{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:BUZ2FM3CS5K4CVV3L22FFOMWJR","short_pith_number":"pith:BUZ2FM3C","canonical_record":{"source":{"id":"1810.06359","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-10-15T14:10:37Z","cross_cats_sorted":[],"title_canon_sha256":"a4578f9e57b25b37d5c4806f0da23b8797dba86498fe4273282be2bc8171b827","abstract_canon_sha256":"76d37743671b414c50b13d7853655f26924b5333f4a7548280bdec1c03d850d1"},"schema_version":"1.0"},"canonical_sha256":"0d33a2b3629755c156bb5eb452b9964c67ba1380bc45b8d492402630e20e571b","source":{"kind":"arxiv","id":"1810.06359","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.06359","created_at":"2026-05-17T23:41:45Z"},{"alias_kind":"arxiv_version","alias_value":"1810.06359v2","created_at":"2026-05-17T23:41:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.06359","created_at":"2026-05-17T23:41:45Z"},{"alias_kind":"pith_short_12","alias_value":"BUZ2FM3CS5K4","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"BUZ2FM3CS5K4CVV3","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"BUZ2FM3C","created_at":"2026-05-18T12:32:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:BUZ2FM3CS5K4CVV3L22FFOMWJR","target":"record","payload":{"canonical_record":{"source":{"id":"1810.06359","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-10-15T14:10:37Z","cross_cats_sorted":[],"title_canon_sha256":"a4578f9e57b25b37d5c4806f0da23b8797dba86498fe4273282be2bc8171b827","abstract_canon_sha256":"76d37743671b414c50b13d7853655f26924b5333f4a7548280bdec1c03d850d1"},"schema_version":"1.0"},"canonical_sha256":"0d33a2b3629755c156bb5eb452b9964c67ba1380bc45b8d492402630e20e571b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:45.860623Z","signature_b64":"bLfbONo0ZjbgNjxCafKk+LiFjbxi9LgYjQHbjwZKEmV3gziiNJiydbSRcrXzlr27DgmLv8a6eky0UBubLMw3CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0d33a2b3629755c156bb5eb452b9964c67ba1380bc45b8d492402630e20e571b","last_reissued_at":"2026-05-17T23:41:45.860154Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:45.860154Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.06359","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:41:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"We62zG48YF9G+y4gX+bk7iObKQneg9CNjAjT5naMEGzzHjxvGcIvUnHEiXW1a5TNOO/8yfXTZz57ALhnkFBYCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T08:38:09.563495Z"},"content_sha256":"983c50a3f25ed1e7d29958c059c9d2bb6d7a7af57bd5b9798faf50da29499d4a","schema_version":"1.0","event_id":"sha256:983c50a3f25ed1e7d29958c059c9d2bb6d7a7af57bd5b9798faf50da29499d4a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:BUZ2FM3CS5K4CVV3L22FFOMWJR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Chaos near a reversible homoclinic bifocus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Alexandre A. P. Rodrigues, Artem Raibekas, Pablo G. Barrientos","submitted_at":"2018-10-15T14:10:37Z","abstract_excerpt":"We show that any neighborhood of a non-degenerate reversible bifocal homoclinic orbit contains chaotic suspended invariant sets on $N$-symbols for all $N\\geq 2$. This will be achieved by showing switching associated with networks of secondary homoclinic orbits. We also prove the existence of super-homoclinic orbits (trajectories homoclinic to a network of homoclinic orbits), whose presence leads to a particularly rich structure."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.06359","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:41:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D49ElxC8tGKKC4rLx9m1mA3g6emGoiRk9mx85t322PG63j0pTZoF0281tDsGjB5d9cnRTgfEXUDX0eIINAOGDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T08:38:09.563836Z"},"content_sha256":"683133c2e6ba678f00d99b8501205c72a5b933ef0762e288a02d38f1b14d6f35","schema_version":"1.0","event_id":"sha256:683133c2e6ba678f00d99b8501205c72a5b933ef0762e288a02d38f1b14d6f35"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BUZ2FM3CS5K4CVV3L22FFOMWJR/bundle.json","state_url":"https://pith.science/pith/BUZ2FM