{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:MHR2FBGQMNFCJJSXY2SQFCIBMD","short_pith_number":"pith:MHR2FBGQ","schema_version":"1.0","canonical_sha256":"61e3a284d0634a24a657c6a502890160fa958e0f66f4a0193c6c0a442ae694ff","source":{"kind":"arxiv","id":"1707.03197","version":1},"attestation_state":"computed","paper":{"title":"On some properties of weak solutions to elliptic equations with divergence-free drifts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Nikolay Filonov, Timofey Shilkin","submitted_at":"2017-07-11T09:42:50Z","abstract_excerpt":"We discuss the local properties of weak solutions to the equation $-\\Delta u + b\\cdot\\nabla u=0$. The corresponding theory is well-known in the case $b\\in L_n$, where $n$ is the dimension of the space. Our main interest is focused on the case $b\\in L_2$. In this case the structure assumption $\\operatorname{div} b=0$ turns out to be crucial."},"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":"1707.03197","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-11T09:42:50Z","cross_cats_sorted":[],"title_canon_sha256":"5dc005b376ed1730b9970292899df0e30290b52a0f528d71d3d1940f7c28ebe1","abstract_canon_sha256":"c90b2f67e63e1b850a344f529836e069db1a9e3d98fa75e76cdad4788b2b8ca3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:42.063977Z","signature_b64":"ymZ9qdFwG0EweCPTLI+af/eTVPZLl9D4CvLd55VwTTJgnahUokw63YXy+zm23sHf8YsFguZis83aYbb3TUaDDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"61e3a284d0634a24a657c6a502890160fa958e0f66f4a0193c6c0a442ae694ff","last_reissued_at":"2026-05-17T23:40:42.063526Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:42.063526Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On some properties of weak solutions to elliptic equations with divergence-free drifts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Nikolay Filonov, Timofey Shilkin","submitted_at":"2017-07-11T09:42:50Z","abstract_excerpt":"We discuss the local properties of weak solutions to the equation $-\\Delta u + b\\cdot\\nabla u=0$. The corresponding theory is well-known in the case $b\\in L_n$, where $n$ is the dimension of the space. Our main interest is focused on the case $b\\in L_2$. In this case the structure assumption $\\operatorname{div} b=0$ turns out to be crucial."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.03197","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":"1707.03197","created_at":"2026-05-17T23:40:42.063593+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.03197v1","created_at":"2026-05-17T23:40:42.063593+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.03197","created_at":"2026-05-17T23:40:42.063593+00:00"},{"alias_kind":"pith_short_12","alias_value":"MHR2FBGQMNFC","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_16","alias_value":"MHR2FBGQMNFCJJSX","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_8","alias_value":"MHR2FBGQ","created_at":"2026-05-18T12:31:31.346846+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/MHR2FBGQMNFCJJSXY2SQFCIBMD","json":"https://pith.science/pith/MHR2FBGQMNFCJJSXY2SQFCIBMD.json","graph_json":"https://pith.science/api/pith-number/MHR2FBGQMNFCJJSXY2SQFCIBMD/graph.json","events_json":"https://pith.science/api/pith-number/MHR2FBGQMNFCJJSXY2SQFCIBMD/events.json","paper":"https://pith.science/paper/MHR2FBGQ"},"agent_actions":{"view_html":"https://pith.science/pith/MHR2FBGQMNFCJJSXY2SQFCIBMD","download_json":"https://pith.science/pith/MHR2FBGQMNFCJJSXY2SQFCIBMD.json","view_paper":"https://pith.science/paper/MHR2FBGQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.03197&json=true","fetch_graph":"https://pith.science/api/pith-number/MHR2FBGQMNFCJJSXY2SQFCIBMD/graph.json","fetch_events":"https://pith.science/api/pith-number/MHR2FBGQMNFCJJSXY2SQFCIBMD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MHR2FBGQMNFCJJSXY2SQFCIBMD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MHR2FBGQMNFCJJSXY2SQFCIBMD/action/storage_attestation","attest_author":"https://pith.science/pith/MHR2FBGQMNFCJJSXY2SQFCIBMD/action/author_attestation","sign_citation":"https://pith.science/pith/MHR2FBGQMNFCJJSXY2SQFCIBMD/action/citation_signature","submit_replication":"https://pith.science/pith/MHR2FBGQMNFCJJSXY2SQFCIBMD/action/replication_record"}},"created_at":"2026-05-17T23:40:42.063593+00:00","updated_at":"2026-05-17T23:40:42.063593+00:00"}