{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:6MWMFYEZCWXOUDNGEOBXYFUWDE","short_pith_number":"pith:6MWMFYEZ","schema_version":"1.0","canonical_sha256":"f32cc2e09915aeea0da623837c16961919c693110750cc43a5a9f20f68a1a2e0","source":{"kind":"arxiv","id":"1404.4860","version":3},"attestation_state":"computed","paper":{"title":"Topological detection of Lyapunov instability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Pedro Teixeira","submitted_at":"2014-04-18T19:20:05Z","abstract_excerpt":"Given an arbitrary continuous flow on a manifold M, let CMin be the set of its compact minimal sets, endowed with the Hausdorff metric, and S the subset of those that are Lyapunov stable. A topological characterization of the interior of S, the set of Lyapunov stable compact minimal sets that are away from Lyapunov unstable ones is given, together with a description of the dynamics around it. In particular, int S is locally a Peano continuum (Peano curve) and each of its countably many connected components admits a complete geodesic metric.\n  This result establishes unexpected connections betw"},"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":"1404.4860","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-04-18T19:20:05Z","cross_cats_sorted":[],"title_canon_sha256":"2504eda60a674cba86821e7ebfaa0d13ebe62bcce0202f014bfa689aff515440","abstract_canon_sha256":"abd4d746b5ae0ef56175ada575929ed3dc028128e045a3da5a35414deeb86733"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:57.174006Z","signature_b64":"KRuZW4Acv8pvKaCZyz/y7FOXz+m6qlwn9tOFnHvPZGBgL8g86CxcTTdf4vcQm6f5vHPBmWf5NNN8jnvGduGtAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f32cc2e09915aeea0da623837c16961919c693110750cc43a5a9f20f68a1a2e0","last_reissued_at":"2026-05-18T02:27:57.173485Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:57.173485Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Topological detection of Lyapunov instability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Pedro Teixeira","submitted_at":"2014-04-18T19:20:05Z","abstract_excerpt":"Given an arbitrary continuous flow on a manifold M, let CMin be the set of its compact minimal sets, endowed with the Hausdorff metric, and S the subset of those that are Lyapunov stable. A topological characterization of the interior of S, the set of Lyapunov stable compact minimal sets that are away from Lyapunov unstable ones is given, together with a description of the dynamics around it. In particular, int S is locally a Peano continuum (Peano curve) and each of its countably many connected components admits a complete geodesic metric.\n  This result establishes unexpected connections betw"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.4860","kind":"arxiv","version":3},"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":"1404.4860","created_at":"2026-05-18T02:27:57.173572+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.4860v3","created_at":"2026-05-18T02:27:57.173572+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.4860","created_at":"2026-05-18T02:27:57.173572+00:00"},{"alias_kind":"pith_short_12","alias_value":"6MWMFYEZCWXO","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_16","alias_value":"6MWMFYEZCWXOUDNG","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_8","alias_value":"6MWMFYEZ","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/6MWMFYEZCWXOUDNGEOBXYFUWDE","json":"https://pith.science/pith/6MWMFYEZCWXOUDNGEOBXYFUWDE.json","graph_json":"https://pith.science/api/pith-number/6MWMFYEZCWXOUDNGEOBXYFUWDE/graph.json","events_json":"https://pith.science/api/pith-number/6MWMFYEZCWXOUDNGEOBXYFUWDE/events.json","paper":"https://pith.science/paper/6MWMFYEZ"},"agent_actions":{"view_html":"https://pith.science/pith/6MWMFYEZCWXOUDNGEOBXYFUWDE","download_json":"https://pith.science/pith/6MWMFYEZCWXOUDNGEOBXYFUWDE.json","view_paper":"https://pith.science/paper/6MWMFYEZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.4860&json=true","fetch_graph":"https://pith.science/api/pith-number/6MWMFYEZCWXOUDNGEOBXYFUWDE/graph.json","fetch_events":"https://pith.science/api/pith-number/6MWMFYEZCWXOUDNGEOBXYFUWDE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6MWMFYEZCWXOUDNGEOBXYFUWDE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6MWMFYEZCWXOUDNGEOBXYFUWDE/action/storage_attestation","attest_author":"https://pith.science/pith/6MWMFYEZCWXOUDNGEOBXYFUWDE/action/author_attestation","sign_citation":"https://pith.science/pith/6MWMFYEZCWXOUDNGEOBXYFUWDE/action/citation_signature","submit_replication":"https://pith.science/pith/6MWMFYEZCWXOUDNGEOBXYFUWDE/action/replication_record"}},"created_at":"2026-05-18T02:27:57.173572+00:00","updated_at":"2026-05-18T02:27:57.173572+00:00"}