{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:JXG5546XFL7QWQPQKOP5JEMURN","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":"749cc1ab579d141f62a3ff4f1e75e0db35627e0b833dfde4ccbb6a73b6989a45","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-30T20:06:17Z","title_canon_sha256":"0730d288ed44fa314d8237b6f1ea23345823bccd895cb1d87dfedf5655d45380"},"schema_version":"1.0","source":{"id":"1812.00039","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.00039","created_at":"2026-05-17T23:59:27Z"},{"alias_kind":"arxiv_version","alias_value":"1812.00039v1","created_at":"2026-05-17T23:59:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.00039","created_at":"2026-05-17T23:59:27Z"},{"alias_kind":"pith_short_12","alias_value":"JXG5546XFL7Q","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"JXG5546XFL7QWQPQ","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"JXG5546X","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:5fae8b57f562ff3be95bd36216fcb7839633ec42f472b9bd44e91807f39863d6","target":"graph","created_at":"2026-05-17T23:59:27Z","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":"We discuss the Lagrangian-Eulerian framework for hydrodynamic models and provide a proof of Lipschitz dependence of solutions on initial data in path space. The paper presents a corrected version of the result in \\cite{c1}.","authors_text":"Joonhyun La, Peter Constantin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-30T20:06:17Z","title":"Note on Lagrangian-Eulerian Methods for Uniqueness in Hydrodynamic Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.00039","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:e02f3416332776123c1aa7a2a7b52c506764f8a78637e5bf997a911f3c903b42","target":"record","created_at":"2026-05-17T23:59:27Z","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":"749cc1ab579d141f62a3ff4f1e75e0db35627e0b833dfde4ccbb6a73b6989a45","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-30T20:06:17Z","title_canon_sha256":"0730d288ed44fa314d8237b6f1ea23345823bccd895cb1d87dfedf5655d45380"},"schema_version":"1.0","source":{"id":"1812.00039","kind":"arxiv","version":1}},"canonical_sha256":"4dcddef3d72aff0b41f0539fd491948b6e3b61b268890a58ce57d5def2b5c167","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4dcddef3d72aff0b41f0539fd491948b6e3b61b268890a58ce57d5def2b5c167","first_computed_at":"2026-05-17T23:59:27.490565Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:27.490565Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4BHKYuyxNJlW7QO3WE4eypah5wJtxy41kthpo9sfu5K1EA1+zmpTPgtUv+MNLPdCTWS00r47gdeugePbG+XQBA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:27.491073Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.00039","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e02f3416332776123c1aa7a2a7b52c506764f8a78637e5bf997a911f3c903b42","sha256:5fae8b57f562ff3be95bd36216fcb7839633ec42f472b9bd44e91807f39863d6"],"state_sha256":"dd658c5c487a3ae1c32aea513369d639d0cf1c017e8a21497d57445140f53abb"}