{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:33YDUGW6KAR3HXQ3IDWD2B3ICF","short_pith_number":"pith:33YDUGW6","canonical_record":{"source":{"id":"2011.09309","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2020-11-17T02:16:36Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"b32e2cb499b706ea6ce1c6b5249be50d3af53852eacfaa9e63ad258d1645cfca","abstract_canon_sha256":"abab7191990d45cdcdc16a1fe3ef28a76921b3c44cb387b13567391b13d5c41c"},"schema_version":"1.0"},"canonical_sha256":"def03a1ade5023b3de1b40ec3d07681152787182efded0c7f64c196a91e5bcf7","source":{"kind":"arxiv","id":"2011.09309","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2011.09309","created_at":"2026-07-05T01:52:42Z"},{"alias_kind":"arxiv_version","alias_value":"2011.09309v1","created_at":"2026-07-05T01:52:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2011.09309","created_at":"2026-07-05T01:52:42Z"},{"alias_kind":"pith_short_12","alias_value":"33YDUGW6KAR3","created_at":"2026-07-05T01:52:42Z"},{"alias_kind":"pith_short_16","alias_value":"33YDUGW6KAR3HXQ3","created_at":"2026-07-05T01:52:42Z"},{"alias_kind":"pith_short_8","alias_value":"33YDUGW6","created_at":"2026-07-05T01:52:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:33YDUGW6KAR3HXQ3IDWD2B3ICF","target":"record","payload":{"canonical_record":{"source":{"id":"2011.09309","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2020-11-17T02:16:36Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"b32e2cb499b706ea6ce1c6b5249be50d3af53852eacfaa9e63ad258d1645cfca","abstract_canon_sha256":"abab7191990d45cdcdc16a1fe3ef28a76921b3c44cb387b13567391b13d5c41c"},"schema_version":"1.0"},"canonical_sha256":"def03a1ade5023b3de1b40ec3d07681152787182efded0c7f64c196a91e5bcf7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:52:42.748573Z","signature_b64":"lp/SApQrvpQajz22O/Wle+bSibd+dQVbW+JyyEUEnxyxtPTqnea/ptRKGgyp8Oppah9vVSAdExpUcISXJRQ+Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"def03a1ade5023b3de1b40ec3d07681152787182efded0c7f64c196a91e5bcf7","last_reissued_at":"2026-07-05T01:52:42.748228Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:52:42.748228Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2011.09309","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":"2026-07-05T01:52:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PGZFheDMb6pyd+rjFjZrzlM2Q6bfGdL8Kx3S2rZiDe8Qg5vWa9KxHBj5Gp6piGf6ZQeFawC4V1HOc/OFxUZ6Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T22:04:23.682779Z"},"content_sha256":"bf317ad2f3fcfa9df43fa705b2e2f81fbf9ed0241ea2c51a60a6943dfaacff8f","schema_version":"1.0","event_id":"sha256:bf317ad2f3fcfa9df43fa705b2e2f81fbf9ed0241ea2c51a60a6943dfaacff8f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:33YDUGW6KAR3HXQ3IDWD2B3ICF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Regularity and convergence of local first integrals of analytic differential systems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.CA","authors_text":"Xiang Zhang","submitted_at":"2020-11-17T02:16:36Z","abstract_excerpt":"Poincar\\'e proved nonexistence of formal first integrals near a nonresonant singularity of analytic autonomous differential systems. In the resonant case with one zero eigenvalue and others nonresonant, there remains an open problem on regularity and convergence of local first integrals. Here we provide an answer to this problem. The system has always a local $C^\\infty$ first integral near the singularity when it is nonisolated. In any finite dimensional space formed by analytic differential systems having the same linear part at the singularity, either all the systems have local analytic firs"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.09309","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2011.09309/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":"2026-07-05T01:52:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f9hxjWuUBWK214Rn6dJW/vkyBUoUd7kOkF4QxF5UeB6bMzqSXZ0O68TUNqo1qSICQbSBtqMBiWgUSSG5IxktBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T22:04:23.683361Z"},"content_sha256":"908398058ec77e52d0aa115f164a25c5663cde7c55b1904f7ac571bcfdbf407f","schema_version":"1.0","event_id":"sha256:908398058ec77e52d0aa115f164a25c5663cde7c55b1904f7ac571bcfdbf407f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/33YDUGW6KAR3HXQ3IDWD2B3ICF/bundle.json","state_url":"https://pith.science/pith/33YDUGW6KAR3HXQ3IDWD