{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:6MWMFYEZCWXOUDNGEOBXYFUWDE","short_pith_number":"pith:6MWMFYEZ","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"},"canonical_sha256":"f32cc2e09915aeea0da623837c16961919c693110750cc43a5a9f20f68a1a2e0","source":{"kind":"arxiv","id":"1404.4860","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.4860","created_at":"2026-05-18T02:27:57Z"},{"alias_kind":"arxiv_version","alias_value":"1404.4860v3","created_at":"2026-05-18T02:27:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.4860","created_at":"2026-05-18T02:27:57Z"},{"alias_kind":"pith_short_12","alias_value":"6MWMFYEZCWXO","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6MWMFYEZCWXOUDNG","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6MWMFYEZ","created_at":"2026-05-18T12:28:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:6MWMFYEZCWXOUDNGEOBXYFUWDE","target":"record","payload":{"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"},"canonical_sha256":"f32cc2e09915aeea0da623837c16961919c693110750cc43a5a9f20f68a1a2e0","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"},"source_kind":"arxiv","source_id":"1404.4860","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:27:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IjfJ9ZGod2Nz8UCj+oRaKUJ9kE1GfbbzD8qHeTt4k2xK/SaSkazU4so8aNROpCSKzXSRkOCL3aeJPPDfmoDNCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T06:47:02.299100Z"},"content_sha256":"c757b59f84f46fec853edb5a3246038716a2ab6d0954a2fe68b984f3f1714169","schema_version":"1.0","event_id":"sha256:c757b59f84f46fec853edb5a3246038716a2ab6d0954a2fe68b984f3f1714169"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:6MWMFYEZCWXOUDNGEOBXYFUWDE","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:27:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RIHErzTrWdBxrEDSwbmuFZEWltsfaniEBP0UoFbIJwcHeB8awLSNsJ37TsRWbBhhzWyXqxvZT/Gaj4Qmhj3LBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T06:47:02.299462Z"},"content_sha256":"acaaeba478c7d1d05224ff6c72c613cfc9025d0943688fca5c4fc01c9e4a0300","schema_version":"1.0","event_id":"sha256:acaaeba478c7d1d05224ff6c72c613cfc9025d0943688fca5c4fc01c9e4a0300"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6MWMFYEZCWXOUDNGEOBXYFUWDE/bundle.json","state_url":"https://pith.science/pith/6MWMFYEZCWXOUDNGEOBXYFUWDE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6MWMFYEZCWXOUDNGEOBXYFUWDE/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-29T06:47:02Z","links":{"resolver":"https://pith.science/pith/6MWMFYEZCWXOUDNGEOBXYFUWDE","bundle":"https://pith.science/pith/6MWMFYEZCWXOUDNGEOBXYFUWDE/bundle.json","state":"https://pith.science/pith/6MWMFYEZCWXOUDNGEOBXYFUWDE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6MWMFYEZCWXOUDNGEOBXYFUWDE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:6MWMFYEZCWXOUDNGEOBXYFUWDE","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":"abd4d746b5ae0ef56175ada575929ed3dc028128e045a3da5a35414deeb86733","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-04-18T19:20:05Z","title_canon_sha256":"2504eda60a674cba86821e7ebfaa0d13ebe62bcce0202f014bfa689aff515440"},"schema_version":"1.0","source":{"id":"1404.4860","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.4860","created_at":"2026-05-18T02:27:57Z"},{"alias_kind":"arxiv_version","alias_value":"1404.4860v3","created_at":"2026-05-18T02:27:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.4860","created_at":"2026-05-18T02:27:57Z"},{"alias_kind":"pith_short_12","alias_value":"6MWMFYEZCWXO","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6MWMFYEZCWXOUDNG","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6MWMFYEZ","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:acaaeba478c7d1d05224ff6c72c613cfc9025d0943688fca5c4fc01c9e4a0300","target":"graph","created_at":"2026-05-18T02:27:57Z","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":"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","authors_text":"Pedro Teixeira","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-04-18T19:20:05Z","title":"Topological detection of Lyapunov instability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.4860","kind":"arxiv","version":3},"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:c757b59f84f46fec853edb5a3246038716a2ab6d0954a2fe68b984f3f1714169","target":"record","created_at":"2026-05-18T02:27:57Z","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":"abd4d746b5ae0ef56175ada575929ed3dc028128e045a3da5a35414deeb86733","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-04-18T19:20:05Z","title_canon_sha256":"2504eda60a674cba86821e7ebfaa0d13ebe62bcce0202f014bfa689aff515440"},"schema_version":"1.0","source":{"id":"1404.4860","kind":"arxiv","version":3}},"canonical_sha256":"f32cc2e09915aeea0da623837c16961919c693110750cc43a5a9f20f68a1a2e0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f32cc2e09915aeea0da623837c16961919c693110750cc43a5a9f20f68a1a2e0","first_computed_at":"2026-05-18T02:27:57.173485Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:57.173485Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KRuZW4Acv8pvKaCZyz/y7FOXz+m6qlwn9tOFnHvPZGBgL8g86CxcTTdf4vcQm6f5vHPBmWf5NNN8jnvGduGtAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:57.174006Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.4860","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c757b59f84f46fec853edb5a3246038716a2ab6d0954a2fe68b984f3f1714169","sha256:acaaeba478c7d1d05224ff6c72c613cfc9025d0943688fca5c4fc01c9e4a0300"],"state_sha256":"b42b34d4a8ec40e23b700e6efc4a31b3cae09681395c2cbd6ecada99cf6df97e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CcjadXUVvv4JyF3ZTQ6B3iXMedfme//k+JdVr29hhbwemJHNPhkMHCZwSZGJR2FTjGe+wx1oBKNrZCClbPF2Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T06:47:02.301354Z","bundle_sha256":"446fe477f6baf8b1df7a405b39af9a6decafd0a2baf4bfa3fa46f49869f5cea3"}}