{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:TKCRFCHEHGOEVPISKSTZ5VZEQ6","short_pith_number":"pith:TKCRFCHE","schema_version":"1.0","canonical_sha256":"9a851288e4399c4abd1254a79ed7248795b9b5a4ce5811a00c26c86ce0b8a0ba","source":{"kind":"arxiv","id":"1302.4589","version":3},"attestation_state":"computed","paper":{"title":"Dimensional variance inequalities of Brascamp-Lieb type and a local approach to dimensional Pr\\'ekopa's theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Van Hoang Nguyen","submitted_at":"2013-02-19T12:13:32Z","abstract_excerpt":"We give a new approach, inspired by H\\\"ormander's $L^2$-method, to weighted variance inequalities which extend results obtained by Bobkov and Ledoux. It provides in particular a local proof of the dimensional functional forms of the Brunn-Minkowski inequalities. We also present several applications of these variance inequalities, including reverse H\\\"older inequalities for convex functions, weighted Brascamp-Lieb inequalities and sharp weighted Poincar\\'{e} inequalities for generalized Cauchy measures."},"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":"1302.4589","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-02-19T12:13:32Z","cross_cats_sorted":[],"title_canon_sha256":"c195ebdd4c741949ff61258a68bef272943f440c65b366b97a051a779dfa5bce","abstract_canon_sha256":"b7ea86d7adbf84afdf8c6957609ac96a704f6a200a0a214cbe1916851a23cfe5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:08:04.290018Z","signature_b64":"EokZjOYsTcYDCHCk8jPoZ2Pa5PisQILrK5d7hjHFBgSMDz9xmbhQ1IqF10QUOSZPqiX/G0u/aILt6VeMxMtcBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a851288e4399c4abd1254a79ed7248795b9b5a4ce5811a00c26c86ce0b8a0ba","last_reissued_at":"2026-05-18T03:08:04.289457Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:08:04.289457Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dimensional variance inequalities of Brascamp-Lieb type and a local approach to dimensional Pr\\'ekopa's theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Van Hoang Nguyen","submitted_at":"2013-02-19T12:13:32Z","abstract_excerpt":"We give a new approach, inspired by H\\\"ormander's $L^2$-method, to weighted variance inequalities which extend results obtained by Bobkov and Ledoux. It provides in particular a local proof of the dimensional functional forms of the Brunn-Minkowski inequalities. We also present several applications of these variance inequalities, including reverse H\\\"older inequalities for convex functions, weighted Brascamp-Lieb inequalities and sharp weighted Poincar\\'{e} inequalities for generalized Cauchy measures."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.4589","kind":"arxiv","version":3},"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":"1302.4589","created_at":"2026-05-18T03:08:04.289552+00:00"},{"alias_kind":"arxiv_version","alias_value":"1302.4589v3","created_at":"2026-05-18T03:08:04.289552+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.4589","created_at":"2026-05-18T03:08:04.289552+00:00"},{"alias_kind":"pith_short_12","alias_value":"TKCRFCHEHGOE","created_at":"2026-05-18T12:28:02.375192+00:00"},{"alias_kind":"pith_short_16","alias_value":"TKCRFCHEHGOEVPIS","created_at":"2026-05-18T12:28:02.375192+00:00"},{"alias_kind":"pith_short_8","alias_value":"TKCRFCHE","created_at":"2026-05-18T12:28:02.375192+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/TKCRFCHEHGOEVPISKSTZ5VZEQ6","json":"https://pith.science/pith/TKCRFCHEHGOEVPISKSTZ5VZEQ6.json","graph_json":"https://pith.science/api/pith-number/TKCRFCHEHGOEVPISKSTZ5VZEQ6/graph.json","events_json":"https://pith.science/api/pith-number/TKCRFCHEHGOEVPISKSTZ5VZEQ6/events.json","paper":"https://pith.science/paper/TKCRFCHE"},"agent_actions":{"view_html":"https://pith.science/pith/TKCRFCHEHGOEVPISKSTZ5VZEQ6","download_json":"https://pith.science/pith/TKCRFCHEHGOEVPISKSTZ5VZEQ6.json","view_paper":"https://pith.science/paper/TKCRFCHE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1302.4589&json=true","fetch_graph":"https://pith.science/api/pith-number/TKCRFCHEHGOEVPISKSTZ5VZEQ6/graph.json","fetch_events":"https://pith.science/api/pith-number/TKCRFCHEHGOEVPISKSTZ5VZEQ6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TKCRFCHEHGOEVPISKSTZ5VZEQ6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TKCRFCHEHGOEVPISKSTZ5VZEQ6/action/storage_attestation","attest_author":"https://pith.science/pith/TKCRFCHEHGOEVPISKSTZ5VZEQ6/action/author_attestation","sign_citation":"https://pith.science/pith/TKCRFCHEHGOEVPISKSTZ5VZEQ6/action/citation_signature","submit_replication":"https://pith.science/pith/TKCRFCHEHGOEVPISKSTZ5VZEQ6/action/replication_record"}},"created_at":"2026-05-18T03:08:04.289552+00:00","updated_at":"2026-05-18T03:08:04.289552+00:00"}