{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:CAIGD64FIRRK7RE5PKY4SXCOSH","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":"5ca60e9e54b81c4df75e1e7e1cb58d1b59c24043a019d778c73d6cd606c83b6c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-12-11T19:51:59Z","title_canon_sha256":"7106b314603222ae7741258587849a32ede9a0a75949fa0a65372881f65d79d8"},"schema_version":"1.0","source":{"id":"1812.04665","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.04665","created_at":"2026-05-17T23:58:29Z"},{"alias_kind":"arxiv_version","alias_value":"1812.04665v1","created_at":"2026-05-17T23:58:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.04665","created_at":"2026-05-17T23:58:29Z"},{"alias_kind":"pith_short_12","alias_value":"CAIGD64FIRRK","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"CAIGD64FIRRK7RE5","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"CAIGD64F","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:0636767c872cdb3383c805d9b4d9475cbfb44568b7f6f752761bbcc78c04e88f","target":"graph","created_at":"2026-05-17T23:58:29Z","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":"In this paper we describe the bifurcation diagram of the$2$-parameter family of vector fields $\\dot z = z(z^k+\\epsilon_1z+\\epsilon_0)$ over $\\mathbb C\\mathbb P^1$ for $(\\epsilon_1,\\epsilon_0)\\in \\mathbb C^2$. There are two kinds of bifurcations: bifurcations of parabolic points and bifurcations of homoclinic loops through infinity. The latter are studied using the tool of the periodgon introduced in a particular case in \\cite{CR}, and then generalized in \\cite{KR}. We apply the results to the bifurcation diagram of a generic germ of 2-parameter analytic unfolding preserving the origin of the v","authors_text":"Christiane Rousseau","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-12-11T19:51:59Z","title":"Two-parameter unfolding of a parabolic point of a vector field in $\\mathbb C$ fixing the origin"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.04665","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":"sha256:35972a0cbed2dd770ece7aa93eeb95b4bd40177d772dd619821586f8e611ca03","target":"record","created_at":"2026-05-17T23:58:29Z","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":"5ca60e9e54b81c4df75e1e7e1cb58d1b59c24043a019d778c73d6cd606c83b6c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-12-11T19:51:59Z","title_canon_sha256":"7106b314603222ae7741258587849a32ede9a0a75949fa0a65372881f65d79d8"},"schema_version":"1.0","source":{"id":"1812.04665","kind":"arxiv","version":1}},"canonical_sha256":"101061fb854462afc49d7ab1c95c4e91db0e05859482b629a9466e2b1b51bff5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"101061fb854462afc49d7ab1c95c4e91db0e05859482b629a9466e2b1b51bff5","first_computed_at":"2026-05-17T23:58:29.884045Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:29.884045Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5mTVxnC+/OVUjsKauT/A/8aUn+MfwSX59WBrIkrSekXidOxmgoGmW/9fuP7ahv2f+/wz9+5Q/T2jtrjPaCBOAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:29.884872Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.04665","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:35972a0cbed2dd770ece7aa93eeb95b4bd40177d772dd619821586f8e611ca03","sha256:0636767c872cdb3383c805d9b4d9475cbfb44568b7f6f752761bbcc78c04e88f"],"state_sha256":"d1402112d03b757ed117ceba9935cfe6b6fb787e1e00dd9c47cd375be76ae59a"}