{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:BR4NMZPWHE67BXKFXQT5SXKH5D","short_pith_number":"pith:BR4NMZPW","schema_version":"1.0","canonical_sha256":"0c78d665f6393df0dd45bc27d95d47e8e2b894be73879032c14e08f759a2dfa5","source":{"kind":"arxiv","id":"1210.7393","version":1},"attestation_state":"computed","paper":{"title":"Backward Uniqueness of Kolmogorov Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Liqun Zhang, Wendong Wang","submitted_at":"2012-10-28T02:43:47Z","abstract_excerpt":"The backward uniqueness of the Kolmogorov operator $L=\\sum_{i,k=1}^n\\partial_{x_i}(a_{i,k}(x,t)\\partial_{x_k})+\\sum_{l=1}^m x_l\\partial_{y_l}-\\partial_t$, was proved in this paper. We obtained a weak Carleman inequality via Littlewood-Paley decomposition for the global backward uniqueness."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1210.7393","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-10-28T02:43:47Z","cross_cats_sorted":[],"title_canon_sha256":"3a15cd1302707680e8e49b320584256710f5f1f7586d7f175999d759262700bd","abstract_canon_sha256":"7830edf86075af677e174a1153f695051957c0c9089d134033fd5416bf210ca0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:42:10.176438Z","signature_b64":"dOvKk0Jni4TYhCNhZcIN6zeiFPr361zNm+KVxRBkxw+XhVutdVTh21+QwLATtGyVaLVs7tFuORaKRI8vrnuoAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0c78d665f6393df0dd45bc27d95d47e8e2b894be73879032c14e08f759a2dfa5","last_reissued_at":"2026-05-18T03:42:10.175679Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:42:10.175679Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Backward Uniqueness of Kolmogorov Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Liqun Zhang, Wendong Wang","submitted_at":"2012-10-28T02:43:47Z","abstract_excerpt":"The backward uniqueness of the Kolmogorov operator $L=\\sum_{i,k=1}^n\\partial_{x_i}(a_{i,k}(x,t)\\partial_{x_k})+\\sum_{l=1}^m x_l\\partial_{y_l}-\\partial_t$, was proved in this paper. We obtained a weak Carleman inequality via Littlewood-Paley decomposition for the global backward uniqueness."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.7393","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":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1210.7393","created_at":"2026-05-18T03:42:10.175808+00:00"},{"alias_kind":"arxiv_version","alias_value":"1210.7393v1","created_at":"2026-05-18T03:42:10.175808+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.7393","created_at":"2026-05-18T03:42:10.175808+00:00"},{"alias_kind":"pith_short_12","alias_value":"BR4NMZPWHE67","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_16","alias_value":"BR4NMZPWHE67BXKF","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_8","alias_value":"BR4NMZPW","created_at":"2026-05-18T12:27:01.376967+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BR4NMZPWHE67BXKFXQT5SXKH5D","json":"https://pith.science/pith/BR4NMZPWHE67BXKFXQT5SXKH5D.json","graph_json":"https://pith.science/api/pith-number/BR4NMZPWHE67BXKFXQT5SXKH5D/graph.json","events_json":"https://pith.science/api/pith-number/BR4NMZPWHE67BXKFXQT5SXKH5D/events.json","paper":"https://pith.science/paper/BR4NMZPW"},"agent_actions":{"view_html":"https://pith.science/pith/BR4NMZPWHE67BXKFXQT5SXKH5D","download_json":"https://pith.science/pith/BR4NMZPWHE67BXKFXQT5SXKH5D.json","view_paper":"https://pith.science/paper/BR4NMZPW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1210.7393&json=true","fetch_graph":"https://pith.science/api/pith-number/BR4NMZPWHE67BXKFXQT5SXKH5D/graph.json","fetch_events":"https://pith.science/api/pith-number/BR4NMZPWHE67BXKFXQT5SXKH5D/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BR4NMZPWHE67BXKFXQT5SXKH5D/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BR4NMZPWHE67BXKFXQT5SXKH5D/action/storage_attestation","attest_author":"https://pith.science/pith/BR4NMZPWHE67BXKFXQT5SXKH5D/action/author_attestation","sign_citation":"https://pith.science/pith/BR4NMZPWHE67BXKFXQT5SXKH5D/action/citation_signature","submit_replication":"https://pith.science/pith/BR4NMZPWHE67BXKFXQT5SXKH5D/action/replication_record"}},"created_at":"2026-05-18T03:42:10.175808+00:00","updated_at":"2026-05-18T03:42:10.175808+00:00"}