{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:PDSBWUH3Z53PLL7F3BYAUNVGD3","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":"4ba6778ad488ff22f2fef3816de547a9b0590da7150a1777bc9ddedfcc8284af","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-11-07T07:56:02Z","title_canon_sha256":"e1f796ac0637bd63a839083a248fce71c98917cdbcc9117d67c307bd0be3963e"},"schema_version":"1.0","source":{"id":"1511.02316","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.02316","created_at":"2026-05-18T01:27:30Z"},{"alias_kind":"arxiv_version","alias_value":"1511.02316v1","created_at":"2026-05-18T01:27:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.02316","created_at":"2026-05-18T01:27:30Z"},{"alias_kind":"pith_short_12","alias_value":"PDSBWUH3Z53P","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PDSBWUH3Z53PLL7F","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PDSBWUH3","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:4692246c8083b73fedf978790d5217ca6b62648c06b2bc4510e04fc4bf51794c","target":"graph","created_at":"2026-05-18T01:27:30Z","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":"This paper is mainly concerned with the Cauchy problem for a generalized Camassa-Holm equation with analytic initial data. The analyticity of its solutions is proved in both variables, globally in space and locally in time.\n  Then, we present a persistence property for strong solutions to the system. Finally, explicit asymptotic profiles illustrate the optimality of these results.","authors_text":"Xi Tu, Zhaoyang Yin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-11-07T07:56:02Z","title":"Analyticity of the Cauchy problem and persistence properties for a generalized Camassa-Holm equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.02316","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":"sha256:270ab72abf59de9d9fe74002e8b398070d797f6cbd0b53acec72fb4bb41d8648","target":"record","created_at":"2026-05-18T01:27:30Z","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":"4ba6778ad488ff22f2fef3816de547a9b0590da7150a1777bc9ddedfcc8284af","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-11-07T07:56:02Z","title_canon_sha256":"e1f796ac0637bd63a839083a248fce71c98917cdbcc9117d67c307bd0be3963e"},"schema_version":"1.0","source":{"id":"1511.02316","kind":"arxiv","version":1}},"canonical_sha256":"78e41b50fbcf76f5afe5d8700a36a61ef9fba047daa63c9112f476072dcf630f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"78e41b50fbcf76f5afe5d8700a36a61ef9fba047daa63c9112f476072dcf630f","first_computed_at":"2026-05-18T01:27:30.699104Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:27:30.699104Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8Q2Arid9PpnBXy97lMT9yMUuYMSs7RDaNFD68qBPibJBs3defK3nrBuqyOuViiQS/xZDguHsVjL14Mbez2eYCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:27:30.699797Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.02316","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:270ab72abf59de9d9fe74002e8b398070d797f6cbd0b53acec72fb4bb41d8648","sha256:4692246c8083b73fedf978790d5217ca6b62648c06b2bc4510e04fc4bf51794c"],"state_sha256":"8612503fa8b5f20b5f8a314e521a4672e13bf089639f42a0b60b4a8ff7dc8d8d"}