{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:44636OR6WWRBHL3PYXOPSRUQ3V","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"ef6f2106e3e8a52f7ed657d4d39eba3137ebb48295383c0d03e6ca7a55144539","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-02-13T18:57:22Z","title_canon_sha256":"94fbf0dfab239f0d68a8ae1ffd5de7f4d5e99372db17d716f17c89821c762578"},"schema_version":"1.0","source":{"id":"1402.3250","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.3250","created_at":"2026-05-18T02:59:07Z"},{"alias_kind":"arxiv_version","alias_value":"1402.3250v1","created_at":"2026-05-18T02:59:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.3250","created_at":"2026-05-18T02:59:07Z"},{"alias_kind":"pith_short_12","alias_value":"44636OR6WWRB","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"44636OR6WWRBHL3P","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"44636OR6","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:89d2b368296c9dfc31e36979f54e088ef4b4fba6c0dc8f9bed3486531b2ce1aa","target":"graph","created_at":"2026-05-18T02:59:07Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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.","authors_text":"C. Schuett, E. M. Werner, J. Lehec, M. Fradelizi, O. Guedon, U. Caglar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-02-13T18:57:22Z","title":"Functional versions of L_p-affine surface area and entropy inequalities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.3250","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:dc141b136aa741d884b45ef03bc12c3f2e910390874da23370a46673905bde6f","target":"record","created_at":"2026-05-18T02:59:07Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"ef6f2106e3e8a52f7ed657d4d39eba3137ebb48295383c0d03e6ca7a55144539","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-02-13T18:57:22Z","title_canon_sha256":"94fbf0dfab239f0d68a8ae1ffd5de7f4d5e99372db17d716f17c89821c762578"},"schema_version":"1.0","source":{"id":"1402.3250","kind":"arxiv","version":1}},"canonical_sha256":"e73dbf3a3eb5a213af6fc5dcf94690dd67e7989ac40dedecebf05e3997dd230b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e73dbf3a3eb5a213af6fc5dcf94690dd67e7989ac40dedecebf05e3997dd230b","first_computed_at":"2026-05-18T02:59:07.109067Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:59:07.109067Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5aeuJQ/e8Ap/Ogq0OpHOon+/QZL/fZmTmwWRnsV41O8qvqV2fqT+qijB5veuGvq/EDDyKHLBcxEFLR4+FL01AA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:59:07.109816Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.3250","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dc141b136aa741d884b45ef03bc12c3f2e910390874da23370a46673905bde6f","sha256:89d2b368296c9dfc31e36979f54e088ef4b4fba6c0dc8f9bed3486531b2ce1aa"],"state_sha256":"0806f82afe45f98c7d694b828fb8b3e29e96f1106978dea19a297806d7671d32"}