{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:PNU34XSSM6FWE4YZMEEHQQPS2P","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":"861a45ef9cfd6ae5bb07252ef9263cda70795b76be02ccac63ed26a1085f840d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-10-19T14:16:43Z","title_canon_sha256":"d4637c6c3adc987b6dcffa16acf2436ec57460f1e501a6bb43ef8b157e5a9a6b"},"schema_version":"1.0","source":{"id":"1310.5233","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.5233","created_at":"2026-05-18T01:46:57Z"},{"alias_kind":"arxiv_version","alias_value":"1310.5233v1","created_at":"2026-05-18T01:46:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.5233","created_at":"2026-05-18T01:46:57Z"},{"alias_kind":"pith_short_12","alias_value":"PNU34XSSM6FW","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"PNU34XSSM6FWE4YZ","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"PNU34XSS","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:9432e4f44f926ae2561d9613af3160d3feee22138ab97d2b4d2a5cb95f85a2e4","target":"graph","created_at":"2026-05-18T01:46:57Z","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":"Let a system of differential equations possess a saddle-node periodic orbit such that every orbit in its unstable manifold is homoclinic, i.e. the unstable manifold is a subset of the (global) stable manifold. We study several bifurcation cases where the splitting of such a homoclinic connection causes the Blue Sky Catastrophe, including the onset of complex dynamics. The birth of an invariant torus or a Klein bottle is also described.","authors_text":"Andrey Shilnikov, Dmitry Turaev, Leonid Shilnikov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-10-19T14:16:43Z","title":"Showcase of Blue Sky Catastrophes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.5233","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:bb8966261b08590e6d89e54b3c6f3eaa4386592616b3e1ab6687346a6354d977","target":"record","created_at":"2026-05-18T01:46:57Z","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":"861a45ef9cfd6ae5bb07252ef9263cda70795b76be02ccac63ed26a1085f840d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-10-19T14:16:43Z","title_canon_sha256":"d4637c6c3adc987b6dcffa16acf2436ec57460f1e501a6bb43ef8b157e5a9a6b"},"schema_version":"1.0","source":{"id":"1310.5233","kind":"arxiv","version":1}},"canonical_sha256":"7b69be5e52678b62731961087841f2d3f08daa81d58681a01b6cb0a698f8c5f6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7b69be5e52678b62731961087841f2d3f08daa81d58681a01b6cb0a698f8c5f6","first_computed_at":"2026-05-18T01:46:57.505845Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:46:57.505845Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FuyEudpwI32xZiXzCsp5xdSLC3HuoLY4IDggBIozRqVsrZRI5JrtOb32n5A1fKsjP+gseZ2LGbwAJSE/pVc+DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:46:57.506636Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.5233","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bb8966261b08590e6d89e54b3c6f3eaa4386592616b3e1ab6687346a6354d977","sha256:9432e4f44f926ae2561d9613af3160d3feee22138ab97d2b4d2a5cb95f85a2e4"],"state_sha256":"7c6ebdca87638eb505928ae37b0c8a17cde70ce50345a2f7598a95029ae8eb07"}