":"MQPEEDXBS2DMVLM7","created_at":"2026-05-18T12:26:10.704358+00:00"},{"alias_kind":"pith_short_8","alias_value":"MQPEEDXB","created_at":"2026-05-18T12:26:10.704358+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/MQPEEDXBS2DMVLM72QVHLHOW3D","json":"https://pith.science/pith/MQPEEDXBS2DMVLM72QVHLHOW3D.json","graph_json":"https://pith.science/api/pith-number/MQPEEDXBS2DMVLM72QVHLHOW3D/graph.json","events_json":"https://pith.science/api/pith-number/MQPEEDXBS2DMVLM72QVHLHOW3D/events.json","paper":"https://pith.science/paper/MQPEEDXB"},"agent_actions":{"view_html":"https://pith.science/pith/MQPEEDXBS2DMVLM72QVHLHOW3D","download_json":"https://pith.science/pith/MQPEEDXBS2DMVLM72QVHLHOW3D.json","view_paper":"https://pith.science/paper/MQPEEDXB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1010.4937&json=true","fetch_graph":"https://pith.science/api/pith-number/MQPEEDXBS2DMVLM72QVHLHOW3D/graph.json","fetch_events":"https://pith.science/api/pith-number/MQPEEDXBS2DMVLM72QVHLHOW3D/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MQPEEDXBS2DMVLM72QVHLHOW3D/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MQPEEDXBS2DMVLM72QVHLHOW3D/action/storage_attestation","attest_author":"https://pith.science/pith/MQPEEDXBS2DMVLM72QVHLHOW3D/action/author_attestation","sign_citation":"https://pith.science/pith/MQPEEDXBS2DMVLM72QVHLHOW3D/action/citation_signature","submit_replication":"https://pith.science/pith/MQPEEDXBS2DMVLM72QVHLHOW3D/action/replication_record"}},"created_at":"2026-05-18T04:04:43.742014+00:00","updated_at":"2026-05-18T04:04:43.742014+00:00"}