{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:66APXV4M22YVFB55WXW6OQR234","short_pith_number":"pith:66APXV4M","schema_version":"1.0","canonical_sha256":"f780fbd78cd6b15287bdb5ede7423adf344477138b7562c7529bf9422d5a75d4","source":{"kind":"arxiv","id":"1104.3942","version":4},"attestation_state":"computed","paper":{"title":"Bilinear Sobolev-Poincare inequalities and Leibniz-type rules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Diego Maldonado (KSU), Frederic Bernicot (LMJL), Kabe Moen, Virginia Naibo (KSU)","submitted_at":"2011-04-20T05:56:59Z","abstract_excerpt":"The dual purpose of this article is to establish bilinear Poincare-type estimates associated to an approximation of the identity and to explore the connections between bilinear pseudo-differential operators and bilinear potential-type operators. The common underlying theme in both topics is their applications to Leibniz-type rules in Sobolev and Campanato-Morrey spaces under Sobolev scaling."},"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":"1104.3942","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-04-20T05:56:59Z","cross_cats_sorted":[],"title_canon_sha256":"6b7aaffd10d855682cbd4b807173a362001d3c97d05fce0361e48f1ed37ad0f1","abstract_canon_sha256":"7fa900e66dd206bd3a990ccae931d220025b6a39c0801c6aa9f17ce9afe75aae"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:43:52.915216Z","signature_b64":"Dh+NpQZPBH1Chwgf8UGVvvdXN+HNKTe5fQF5yyrCJ5v4QR0dA50kVGITSLpDE9Kjyj2UnWl5h3oq9PC0d4LTCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f780fbd78cd6b15287bdb5ede7423adf344477138b7562c7529bf9422d5a75d4","last_reissued_at":"2026-05-18T03:43:52.914645Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:43:52.914645Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bilinear Sobolev-Poincare inequalities and Leibniz-type rules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Diego Maldonado (KSU), Frederic Bernicot (LMJL), Kabe Moen, Virginia Naibo (KSU)","submitted_at":"2011-04-20T05:56:59Z","abstract_excerpt":"The dual purpose of this article is to establish bilinear Poincare-type estimates associated to an approximation of the identity and to explore the connections between bilinear pseudo-differential operators and bilinear potential-type operators. The common underlying theme in both topics is their applications to Leibniz-type rules in Sobolev and Campanato-Morrey spaces under Sobolev scaling."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.3942","kind":"arxiv","version":4},"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":"1104.3942","created_at":"2026-05-18T03:43:52.914742+00:00"},{"alias_kind":"arxiv_version","alias_value":"1104.3942v4","created_at":"2026-05-18T03:43:52.914742+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.3942","created_at":"2026-05-18T03:43:52.914742+00:00"},{"alias_kind":"pith_short_12","alias_value":"66APXV4M22YV","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_16","alias_value":"66APXV4M22YVFB55","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_8","alias_value":"66APXV4M","created_at":"2026-05-18T12:26:22.705136+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/66APXV4M22YVFB55WXW6OQR234","json":"https://pith.science/pith/66APXV4M22YVFB55WXW6OQR234.json","graph_json":"https://pith.science/api/pith-number/66APXV4M22YVFB55WXW6OQR234/graph.json","events_json":"https://pith.science/api/pith-number/66APXV4M22YVFB55WXW6OQR234/events.json","paper":"https://pith.science/paper/66APXV4M"},"agent_actions":{"view_html":"https://pith.science/pith/66APXV4M22YVFB55WXW6OQR234","download_json":"https://pith.science/pith/66APXV4M22YVFB55WXW6OQR234.json","view_paper":"https://pith.science/paper/66APXV4M","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1104.3942&json=true","fetch_graph":"https://pith.science/api/pith-number/66APXV4M22YVFB55WXW6OQR234/graph.json","fetch_events":"https://pith.science/api/pith-number/66APXV4M22YVFB55WXW6OQR234/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/66APXV4M22YVFB55WXW6OQR234/action/timestamp_anchor","attest_storage":"https://pith.science/pith/66APXV4M22YVFB55WXW6OQR234/action/storage_attestation","attest_author":"https://pith.science/pith/66APXV4M22YVFB55WXW6OQR234/action/author_attestation","sign_citation":"https://pith.science/pith/66APXV4M22YVFB55WXW6OQR234/action/citation_signature","submit_replication":"https://pith.science/pith/66APXV4M22YVFB55WXW6OQR234/action/replication_record"}},"created_at":"2026-05-18T03:43:52.914742+00:00","updated_at":"2026-05-18T03:43:52.914742+00:00"}