{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:4C34GDPY6BC3PNX2MXYV4CDY3I","short_pith_number":"pith:4C34GDPY","schema_version":"1.0","canonical_sha256":"e0b7c30df8f045b7b6fa65f15e0878da10adbe7be0e2a91603ee83fd247a49ef","source":{"kind":"arxiv","id":"0705.1609","version":2},"attestation_state":"computed","paper":{"title":"Perturbations of quadratic centers of genus one","license":"","headline":"","cross_cats":["math.CA"],"primary_cat":"math.DS","authors_text":"Iliya D. Iliev, Lubomir Gavrilov, Sebastien Gautier","submitted_at":"2007-05-11T09:30:23Z","abstract_excerpt":"We propose a program for finding the cyclicity of period annuli of quadratic systems with centers of genus one. As a first step, we classify all such systems and determine the essential one-parameter quadratic perturbations which produce the maximal number of limit cycles. We compute the associated Poincare-Pontryagin-Melnikov functions whose zeros control the number of limit cycles. To illustrate our approach, we determine the cyclicity of the annuli of two particular reversible systems."},"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":"0705.1609","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.DS","submitted_at":"2007-05-11T09:30:23Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"6700b387b9d6643999f759eecb8383ed9b92803c52aaa2bb5ee8a918b6386277","abstract_canon_sha256":"8406e5c8f37124dd77bb32dd9e1c441091209abcd5a29b4870eb1a2e76f64640"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:25:37.993091Z","signature_b64":"UKy2vR4AWDkJLIl4nb6jJh82u9scHXizGDZ06SNC+VmNKBguGCER3DhHcnCUkgZDwaPo2P52+6vRCtI6exd+AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e0b7c30df8f045b7b6fa65f15e0878da10adbe7be0e2a91603ee83fd247a49ef","last_reissued_at":"2026-05-18T04:25:37.992658Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:25:37.992658Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Perturbations of quadratic centers of genus one","license":"","headline":"","cross_cats":["math.CA"],"primary_cat":"math.DS","authors_text":"Iliya D. Iliev, Lubomir Gavrilov, Sebastien Gautier","submitted_at":"2007-05-11T09:30:23Z","abstract_excerpt":"We propose a program for finding the cyclicity of period annuli of quadratic systems with centers of genus one. As a first step, we classify all such systems and determine the essential one-parameter quadratic perturbations which produce the maximal number of limit cycles. We compute the associated Poincare-Pontryagin-Melnikov functions whose zeros control the number of limit cycles. To illustrate our approach, we determine the cyclicity of the annuli of two particular reversible systems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0705.1609","kind":"arxiv","version":2},"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":"0705.1609","created_at":"2026-05-18T04:25:37.992728+00:00"},{"alias_kind":"arxiv_version","alias_value":"0705.1609v2","created_at":"2026-05-18T04:25:37.992728+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0705.1609","created_at":"2026-05-18T04:25:37.992728+00:00"},{"alias_kind":"pith_short_12","alias_value":"4C34GDPY6BC3","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_16","alias_value":"4C34GDPY6BC3PNX2","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_8","alias_value":"4C34GDPY","created_at":"2026-05-18T12:25:54.717736+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/4C34GDPY6BC3PNX2MXYV4CDY3I","json":"https://pith.science/pith/4C34GDPY6BC3PNX2MXYV4CDY3I.json","graph_json":"https://pith.science/api/pith-number/4C34GDPY6BC3PNX2MXYV4CDY3I/graph.json","events_json":"https://pith.science/api/pith-number/4C34GDPY6BC3PNX2MXYV4CDY3I/events.json","paper":"https://pith.science/paper/4C34GDPY"},"agent_actions":{"view_html":"https://pith.science/pith/4C34GDPY6BC3PNX2MXYV4CDY3I","download_json":"https://pith.science/pith/4C34GDPY6BC3PNX2MXYV4CDY3I.json","view_paper":"https://pith.science/paper/4C34GDPY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0705.1609&json=true","fetch_graph":"https://pith.science/api/pith-number/4C34GDPY6BC3PNX2MXYV4CDY3I/graph.json","fetch_events":"https://pith.science/api/pith-number/4C34GDPY6BC3PNX2MXYV4CDY3I/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4C34GDPY6BC3PNX2MXYV4CDY3I/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4C34GDPY6BC3PNX2MXYV4CDY3I/action/storage_attestation","attest_author":"https://pith.science/pith/4C34GDPY6BC3PNX2MXYV4CDY3I/action/author_attestation","sign_citation":"https://pith.science/pith/4C34GDPY6BC3PNX2MXYV4CDY3I/action/citation_signature","submit_replication":"https://pith.science/pith/4C34GDPY6BC3PNX2MXYV4CDY3I/action/replication_record"}},"created_at":"2026-05-18T04:25:37.992728+00:00","updated_at":"2026-05-18T04:25:37.992728+00:00"}