3CS5K4CVV3L22FFOMWJR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BUZ2FM3CS5K4CVV3L22FFOMWJR/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":"2026-06-29T08:38:09Z","links":{"resolver":"https://pith.science/pith/BUZ2FM3CS5K4CVV3L22FFOMWJR","bundle":"https://pith.science/pith/BUZ2FM3CS5K4CVV3L22FFOMWJR/bundle.json","state":"https://pith.science/pith/BUZ2FM3CS5K4CVV3L22FFOMWJR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BUZ2FM3CS5K4CVV3L22FFOMWJR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:BUZ2FM3CS5K4CVV3L22FFOMWJR","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":"76d37743671b414c50b13d7853655f26924b5333f4a7548280bdec1c03d850d1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-10-15T14:10:37Z","title_canon_sha256":"a4578f9e57b25b37d5c4806f0da23b8797dba86498fe4273282be2bc8171b827"},"schema_version":"1.0","source":{"id":"1810.06359","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.06359","created_at":"2026-05-17T23:41:45Z"},{"alias_kind":"arxiv_version","alias_value":"1810.06359v2","created_at":"2026-05-17T23:41:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.06359","created_at":"2026-05-17T23:41:45Z"},{"alias_kind":"pith_short_12","alias_value":"BUZ2FM3CS5K4","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"BUZ2FM3CS5K4CVV3","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"BUZ2FM3C","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:683133c2e6ba678f00d99b8501205c72a5b933ef0762e288a02d38f1b14d6f35","target":"graph","created_at":"2026-05-17T23:41:45Z","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 show that any neighborhood of a non-degenerate reversible bifocal homoclinic orbit contains chaotic suspended invariant sets on $N$-symbols for all $N\\geq 2$. This will be achieved by showing switching associated with networks of secondary homoclinic orbits. We also prove the existence of super-homoclinic orbits (trajectories homoclinic to a network of homoclinic orbits), whose presence leads to a particularly rich structure.","authors_text":"Alexandre A. P. Rodrigues, Artem Raibekas, Pablo G. Barrientos","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-10-15T14:10:37Z","title":"Chaos near a reversible homoclinic bifocus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.06359","kind":"arxiv","version":2},"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":"sha256:983c50a3f25ed1e7d29958c059c9d2bb6d7a7af57bd5b9798faf50da29499d4a","target":"record","created_at":"2026-05-17T23:41:45Z","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":"76d37743671b414c50b13d7853655f26924b5333f4a7548280bdec1c03d850d1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-10-15T14:10:37Z","title_canon_sha256":"a4578f9e57b25b37d5c4806f0da23b8797dba86498fe4273282be2bc8171b827"},"schema_version":"1.0","source":{"id":"1810.06359","kind":"arxiv","version":2}},"canonical_sha256":"0d33a2b3629755c156bb5eb452b9964c67ba1380bc45b8d492402630e20e571b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0d33a2b3629755c156bb5eb452b9964c67ba1380bc45b8d492402630e20e571b","first_computed_at":"2026-05-17T23:41:45.860154Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:45.860154Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bLfbONo0ZjbgNjxCafKk+LiFjbxi9LgYjQHbjwZKEmV3gziiNJiydbSRcrXzlr27DgmLv8a6eky0UBubLMw3CA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:45.860623Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.06359","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:983c50a3f25ed1e7d29958c059c9d2bb6d7a7af57bd5b9798faf50da29499d4a","sha256:683133c2e6ba678f00d99b8501205c72a5b933ef0762e288a02d38f1b14d6f35"],"state_sha256":"3d9665daf18cec9f60453cd1664acb1520ea912266e37ee9c5f9559e487f3a4f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cmjYdH+8t3lF5yin9dMgWdKwpISfrZfR5F8t8we62rV3VhUp3Uy0SwpT+4GzgRy0w0RdZ98uxm6Y/zzlyq0dCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T08:38:09.565684Z","bundle_sha256":"50a3ac69e538d7b488ebec6ce29d73056724c6b68a98241ee6c71979a68c6e59"}}