{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:VHQCUV5H4UZY7UVZMCU37YFR7U","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":"44366e94ab3394fc81f40c243a331a9d4b59542338a9dc8e4a60d3ed9b49e4ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-12-17T18:53:35Z","title_canon_sha256":"877b3ee4da4798f065eca5e5e256182a48926f9b9745413beb13ef2893a88fe6"},"schema_version":"1.0","source":{"id":"0912.3490","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.3490","created_at":"2026-05-18T02:10:15Z"},{"alias_kind":"arxiv_version","alias_value":"0912.3490v1","created_at":"2026-05-18T02:10:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.3490","created_at":"2026-05-18T02:10:15Z"},{"alias_kind":"pith_short_12","alias_value":"VHQCUV5H4UZY","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"VHQCUV5H4UZY7UVZ","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"VHQCUV5H","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:9f4ef00f5e4f1e9d0698b86c7f560adb582b264fc8d573ada0f713e688e82f6d","target":"graph","created_at":"2026-05-18T02:10:15Z","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":"Consider a family of planar systems depending on two parameters $(n,b)$ and having at most one limit cycle. Assume that the limit cycle disappears at some homoclinic (or heteroclinic) connection when $\\Phi(n,b)=0.$ We present a method that allows to obtain a sequence of explicit algebraic lower and upper bounds for the bifurcation set ${\\Phi(n,b)=0}.$ The method is applied to two quadratic families, one of them is the well-known Bogdanov-Takens system. One of the results that we obtain for this system is the bifurcation curve for small values of $n$, given by $b=\\frac5 7 n^{1/2}+{72/2401}n- {3","authors_text":"Armengol Gasull, Hector Giacomini, Joan Torregrosa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-12-17T18:53:35Z","title":"Some results on homoclinic and heteroclinic connections in planar systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.3490","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":"sha256:8b2dc1cbd93978d056c5b9dfea9917d698ff1d01726c9ad91531ab05a1a31097","target":"record","created_at":"2026-05-18T02:10:15Z","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":"44366e94ab3394fc81f40c243a331a9d4b59542338a9dc8e4a60d3ed9b49e4ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-12-17T18:53:35Z","title_canon_sha256":"877b3ee4da4798f065eca5e5e256182a48926f9b9745413beb13ef2893a88fe6"},"schema_version":"1.0","source":{"id":"0912.3490","kind":"arxiv","version":1}},"canonical_sha256":"a9e02a57a7e5338fd2b960a9bfe0b1fd0321bb601613c0a68d2ea0976844b300","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a9e02a57a7e5338fd2b960a9bfe0b1fd0321bb601613c0a68d2ea0976844b300","first_computed_at":"2026-05-18T02:10:15.877157Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:10:15.877157Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b151MvUGPtM4ly18aLIqjfaS4H9MrtZDIrD2dGzorqiONG1lD3ylBjjsbC2BQLVxoI14DEDgSSjOEoSF/mUIAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:10:15.877741Z","signed_message":"canonical_sha256_bytes"},"source_id":"0912.3490","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8b2dc1cbd93978d056c5b9dfea9917d698ff1d01726c9ad91531ab05a1a31097","sha256:9f4ef00f5e4f1e9d0698b86c7f560adb582b264fc8d573ada0f713e688e82f6d"],"state_sha256":"31a72b1d116a53e982b39367f42571ab02b4e094cf94645df583b8624f84d845"}