{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:V6CHS6QFTAQY2VI654WFSUBDB7","short_pith_number":"pith:V6CHS6QF","canonical_record":{"source":{"id":"1308.1734","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-08-08T02:03:44Z","cross_cats_sorted":[],"title_canon_sha256":"02b662aee51b8205fb0e74bd462e0acd62accf70c57795a8330a6fdc6a85b531","abstract_canon_sha256":"787190af29be8be44cff9561786023164c7cb0e4718b00db818a9a2d5ff5b2de"},"schema_version":"1.0"},"canonical_sha256":"af84797a0598218d551eef2c5950230feea6f755de0dec7bed3d3bd9f4fb1e20","source":{"kind":"arxiv","id":"1308.1734","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.1734","created_at":"2026-05-18T03:16:27Z"},{"alias_kind":"arxiv_version","alias_value":"1308.1734v1","created_at":"2026-05-18T03:16:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.1734","created_at":"2026-05-18T03:16:27Z"},{"alias_kind":"pith_short_12","alias_value":"V6CHS6QFTAQY","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"V6CHS6QFTAQY2VI6","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"V6CHS6QF","created_at":"2026-05-18T12:28:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:V6CHS6QFTAQY2VI654WFSUBDB7","target":"record","payload":{"canonical_record":{"source":{"id":"1308.1734","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-08-08T02:03:44Z","cross_cats_sorted":[],"title_canon_sha256":"02b662aee51b8205fb0e74bd462e0acd62accf70c57795a8330a6fdc6a85b531","abstract_canon_sha256":"787190af29be8be44cff9561786023164c7cb0e4718b00db818a9a2d5ff5b2de"},"schema_version":"1.0"},"canonical_sha256":"af84797a0598218d551eef2c5950230feea6f755de0dec7bed3d3bd9f4fb1e20","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:16:27.912256Z","signature_b64":"8Adqhs18VZfRqxEjmysiH8/v+xZ8EVKIDzOb6OkdO26OMdu6zBjr4XGPfIH7Y67Vxnw6oR+h41QyDi+8rHYnCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"af84797a0598218d551eef2c5950230feea6f755de0dec7bed3d3bd9f4fb1e20","last_reissued_at":"2026-05-18T03:16:27.911692Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:16:27.911692Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.1734","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:16:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Eac03fzgo1n3s0bzF6Q1Td2WqCBBtzk/B6uEwCHvlp3UeyL/5Fx8VevKpngzGgm79l63ZR0VUONybc80eIQMDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T17:22:02.638547Z"},"content_sha256":"fc37553f3aab470aa9262da05d222789af1294e933d81b33b0154fcb4974b0e7","schema_version":"1.0","event_id":"sha256:fc37553f3aab470aa9262da05d222789af1294e933d81b33b0154fcb4974b0e7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:V6CHS6QFTAQY2VI654WFSUBDB7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Existence of attractors, homoclinic tangencies and singular hyperbolicity for flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"A. Arbieto, A. Rojas, B. Santiago","submitted_at":"2013-08-08T02:03:44Z","abstract_excerpt":"We prove that every $C^1$ generic three-dimensional flow has either infinitely many sinks, or, infinitely many hyperbolic or singular-hyperbolic attractors whose basins form a full Lebesgue measure set. We also prove in the orientable case that the set of accumulation points of the sinks of a $C^1$ generic three-dimensional flow has no dominated splitting with respect to the linear Poincar\\'e flow. As a corollary we obtain that every three-dimensional flow can be $C^1$ approximated by flows with homoclinic tangencies or by singular-Axiom A flows."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.1734","kind":"arxiv","version":1},"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":"2026-05-18T03:16:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ViWezZ/3LRGMoHamBP25rqRoTLveIhqMqb4kwjMVUPmQflb5ACCtTIiuQk42dt/KKFox8IuKjXd2c+XQ9g1GDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T17:22:02.639332Z"},"content_sha256":"a8271751308c1b43178b6fd1c52bb7451eecef8c5804e67e63139e1c154c3635","schema_version":"1.0","event_id":"sha256:a8271751308c1b43178b6fd1c52bb7451eecef8c5804e67e63139e1c154c3635"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V6CHS6QFTAQY2VI654WFSUBDB7/bundle.json","state