{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:IMQKS32IWXGHYJ5DONAHGBMS7X","short_pith_number":"pith:IMQKS32I","schema_version":"1.0","canonical_sha256":"4320a96f48b5cc7c27a37340730592fdd967346450f0c312f71c4995d6ace5a6","source":{"kind":"arxiv","id":"1504.03313","version":1},"attestation_state":"computed","paper":{"title":"Bounded limit cycles of polynomial foliations of $\\mathbb CP^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.CV","authors_text":"Nataliya Goncharuk, Yury Kudryashov","submitted_at":"2015-04-13T19:49:35Z","abstract_excerpt":"In this article we prove in a new way that a generic polynomial vector field in $\\mathbb C^2$ possesses countably many homologically independent limit cycles. The new proof needs no estimates on integrals, provides thinner exceptional set for quadratic vector fields, and provides limit cycles that stay in a bounded domain."},"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":"1504.03313","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-04-13T19:49:35Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"4a8f0826e5f3aeb3d60621ba4ec9608cd473dc21cecad1ffe68cbb013b1675e6","abstract_canon_sha256":"9ce518ef6a0820a0c2e77e44549cc53b8798b80e793dae87adecc7b08569dc74"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:41.870898Z","signature_b64":"kfpNr/R+zRTTA0ziQqPIBfaiCZqY1wHncVqUcB7FKzcFNuW/mLVOcAF8rUxJMvK+eWeFGrami0XjcLKVo7fdAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4320a96f48b5cc7c27a37340730592fdd967346450f0c312f71c4995d6ace5a6","last_reissued_at":"2026-05-18T00:18:41.870387Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:41.870387Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bounded limit cycles of polynomial foliations of $\\mathbb CP^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.CV","authors_text":"Nataliya Goncharuk, Yury Kudryashov","submitted_at":"2015-04-13T19:49:35Z","abstract_excerpt":"In this article we prove in a new way that a generic polynomial vector field in $\\mathbb C^2$ possesses countably many homologically independent limit cycles. The new proof needs no estimates on integrals, provides thinner exceptional set for quadratic vector fields, and provides limit cycles that stay in a bounded domain."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.03313","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":"1504.03313","created_at":"2026-05-18T00:18:41.870468+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.03313v1","created_at":"2026-05-18T00:18:41.870468+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.03313","created_at":"2026-05-18T00:18:41.870468+00:00"},{"alias_kind":"pith_short_12","alias_value":"IMQKS32IWXGH","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_16","alias_value":"IMQKS32IWXGHYJ5D","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_8","alias_value":"IMQKS32I","created_at":"2026-05-18T12:29:25.134429+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/IMQKS32IWXGHYJ5DONAHGBMS7X","json":"https://pith.science/pith/IMQKS32IWXGHYJ5DONAHGBMS7X.json","graph_json":"https://pith.science/api/pith-number/IMQKS32IWXGHYJ5DONAHGBMS7X/graph.json","events_json":"https://pith.science/api/pith-number/IMQKS32IWXGHYJ5DONAHGBMS7X/events.json","paper":"https://pith.science/paper/IMQKS32I"},"agent_actions":{"view_html":"https://pith.science/pith/IMQKS32IWXGHYJ5DONAHGBMS7X","download_json":"https://pith.science/pith/IMQKS32IWXGHYJ5DONAHGBMS7X.json","view_paper":"https://pith.science/paper/IMQKS32I","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.03313&json=true","fetch_graph":"https://pith.science/api/pith-number/IMQKS32IWXGHYJ5DONAHGBMS7X/graph.json","fetch_events":"https://pith.science/api/pith-number/IMQKS32IWXGHYJ5DONAHGBMS7X/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IMQKS32IWXGHYJ5DONAHGBMS7X/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IMQKS32IWXGHYJ5DONAHGBMS7X/action/storage_attestation","attest_author":"https://pith.science/pith/IMQKS32IWXGHYJ5DONAHGBMS7X/action/author_attestation","sign_citation":"https://pith.science/pith/IMQKS32IWXGHYJ5DONAHGBMS7X/action/citation_signature","submit_replication":"https://pith.science/pith/IMQKS32IWXGHYJ5DONAHGBMS7X/action/replication_record"}},"created_at":"2026-05-18T00:18:41.870468+00:00","updated_at":"2026-05-18T00:18:41.870468+00:00"}