{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:5JTPLVF5BBAY5YTSQ3J3CHIO7Y","short_pith_number":"pith:5JTPLVF5","schema_version":"1.0","canonical_sha256":"ea66f5d4bd08418ee27286d3b11d0efe122e9932f31daf912de2d3ca3f7945ef","source":{"kind":"arxiv","id":"1210.6205","version":1},"attestation_state":"computed","paper":{"title":"Numerical periodic normalization for codim 2 bifurcations of limit cycles with center manifold of dimension higher than 3","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.DS","authors_text":"Hil Meijer, Virginie De Witte, Willy Govaerts, Yuri A. Kuznetsov","submitted_at":"2012-10-23T11:36:51Z","abstract_excerpt":"Explicit computational formulas for coefficients of the periodic normal forms of the three most complex codim 2 bifurcations of limit cycles with dimension of the center manifold equal to 4 or to 5 in generic autonomous ODEs are derived. The resulting formulas are independent of the dimension of the phase space and involve solutions of certain boundary-value problems as well as multilinear functions from the Taylor expansion of the ODE right-hand side near the cycle. The formulas allow one to distinguish between the complicated bifurcation scenarios which can happen near these codim 2 bifurcat"},"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":"1210.6205","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-10-23T11:36:51Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"ca8d660bac986a55f49657531324a713aaf204c0b0f4f14f96cf92d46f50c52d","abstract_canon_sha256":"c8e19b1848e360dd05a7b3ec9a165d29f31f03ca0e4e8099da6370c89b0e56d0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:42:32.900295Z","signature_b64":"vGu0eA/4hvl2aYxzblLMugUyPKtSvREuz+fOaazON1Wmg4A+PPlhy9ahntd5CJEQLOfe1CjeClujGi3f8X01CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ea66f5d4bd08418ee27286d3b11d0efe122e9932f31daf912de2d3ca3f7945ef","last_reissued_at":"2026-05-18T03:42:32.899819Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:42:32.899819Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Numerical periodic normalization for codim 2 bifurcations of limit cycles with center manifold of dimension higher than 3","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.DS","authors_text":"Hil Meijer, Virginie De Witte, Willy Govaerts, Yuri A. Kuznetsov","submitted_at":"2012-10-23T11:36:51Z","abstract_excerpt":"Explicit computational formulas for coefficients of the periodic normal forms of the three most complex codim 2 bifurcations of limit cycles with dimension of the center manifold equal to 4 or to 5 in generic autonomous ODEs are derived. The resulting formulas are independent of the dimension of the phase space and involve solutions of certain boundary-value problems as well as multilinear functions from the Taylor expansion of the ODE right-hand side near the cycle. The formulas allow one to distinguish between the complicated bifurcation scenarios which can happen near these codim 2 bifurcat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.6205","kind":"arxiv","version":1},"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":"1210.6205","created_at":"2026-05-18T03:42:32.899901+00:00"},{"alias_kind":"arxiv_version","alias_value":"1210.6205v1","created_at":"2026-05-18T03:42:32.899901+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.6205","created_at":"2026-05-18T03:42:32.899901+00:00"},{"alias_kind":"pith_short_12","alias_value":"5JTPLVF5BBAY","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_16","alias_value":"5JTPLVF5BBAY5YTS","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_8","alias_value":"5JTPLVF5","created_at":"2026-05-18T12:26:53.410803+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/5JTPLVF5BBAY5YTSQ3J3CHIO7Y","json":"https://pith.science/pith/5JTPLVF5BBAY5YTSQ3J3CHIO7Y.json","graph_json":"https://pith.science/api/pith-number/5JTPLVF5BBAY5YTSQ3J3CHIO7Y/graph.json","events_json":"https://pith.science/api/pith-number/5JTPLVF5BBAY5YTSQ3J3CHIO7Y/events.json","paper":"https://pith.science/paper/5JTPLVF5"},"agent_actions":{"view_html":"https://pith.science/pith/5JTPLVF5BBAY5YTSQ3J3CHIO7Y","download_json":"https://pith.science/pith/5JTPLVF5BBAY5YTSQ3J3CHIO7Y.json","view_paper":"https://pith.science/paper/5JTPLVF5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1210.6205&json=true","fetch_graph":"https://pith.science/api/pith-number/5JTPLVF5BBAY5YTSQ3J3CHIO7Y/graph.json","fetch_events":"https://pith.science/api/pith-number/5JTPLVF5BBAY5YTSQ3J3CHIO7Y/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5JTPLVF5BBAY5YTSQ3J3CHIO7Y/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5JTPLVF5BBAY5YTSQ3J3CHIO7Y/action/storage_attestation","attest_author":"https://pith.science/pith/5JTPLVF5BBAY5YTSQ3J3CHIO7Y/action/author_attestation","sign_citation":"https://pith.science/pith/5JTPLVF5BBAY5YTSQ3J3CHIO7Y/action/citation_signature","submit_replication":"https://pith.science/pith/5JTPLVF5BBAY5YTSQ3J3CHIO7Y/action/replication_record"}},"created_at":"2026-05-18T03:42:32.899901+00:00","updated_at":"2026-05-18T03:42:32.899901+00:00"}