{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:5ORYC3DTWLRYVKSSV5FQ3EVDPX","short_pith_number":"pith:5ORYC3DT","canonical_record":{"source":{"id":"2603.09941","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2026-03-10T17:32:40Z","cross_cats_sorted":[],"title_canon_sha256":"023f3b1bcbafb5475966c6b141dce26a2838c5ad78030cbf9ae5d1953bd96d2b","abstract_canon_sha256":"49bca6ee46080e77d7e129d567489d9241fc1fcaf106792ac238bf4619b6fdc2"},"schema_version":"1.0"},"canonical_sha256":"eba3816c73b2e38aaa52af4b0d92a37df5b1c7cc6b0c48b18ef9ce2aeebd9a96","source":{"kind":"arxiv","id":"2603.09941","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2603.09941","created_at":"2026-06-11T01:10:34Z"},{"alias_kind":"arxiv_version","alias_value":"2603.09941v2","created_at":"2026-06-11T01:10:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.09941","created_at":"2026-06-11T01:10:34Z"},{"alias_kind":"pith_short_12","alias_value":"5ORYC3DTWLRY","created_at":"2026-06-11T01:10:34Z"},{"alias_kind":"pith_short_16","alias_value":"5ORYC3DTWLRYVKSS","created_at":"2026-06-11T01:10:34Z"},{"alias_kind":"pith_short_8","alias_value":"5ORYC3DT","created_at":"2026-06-11T01:10:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:5ORYC3DTWLRYVKSSV5FQ3EVDPX","target":"record","payload":{"canonical_record":{"source":{"id":"2603.09941","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2026-03-10T17:32:40Z","cross_cats_sorted":[],"title_canon_sha256":"023f3b1bcbafb5475966c6b141dce26a2838c5ad78030cbf9ae5d1953bd96d2b","abstract_canon_sha256":"49bca6ee46080e77d7e129d567489d9241fc1fcaf106792ac238bf4619b6fdc2"},"schema_version":"1.0"},"canonical_sha256":"eba3816c73b2e38aaa52af4b0d92a37df5b1c7cc6b0c48b18ef9ce2aeebd9a96","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-11T01:10:34.781636Z","signature_b64":"85Yl+STs/ecK2aaque++wl74JRjTyCDOXSu/EInQL99nDoa3qpsRr7Y80fSIgxCCIgXsgSS+IPNZzYmsTDoDCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eba3816c73b2e38aaa52af4b0d92a37df5b1c7cc6b0c48b18ef9ce2aeebd9a96","last_reissued_at":"2026-06-11T01:10:34.780580Z","signature_status":"signed_v1","first_computed_at":"2026-06-11T01:10:34.780580Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2603.09941","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-11T01:10:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I8XXV0M+3/6+vk+TFDiJL44HBss63MAiRKKA9fLZZqmBY8+gXd9Wx0w0XVxDFvTcpjYyKp9AVmhtHX61NE/eDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T03:45:20.521133Z"},"content_sha256":"5ff7ba4321a9bf3d610262020f3af08a03e0ee96970cd9c177429f9d36a5e87b","schema_version":"1.0","event_id":"sha256:5ff7ba4321a9bf3d610262020f3af08a03e0ee96970cd9c177429f9d36a5e87b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:5ORYC3DTWLRYVKSSV5FQ3EVDPX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A new approach to the Poincar\\'e center problem","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Isaac A. Garc\\'ia, Jaume Gin\\'e","submitted_at":"2026-03-10T17:32:40Z","abstract_excerpt":"We address the classical (degenerate or non-degenerate) center problem posed by Poincar\\'e in the 19th century for monodromic singularities of analytic families of planar vector fields $\\mathcal{X}$. We prove that every analytic center admits a Laurent inverse integrating factor $V$ in weighted polar coordinates. Moreover, we show that when $\\mathcal{X}$ has no local curves of zero angular speed, the Poincar\\'e map is analytic. Based on this result, we derive a theoretical procedure to determine parameter constraints within the family that characterize centers without curves of zero angular sp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.09941","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2603.09941/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-06-11T01:10:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FyEfjT3IdtodyGg2TKcPB25vNJx31MpGegj6BbJsal2Hisb0/lempWlXwDKIPf7bZQ0OmytkrS1N1mIgo5ImCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T03:45:20.521524Z"},"content_sha256":"64f2ad15fa981829354c3fe9d8c703c2d94b9aa5fe610091611efd7ad2445872","schema_version":"1.0","event_id":"sha256:64f2ad15fa981829354c3fe9d8c703c2d94b9aa5fe610091611efd7ad2445872"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5ORYC3DTWLRYVKSSV5FQ3EVDPX/bundle.json","state_url":"https://pith.science/pith/5ORYC3DTWLRYVKSSV5FQ3EVDPX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5ORYC3DTWLRYVKSSV5FQ3EVDPX/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":"2026-06-21T03:45:20Z","links":{"resolver":"https://pith.science/pith/5ORYC3DTWLRYVKSSV5FQ3EVDPX","bundle":"https://pith.science/pith/5ORYC3DTWLRYVKSSV5FQ3EVDPX/bundle.json","state":"https://pith.science/pith/5ORYC3DTWLRYVKSSV5FQ3EVDPX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5ORYC3DTWLRYVKSSV5FQ3EVDPX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:5ORYC3DTWLRYVKSSV5FQ3EVDPX","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":"49bca6ee46080e77d7e129d567489d9241fc1fcaf106792ac238bf4619b6fdc2","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2026-03-10T17:32:40Z","title_canon_sha256":"023f3b1bcbafb5475966c6b141dce26a2838c5ad78030cbf9ae5d1953bd96d2b"},"schema_version":"1.0","source":{"id":"2603.09941","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2603.09941","created_at":"2026-06-11T01:10:34Z"},{"alias_kind":"arxiv_version","alias_value":"2603.09941v2","created_at":"2026-06-11T01:10:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.09941","created_at":"2026-06-11T01:10:34Z"},{"alias_kind":"pith_short_12","alias_value":"5ORYC3DTWLRY","created_at":"2026-06-11T01:10:34Z"},{"alias_kind":"pith_short_16","alias_value":"5ORYC3DTWLRYVKSS","created_at":"2026-06-11T01:10:34Z"},{"alias_kind":"pith_short_8","alias_value":"5ORYC3DT","created_at":"2026-06-11T01:10:34Z"}],"graph_snapshots":[{"event_id":"sha256:64f2ad15fa981829354c3fe9d8c703c2d94b9aa5fe610091611efd7ad2445872","target":"graph","created_at":"2026-06-11T01:10:34Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2603.09941/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We address the classical (degenerate or non-degenerate) center problem posed by Poincar\\'e in the 19th century for monodromic singularities of analytic families of planar vector fields $\\mathcal{X}$. We prove that every analytic center admits a Laurent inverse integrating factor $V$ in weighted polar coordinates. Moreover, we show that when $\\mathcal{X}$ has no local curves of zero angular speed, the Poincar\\'e map is analytic. Based on this result, we derive a theoretical procedure to determine parameter constraints within the family that characterize centers without curves of zero angular sp","authors_text":"Isaac A. Garc\\'ia, Jaume Gin\\'e","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2026-03-10T17:32:40Z","title":"A new approach to the Poincar\\'e center problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.09941","kind":"arxiv","version":2},"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":"sha256:5ff7ba4321a9bf3d610262020f3af08a03e0ee96970cd9c177429f9d36a5e87b","target":"record","created_at":"2026-06-11T01:10:34Z","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":"49bca6ee46080e77d7e129d567489d9241fc1fcaf106792ac238bf4619b6fdc2","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2026-03-10T17:32:40Z","title_canon_sha256":"023f3b1bcbafb5475966c6b141dce26a2838c5ad78030cbf9ae5d1953bd96d2b"},"schema_version":"1.0","source":{"id":"2603.09941","kind":"arxiv","version":2}},"canonical_sha256":"eba3816c73b2e38aaa52af4b0d92a37df5b1c7cc6b0c48b18ef9ce2aeebd9a96","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eba3816c73b2e38aaa52af4b0d92a37df5b1c7cc6b0c48b18ef9ce2aeebd9a96","first_computed_at":"2026-06-11T01:10:34.780580Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-11T01:10:34.780580Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"85Yl+STs/ecK2aaque++wl74JRjTyCDOXSu/EInQL99nDoa3qpsRr7Y80fSIgxCCIgXsgSS+IPNZzYmsTDoDCw==","signature_status":"signed_v1","signed_at":"2026-06-11T01:10:34.781636Z","signed_message":"canonical_sha256_bytes"},"source_id":"2603.09941","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5ff7ba4321a9bf3d610262020f3af08a03e0ee96970cd9c177429f9d36a5e87b","sha256:64f2ad15fa981829354c3fe9d8c703c2d94b9aa5fe610091611efd7ad2445872"],"state_sha256":"92b1558482b03eef9ec59c145113b8071a050370e59834ae2f397a9efbb50a19"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WqCcHhzWmP3Ya/iFUWrCDtyI5h9jXCRfqmOCUPID48tS8qeCdvYAMy+bqCSuZ28ytcme8FghUz+7pCKOtPf7BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T03:45:20.523568Z","bundle_sha256":"82a911f63df07380b3565220551714749c90d473ff5f8e4ce13baa68078e0331"}}