{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:IMQKS32IWXGHYJ5DONAHGBMS7X","short_pith_number":"pith:IMQKS32I","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"},"canonical_sha256":"4320a96f48b5cc7c27a37340730592fdd967346450f0c312f71c4995d6ace5a6","source":{"kind":"arxiv","id":"1504.03313","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.03313","created_at":"2026-05-18T00:18:41Z"},{"alias_kind":"arxiv_version","alias_value":"1504.03313v1","created_at":"2026-05-18T00:18:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.03313","created_at":"2026-05-18T00:18:41Z"},{"alias_kind":"pith_short_12","alias_value":"IMQKS32IWXGH","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"IMQKS32IWXGHYJ5D","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"IMQKS32I","created_at":"2026-05-18T12:29:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:IMQKS32IWXGHYJ5DONAHGBMS7X","target":"record","payload":{"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"},"canonical_sha256":"4320a96f48b5cc7c27a37340730592fdd967346450f0c312f71c4995d6ace5a6","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"},"source_kind":"arxiv","source_id":"1504.03313","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:18:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UMuoPD62G6i7E7SvAZlVNv0w9oT/K0oXsccHAlF9FS7GBKiTwFBfAJugtHdD21qRQzejvPWuJr7lQ8tX5iJgDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T03:24:04.850490Z"},"content_sha256":"3720dc57b0d0510953910235bd34796a5050acd7000fa0c6f79303261bab2b98","schema_version":"1.0","event_id":"sha256:3720dc57b0d0510953910235bd34796a5050acd7000fa0c6f79303261bab2b98"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:IMQKS32IWXGHYJ5DONAHGBMS7X","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:18:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bU2e55/NGrqY192AElFTHEH6kFUtSDM/XceAXX5ryUiIoEaQolrGG3/dDHtQINNV4EDsxO03xKiJGPK2zjB+BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T03:24:04.851254Z"},"content_sha256":"b6acc917cec72abbb2c468d76c75c4d6448774814360db47163206a11270f426","schema_version":"1.0","event_id":"sha256:b6acc917cec72abbb2c468d76c75c4d6448774814360db47163206a11270f426"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IMQKS32IWXGHYJ5DONAHGBMS7X/bundle.json","state_url":"https://pith.science/pith/IMQKS32IWXGHYJ5DONAHGBMS7X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IMQKS32IWXGHYJ5DONAHGBMS7X/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-12T03:24:04Z","links":{"resolver":"https://pith.science/pith/IMQKS32IWXGHYJ5DONAHGBMS7X","bundle":"https://pith.science/pith/IMQKS32IWXGHYJ5DONAHGBMS7X/bundle.json","state":"https://pith.science/pith/IMQKS32IWXGHYJ5DONAHGBMS7X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IMQKS32IWXGHYJ5DONAHGBMS7X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:IMQKS32IWXGHYJ5DONAHGBMS7X","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":"9ce518ef6a0820a0c2e77e44549cc53b8798b80e793dae87adecc7b08569dc74","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-04-13T19:49:35Z","title_canon_sha256":"4a8f0826e5f3aeb3d60621ba4ec9608cd473dc21cecad1ffe68cbb013b1675e6"},"schema_version":"1.0","source":{"id":"1504.03313","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.03313","created_at":"2026-05-18T00:18:41Z"},{"alias_kind":"arxiv_version","alias_value":"1504.03313v1","created_at":"2026-05-18T00:18:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.03313","created_at":"2026-05-18T00:18:41Z"},{"alias_kind":"pith_short_12","alias_value":"IMQKS32IWXGH","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"IMQKS32IWXGHYJ5D","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"IMQKS32I","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:b6acc917cec72abbb2c468d76c75c4d6448774814360db47163206a11270f426","target":"graph","created_at":"2026-05-18T00:18:41Z","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 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.","authors_text":"Nataliya Goncharuk, Yury Kudryashov","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-04-13T19:49:35Z","title":"Bounded limit cycles of polynomial foliations of $\\mathbb CP^2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.03313","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":"sha256:3720dc57b0d0510953910235bd34796a5050acd7000fa0c6f79303261bab2b98","target":"record","created_at":"2026-05-18T00:18:41Z","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":"9ce518ef6a0820a0c2e77e44549cc53b8798b80e793dae87adecc7b08569dc74","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-04-13T19:49:35Z","title_canon_sha256":"4a8f0826e5f3aeb3d60621ba4ec9608cd473dc21cecad1ffe68cbb013b1675e6"},"schema_version":"1.0","source":{"id":"1504.03313","kind":"arxiv","version":1}},"canonical_sha256":"4320a96f48b5cc7c27a37340730592fdd967346450f0c312f71c4995d6ace5a6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4320a96f48b5cc7c27a37340730592fdd967346450f0c312f71c4995d6ace5a6","first_computed_at":"2026-05-18T00:18:41.870387Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:41.870387Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kfpNr/R+zRTTA0ziQqPIBfaiCZqY1wHncVqUcB7FKzcFNuW/mLVOcAF8rUxJMvK+eWeFGrami0XjcLKVo7fdAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:41.870898Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.03313","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3720dc57b0d0510953910235bd34796a5050acd7000fa0c6f79303261bab2b98","sha256:b6acc917cec72abbb2c468d76c75c4d6448774814360db47163206a11270f426"],"state_sha256":"1f3abb9d9b8ea90e9a80a71fb52ecd1f9629d990d66206b89103f71d0d3d3e6d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+18TYBKKe9CzXImOmTKxv2mMQ4IewdlG8nWFYhJu/e3LOq7HphZ7iCQJJLtwykaDhSqCwFiSOAW45cClBOE1Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T03:24:04.856079Z","bundle_sha256":"f94520ce038ada5bbee670431ae022efec5e26d419e9561e2ad584098d70fff6"}}