{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:CJRO24CXA6MQ7QFKRV2KEELAJX","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":"540a0b2c7dd87de780c3f300ce9370ff7204df86f6e999026aad2737f4aa7047","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-11-27T07:52:35Z","title_canon_sha256":"20bc0b13e47661d316c7ba67ad1c881e3b24ff56a7daa252290ba813a6cbc130"},"schema_version":"1.0","source":{"id":"1711.09567","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.09567","created_at":"2026-05-18T00:29:35Z"},{"alias_kind":"arxiv_version","alias_value":"1711.09567v1","created_at":"2026-05-18T00:29:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.09567","created_at":"2026-05-18T00:29:35Z"},{"alias_kind":"pith_short_12","alias_value":"CJRO24CXA6MQ","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"CJRO24CXA6MQ7QFK","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"CJRO24CX","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:d002392aa5f6f77603a2079c10b71df2e31e8a646f8b9ad39d9b0e0f1ea4a20d","target":"graph","created_at":"2026-05-18T00:29:35Z","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 prove the backward uniqueness for general parabolic operators of second order in the whole space under assumptions that the leading coefficients of the operator are Lipschitz and their gradients satisfy certain decay conditions. This result extends in some ways a classical result of Lions and Malgrange [12] and a recent result of the authors [10].","authors_text":"Jie Wu, Liqun Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-11-27T07:52:35Z","title":"Backward uniqueness for general parabolic operators in the whole space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.09567","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":"sha256:82066b2736de0b4baae5014f3da60b8721c17cc0fa8cb14336966a798dcd920c","target":"record","created_at":"2026-05-18T00:29:35Z","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":"540a0b2c7dd87de780c3f300ce9370ff7204df86f6e999026aad2737f4aa7047","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-11-27T07:52:35Z","title_canon_sha256":"20bc0b13e47661d316c7ba67ad1c881e3b24ff56a7daa252290ba813a6cbc130"},"schema_version":"1.0","source":{"id":"1711.09567","kind":"arxiv","version":1}},"canonical_sha256":"1262ed705707990fc0aa8d74a211604dc7251ea84af38e3cda943ccf5b4d06d4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1262ed705707990fc0aa8d74a211604dc7251ea84af38e3cda943ccf5b4d06d4","first_computed_at":"2026-05-18T00:29:35.104518Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:35.104518Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Knqd+1pYB5VHJLEU6Y9K7HdbyJnu6JgepIs6JnztMxaMsmLuUyaeP3hHS1G4kpW83mzpa4RZ4N+VCegMyKTvBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:35.105137Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.09567","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:82066b2736de0b4baae5014f3da60b8721c17cc0fa8cb14336966a798dcd920c","sha256:d002392aa5f6f77603a2079c10b71df2e31e8a646f8b9ad39d9b0e0f1ea4a20d"],"state_sha256":"f84847c6c6f31c988e55c4392457999d58990be2a91f0597ff4952f19cc499f6"}