2B3ICF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/33YDUGW6KAR3HXQ3IDWD2B3ICF/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":"2026-08-03T22:04:23Z","links":{"resolver":"https://pith.science/pith/33YDUGW6KAR3HXQ3IDWD2B3ICF","bundle":"https://pith.science/pith/33YDUGW6KAR3HXQ3IDWD2B3ICF/bundle.json","state":"https://pith.science/pith/33YDUGW6KAR3HXQ3IDWD2B3ICF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/33YDUGW6KAR3HXQ3IDWD2B3ICF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:33YDUGW6KAR3HXQ3IDWD2B3ICF","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":"abab7191990d45cdcdc16a1fe3ef28a76921b3c44cb387b13567391b13d5c41c","cross_cats_sorted":["math.DS"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2020-11-17T02:16:36Z","title_canon_sha256":"b32e2cb499b706ea6ce1c6b5249be50d3af53852eacfaa9e63ad258d1645cfca"},"schema_version":"1.0","source":{"id":"2011.09309","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2011.09309","created_at":"2026-07-05T01:52:42Z"},{"alias_kind":"arxiv_version","alias_value":"2011.09309v1","created_at":"2026-07-05T01:52:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2011.09309","created_at":"2026-07-05T01:52:42Z"},{"alias_kind":"pith_short_12","alias_value":"33YDUGW6KAR3","created_at":"2026-07-05T01:52:42Z"},{"alias_kind":"pith_short_16","alias_value":"33YDUGW6KAR3HXQ3","created_at":"2026-07-05T01:52:42Z"},{"alias_kind":"pith_short_8","alias_value":"33YDUGW6","created_at":"2026-07-05T01:52:42Z"}],"graph_snapshots":[{"event_id":"sha256:908398058ec77e52d0aa115f164a25c5663cde7c55b1904f7ac571bcfdbf407f","target":"graph","created_at":"2026-07-05T01:52:42Z","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/2011.09309/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Poincar\\'e proved nonexistence of formal first integrals near a nonresonant singularity of analytic autonomous differential systems. In the resonant case with one zero eigenvalue and others nonresonant, there remains an open problem on regularity and convergence of local first integrals. Here we provide an answer to this problem. The system has always a local $C^\\infty$ first integral near the singularity when it is nonisolated. In any finite dimensional space formed by analytic differential systems having the same linear part at the singularity, either all the systems have local analytic firs","authors_text":"Xiang Zhang","cross_cats":["math.DS"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2020-11-17T02:16:36Z","title":"Regularity and convergence of local first integrals of analytic differential systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.09309","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:bf317ad2f3fcfa9df43fa705b2e2f81fbf9ed0241ea2c51a60a6943dfaacff8f","target":"record","created_at":"2026-07-05T01:52:42Z","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":"abab7191990d45cdcdc16a1fe3ef28a76921b3c44cb387b13567391b13d5c41c","cross_cats_sorted":["math.DS"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2020-11-17T02:16:36Z","title_canon_sha256":"b32e2cb499b706ea6ce1c6b5249be50d3af53852eacfaa9e63ad258d1645cfca"},"schema_version":"1.0","source":{"id":"2011.09309","kind":"arxiv","version":1}},"canonical_sha256":"def03a1ade5023b3de1b40ec3d07681152787182efded0c7f64c196a91e5bcf7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"def03a1ade5023b3de1b40ec3d07681152787182efded0c7f64c196a91e5bcf7","first_computed_at":"2026-07-05T01:52:42.748228Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:52:42.748228Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lp/SApQrvpQajz22O/Wle+bSibd+dQVbW+JyyEUEnxyxtPTqnea/ptRKGgyp8Oppah9vVSAdExpUcISXJRQ+Cg==","signature_status":"signed_v1","signed_at":"2026-07-05T01:52:42.748573Z","signed_message":"canonical_sha256_bytes"},"source_id":"2011.09309","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bf317ad2f3fcfa9df43fa705b2e2f81fbf9ed0241ea2c51a60a6943dfaacff8f","sha256:908398058ec77e52d0aa115f164a25c5663cde7c55b1904f7ac571bcfdbf407f"],"state_sha256":"ab8b2c1726ab518f1fc551eaccfb12e6effd1901cb00a7b5f05ffea61b28f5b0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mj+OOtc4GDFJi/WkiXJHdHCesCDE2ZvWUhyfnPhXnX3b6b4W29RSgwc7Wy4t8BglNNOyVmPF0dupJXgDsQW1DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T22:04:23.688395Z","bundle_sha256":"1b0602d5d3e712d8d83174b340ded3930bbfdb82fccbb2d198a0ff0f5f05c748"}}