{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:K2MCIUKPBNSBC7RBIOET57OLLH","short_pith_number":"pith:K2MCIUKP","schema_version":"1.0","canonical_sha256":"569824514f0b64117e2143893efdcb59e3707b4198b12586d2ef15486c0e4094","source":{"kind":"arxiv","id":"1807.03262","version":1},"attestation_state":"computed","paper":{"title":"On the Sobolev space of functions with derivative of logarithmic order","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CA","authors_text":"Elia Bru\\`e, Quoc-Hung Nguyen","submitted_at":"2018-07-09T16:31:20Z","abstract_excerpt":"Two notions of \"having a derivative of logarithmic order\" have been studied. They come from the study of regularity of flows and renormalized solutions for the transport and continuity equation associated to weakly differentiable drifts."},"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":"1807.03262","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-07-09T16:31:20Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"02210c1332b7118c971315d4408c8f286386f474e60529542a54a6a064a331c9","abstract_canon_sha256":"955f1a6a397f3f62ccdf791f3518dae653312f54e363c64830f840a3ac398ad0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:12.251873Z","signature_b64":"B/N2QT77jGmQV1qzi6igfg6FT8d1aMFiPFFoT5VSieKcEJHdwwkpruqb3lQv83hTkGjta0fWKxfHhtwfElNMAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"569824514f0b64117e2143893efdcb59e3707b4198b12586d2ef15486c0e4094","last_reissued_at":"2026-05-18T00:11:12.250982Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:12.250982Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Sobolev space of functions with derivative of logarithmic order","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CA","authors_text":"Elia Bru\\`e, Quoc-Hung Nguyen","submitted_at":"2018-07-09T16:31:20Z","abstract_excerpt":"Two notions of \"having a derivative of logarithmic order\" have been studied. They come from the study of regularity of flows and renormalized solutions for the transport and continuity equation associated to weakly differentiable drifts."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.03262","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":"1807.03262","created_at":"2026-05-18T00:11:12.251077+00:00"},{"alias_kind":"arxiv_version","alias_value":"1807.03262v1","created_at":"2026-05-18T00:11:12.251077+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.03262","created_at":"2026-05-18T00:11:12.251077+00:00"},{"alias_kind":"pith_short_12","alias_value":"K2MCIUKPBNSB","created_at":"2026-05-18T12:32:33.847187+00:00"},{"alias_kind":"pith_short_16","alias_value":"K2MCIUKPBNSBC7RB","created_at":"2026-05-18T12:32:33.847187+00:00"},{"alias_kind":"pith_short_8","alias_value":"K2MCIUKP","created_at":"2026-05-18T12:32:33.847187+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/K2MCIUKPBNSBC7RBIOET57OLLH","json":"https://pith.science/pith/K2MCIUKPBNSBC7RBIOET57OLLH.json","graph_json":"https://pith.science/api/pith-number/K2MCIUKPBNSBC7RBIOET57OLLH/graph.json","events_json":"https://pith.science/api/pith-number/K2MCIUKPBNSBC7RBIOET57OLLH/events.json","paper":"https://pith.science/paper/K2MCIUKP"},"agent_actions":{"view_html":"https://pith.science/pith/K2MCIUKPBNSBC7RBIOET57OLLH","download_json":"https://pith.science/pith/K2MCIUKPBNSBC7RBIOET57OLLH.json","view_paper":"https://pith.science/paper/K2MCIUKP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1807.03262&json=true","fetch_graph":"https://pith.science/api/pith-number/K2MCIUKPBNSBC7RBIOET57OLLH/graph.json","fetch_events":"https://pith.science/api/pith-number/K2MCIUKPBNSBC7RBIOET57OLLH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/K2MCIUKPBNSBC7RBIOET57OLLH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/K2MCIUKPBNSBC7RBIOET57OLLH/action/storage_attestation","attest_author":"https://pith.science/pith/K2MCIUKPBNSBC7RBIOET57OLLH/action/author_attestation","sign_citation":"https://pith.science/pith/K2MCIUKPBNSBC7RBIOET57OLLH/action/citation_signature","submit_replication":"https://pith.science/pith/K2MCIUKPBNSBC7RBIOET57OLLH/action/replication_record"}},"created_at":"2026-05-18T00:11:12.251077+00:00","updated_at":"2026-05-18T00:11:12.251077+00:00"}