{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:44636OR6WWRBHL3PYXOPSRUQ3V","short_pith_number":"pith:44636OR6","schema_version":"1.0","canonical_sha256":"e73dbf3a3eb5a213af6fc5dcf94690dd67e7989ac40dedecebf05e3997dd230b","source":{"kind":"arxiv","id":"1402.3250","version":1},"attestation_state":"computed","paper":{"title":"Functional versions of L_p-affine surface area and entropy inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"C. Schuett, E. M. Werner, J. Lehec, M. Fradelizi, O. Guedon, U. Caglar","submitted_at":"2014-02-13T18:57:22Z","abstract_excerpt":"In contemporary convex geometry, the rapidly developing L_p-Brunn Minkowski theory is a modern analogue of the classical Brunn Minkowski theory. A cornerstone of this theory is the L_p-affine surface area for convex bodies. Here, we introduce a functional form of this concept, for log concave and s-concave functions. We show that the new functional form is a generalization of the original L_p-affine surface area. We prove duality relations and affine isoperimetric inequalities for log concave and s-concave functions. This leads to a new inverse log-Sobolev inequality for s-concave densities."},"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":"1402.3250","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-02-13T18:57:22Z","cross_cats_sorted":[],"title_canon_sha256":"94fbf0dfab239f0d68a8ae1ffd5de7f4d5e99372db17d716f17c89821c762578","abstract_canon_sha256":"ef6f2106e3e8a52f7ed657d4d39eba3137ebb48295383c0d03e6ca7a55144539"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:59:07.109816Z","signature_b64":"5aeuJQ/e8Ap/Ogq0OpHOon+/QZL/fZmTmwWRnsV41O8qvqV2fqT+qijB5veuGvq/EDDyKHLBcxEFLR4+FL01AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e73dbf3a3eb5a213af6fc5dcf94690dd67e7989ac40dedecebf05e3997dd230b","last_reissued_at":"2026-05-18T02:59:07.109067Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:59:07.109067Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Functional versions of L_p-affine surface area and entropy inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"C. Schuett, E. M. Werner, J. Lehec, M. Fradelizi, O. Guedon, U. Caglar","submitted_at":"2014-02-13T18:57:22Z","abstract_excerpt":"In contemporary convex geometry, the rapidly developing L_p-Brunn Minkowski theory is a modern analogue of the classical Brunn Minkowski theory. A cornerstone of this theory is the L_p-affine surface area for convex bodies. Here, we introduce a functional form of this concept, for log concave and s-concave functions. We show that the new functional form is a generalization of the original L_p-affine surface area. We prove duality relations and affine isoperimetric inequalities for log concave and s-concave functions. This leads to a new inverse log-Sobolev inequality for s-concave densities."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.3250","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":"1402.3250","created_at":"2026-05-18T02:59:07.109178+00:00"},{"alias_kind":"arxiv_version","alias_value":"1402.3250v1","created_at":"2026-05-18T02:59:07.109178+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.3250","created_at":"2026-05-18T02:59:07.109178+00:00"},{"alias_kind":"pith_short_12","alias_value":"44636OR6WWRB","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_16","alias_value":"44636OR6WWRBHL3P","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_8","alias_value":"44636OR6","created_at":"2026-05-18T12:28:11.866339+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/44636OR6WWRBHL3PYXOPSRUQ3V","json":"https://pith.science/pith/44636OR6WWRBHL3PYXOPSRUQ3V.json","graph_json":"https://pith.science/api/pith-number/44636OR6WWRBHL3PYXOPSRUQ3V/graph.json","events_json":"https://pith.science/api/pith-number/44636OR6WWRBHL3PYXOPSRUQ3V/events.json","paper":"https://pith.science/paper/44636OR6"},"agent_actions":{"view_html":"https://pith.science/pith/44636OR6WWRBHL3PYXOPSRUQ3V","download_json":"https://pith.science/pith/44636OR6WWRBHL3PYXOPSRUQ3V.json","view_paper":"https://pith.science/paper/44636OR6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1402.3250&json=true","fetch_graph":"https://pith.science/api/pith-number/44636OR6WWRBHL3PYXOPSRUQ3V/graph.json","fetch_events":"https://pith.science/api/pith-number/44636OR6WWRBHL3PYXOPSRUQ3V/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/44636OR6WWRBHL3PYXOPSRUQ3V/action/timestamp_anchor","attest_storage":"https://pith.science/pith/44636OR6WWRBHL3PYXOPSRUQ3V/action/storage_attestation","attest_author":"https://pith.science/pith/44636OR6WWRBHL3PYXOPSRUQ3V/action/author_attestation","sign_citation":"https://pith.science/pith/44636OR6WWRBHL3PYXOPSRUQ3V/action/citation_signature","submit_replication":"https://pith.science/pith/44636OR6WWRBHL3PYXOPSRUQ3V/action/replication_record"}},"created_at":"2026-05-18T02:59:07.109178+00:00","updated_at":"2026-05-18T02:59:07.109178+00:00"}