_url":"https://pith.science/pith/V6CHS6QFTAQY2VI654WFSUBDB7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V6CHS6QFTAQY2VI654WFSUBDB7/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":"2026-05-31T17:22:02Z","links":{"resolver":"https://pith.science/pith/V6CHS6QFTAQY2VI654WFSUBDB7","bundle":"https://pith.science/pith/V6CHS6QFTAQY2VI654WFSUBDB7/bundle.json","state":"https://pith.science/pith/V6CHS6QFTAQY2VI654WFSUBDB7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V6CHS6QFTAQY2VI654WFSUBDB7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:V6CHS6QFTAQY2VI654WFSUBDB7","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":"787190af29be8be44cff9561786023164c7cb0e4718b00db818a9a2d5ff5b2de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-08-08T02:03:44Z","title_canon_sha256":"02b662aee51b8205fb0e74bd462e0acd62accf70c57795a8330a6fdc6a85b531"},"schema_version":"1.0","source":{"id":"1308.1734","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.1734","created_at":"2026-05-18T03:16:27Z"},{"alias_kind":"arxiv_version","alias_value":"1308.1734v1","created_at":"2026-05-18T03:16:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.1734","created_at":"2026-05-18T03:16:27Z"},{"alias_kind":"pith_short_12","alias_value":"V6CHS6QFTAQY","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"V6CHS6QFTAQY2VI6","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"V6CHS6QF","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:a8271751308c1b43178b6fd1c52bb7451eecef8c5804e67e63139e1c154c3635","target":"graph","created_at":"2026-05-18T03:16:27Z","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 prove that every $C^1$ generic three-dimensional flow has either infinitely many sinks, or, infinitely many hyperbolic or singular-hyperbolic attractors whose basins form a full Lebesgue measure set. We also prove in the orientable case that the set of accumulation points of the sinks of a $C^1$ generic three-dimensional flow has no dominated splitting with respect to the linear Poincar\\'e flow. As a corollary we obtain that every three-dimensional flow can be $C^1$ approximated by flows with homoclinic tangencies or by singular-Axiom A flows.","authors_text":"A. Arbieto, A. Rojas, B. Santiago","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-08-08T02:03:44Z","title":"Existence of attractors, homoclinic tangencies and singular hyperbolicity for flows"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.1734","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:fc37553f3aab470aa9262da05d222789af1294e933d81b33b0154fcb4974b0e7","target":"record","created_at":"2026-05-18T03:16:27Z","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":"787190af29be8be44cff9561786023164c7cb0e4718b00db818a9a2d5ff5b2de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-08-08T02:03:44Z","title_canon_sha256":"02b662aee51b8205fb0e74bd462e0acd62accf70c57795a8330a6fdc6a85b531"},"schema_version":"1.0","source":{"id":"1308.1734","kind":"arxiv","version":1}},"canonical_sha256":"af84797a0598218d551eef2c5950230feea6f755de0dec7bed3d3bd9f4fb1e20","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"af84797a0598218d551eef2c5950230feea6f755de0dec7bed3d3bd9f4fb1e20","first_computed_at":"2026-05-18T03:16:27.911692Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:16:27.911692Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8Adqhs18VZfRqxEjmysiH8/v+xZ8EVKIDzOb6OkdO26OMdu6zBjr4XGPfIH7Y67Vxnw6oR+h41QyDi+8rHYnCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:16:27.912256Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.1734","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fc37553f3aab470aa9262da05d222789af1294e933d81b33b0154fcb4974b0e7","sha256:a8271751308c1b43178b6fd1c52bb7451eecef8c5804e67e63139e1c154c3635"],"state_sha256":"6a7efe7808cfa406044fe005d12901ce19be6901879c1528fb11b2824bc73f26"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CYrcPE2sNhFWUjbTB/JDO2nasNxrzKTebfbEM31PL7PPSg9hgrGqjHXJ5i8uelVlN6qYUT/81uw2xEysOVWQBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T17:22:02.643391Z","bundle_sha256":"33cc8cbf3e99c54acc703e3dbe011f9257968cbff27053c0786bef76c27800d4"}}