{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:ZAO3ZUEUQEFT5TLN6NWRFRMIOU","short_pith_number":"pith:ZAO3ZUEU","schema_version":"1.0","canonical_sha256":"c81dbcd094810b3ecd6df36d12c588753c4c8992a7296294b48fbb7fdb8bd11e","source":{"kind":"arxiv","id":"1604.00431","version":3},"attestation_state":"computed","paper":{"title":"Homoclinic Bifurcations that Give Rise to Heterodimensional Cycles near A Saddle-Focus Equilibrium","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Dongchen Li","submitted_at":"2016-04-01T23:13:14Z","abstract_excerpt":"We show that heterodimensional cycles can be born at the bifurcations of a pair of homoclinic loops to a saddle-focus equilibrium for flows in dimension 4 and higher. In addition to the classical heterodimensional connection between two periodic orbits, we found two new types of heterodimensional connections: one is a heteroclinic between a periodic orbit of index 2 and a homoclinic loop, and the other connects a periodic orbit of index 3 to the saddle-focus equilibrium."},"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":"1604.00431","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-04-01T23:13:14Z","cross_cats_sorted":[],"title_canon_sha256":"605e9beb598f72b9658566b803f0b100d62724d7263cd669e4ec5b4ce6135598","abstract_canon_sha256":"4dd83c2b5de104950d3f04dca0b7406cbc2e2087bbcdd985b49e7eaf187bd9fc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:37.100700Z","signature_b64":"5n07uCBJmg6VT9gI7ATH7OdzM99ehW03YX+l5/DLhMK1A/IJBhjpwOwJ4b4yBNPeUjblC3zEf17N75yz+sNACA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c81dbcd094810b3ecd6df36d12c588753c4c8992a7296294b48fbb7fdb8bd11e","last_reissued_at":"2026-05-18T00:54:37.100069Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:37.100069Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Homoclinic Bifurcations that Give Rise to Heterodimensional Cycles near A Saddle-Focus Equilibrium","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Dongchen Li","submitted_at":"2016-04-01T23:13:14Z","abstract_excerpt":"We show that heterodimensional cycles can be born at the bifurcations of a pair of homoclinic loops to a saddle-focus equilibrium for flows in dimension 4 and higher. In addition to the classical heterodimensional connection between two periodic orbits, we found two new types of heterodimensional connections: one is a heteroclinic between a periodic orbit of index 2 and a homoclinic loop, and the other connects a periodic orbit of index 3 to the saddle-focus equilibrium."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.00431","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":"1604.00431","created_at":"2026-05-18T00:54:37.100159+00:00"},{"alias_kind":"arxiv_version","alias_value":"1604.00431v3","created_at":"2026-05-18T00:54:37.100159+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.00431","created_at":"2026-05-18T00:54:37.100159+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZAO3ZUEUQEFT","created_at":"2026-05-18T12:30:53.716459+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZAO3ZUEUQEFT5TLN","created_at":"2026-05-18T12:30:53.716459+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZAO3ZUEU","created_at":"2026-05-18T12:30:53.716459+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/ZAO3ZUEUQEFT5TLN6NWRFRMIOU","json":"https://pith.science/pith/ZAO3ZUEUQEFT5TLN6NWRFRMIOU.json","graph_json":"https://pith.science/api/pith-number/ZAO3ZUEUQEFT5TLN6NWRFRMIOU/graph.json","events_json":"https://pith.science/api/pith-number/ZAO3ZUEUQEFT5TLN6NWRFRMIOU/events.json","paper":"https://pith.science/paper/ZAO3ZUEU"},"agent_actions":{"view_html":"https://pith.science/pith/ZAO3ZUEUQEFT5TLN6NWRFRMIOU","download_json":"https://pith.science/pith/ZAO3ZUEUQEFT5TLN6NWRFRMIOU.json","view_paper":"https://pith.science/paper/ZAO3ZUEU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1604.00431&json=true","fetch_graph":"https://pith.science/api/pith-number/ZAO3ZUEUQEFT5TLN6NWRFRMIOU/graph.json","fetch_events":"https://pith.science/api/pith-number/ZAO3ZUEUQEFT5TLN6NWRFRMIOU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZAO3ZUEUQEFT5TLN6NWRFRMIOU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZAO3ZUEUQEFT5TLN6NWRFRMIOU/action/storage_attestation","attest_author":"https://pith.science/pith/ZAO3ZUEUQEFT5TLN6NWRFRMIOU/action/author_attestation","sign_citation":"https://pith.science/pith/ZAO3ZUEUQEFT5TLN6NWRFRMIOU/action/citation_signature","submit_replication":"https://pith.science/pith/ZAO3ZUEUQEFT5TLN6NWRFRMIOU/action/replication_record"}},"created_at":"2026-05-18T00:54:37.100159+00:00","updated_at":"2026-05-18T00:54:37.100159+00:00"}