{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:TTKOC3SDA3VAGC7ZQRQAGH4CXP","short_pith_number":"pith:TTKOC3SD","schema_version":"1.0","canonical_sha256":"9cd4e16e4306ea030bf98460031f82bbea46eeee0fe64d8523e8ce3fff488e18","source":{"kind":"arxiv","id":"1908.06426","version":3},"attestation_state":"computed","paper":{"title":"On a generalization of the Hermite-Hadamard inequality and applications in convex geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.FA","authors_text":"Bernardo Gonz\\'alez Merino","submitted_at":"2019-08-18T11:30:43Z","abstract_excerpt":"In this paper we show the following result: if C is an n-dimensional 0-symmetric convex compact set, $f:C\\rightarrow[0,1)$ is concave, and $g:[0,1)\\rightarrow[0,1)$ is not identically zero, convex, with g(0)=0, then \\[ \\frac{1}{|C|}\\int_C g(f(x))dx \\leq \\frac12 \\int_{-1}^1g(f(0)(1+t))dt, \\] where |C| denotes the volume of C. If g? is strictly convex, equality holds if and only if f is affine, C is a generalized symmetric cylinder and f becomes 0 at one of the basis of C.\n  We exploit this inequality to answer a question of Francisco Santos on estimating the volume of a convex set by means of t"},"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":"1908.06426","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-08-18T11:30:43Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"b67e141e0ab24ee0b5cf65e5e8eb316e82586b65d61fce26bc4b1d8374955120","abstract_canon_sha256":"14024a0d8706cac682afcaa15195496549c699820465dd415f3b6717f049f12d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:58:36.735382Z","signature_b64":"7yLwhoODfV+hEn2nP7Ahl12f+mqJ0PLXb53PMRrfC8RvNkV+2F1qaVsxzG9frmwThjnkGtYr3uk36P4To7DnDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9cd4e16e4306ea030bf98460031f82bbea46eeee0fe64d8523e8ce3fff488e18","last_reissued_at":"2026-07-05T00:58:36.734986Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:58:36.734986Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On a generalization of the Hermite-Hadamard inequality and applications in convex geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.FA","authors_text":"Bernardo Gonz\\'alez Merino","submitted_at":"2019-08-18T11:30:43Z","abstract_excerpt":"In this paper we show the following result: if C is an n-dimensional 0-symmetric convex compact set, $f:C\\rightarrow[0,1)$ is concave, and $g:[0,1)\\rightarrow[0,1)$ is not identically zero, convex, with g(0)=0, then \\[ \\frac{1}{|C|}\\int_C g(f(x))dx \\leq \\frac12 \\int_{-1}^1g(f(0)(1+t))dt, \\] where |C| denotes the volume of C. If g? is strictly convex, equality holds if and only if f is affine, C is a generalized symmetric cylinder and f becomes 0 at one of the basis of C.\n  We exploit this inequality to answer a question of Francisco Santos on estimating the volume of a convex set by means of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.06426","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.06426/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1908.06426","created_at":"2026-07-05T00:58:36.735043+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.06426v3","created_at":"2026-07-05T00:58:36.735043+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.06426","created_at":"2026-07-05T00:58:36.735043+00:00"},{"alias_kind":"pith_short_12","alias_value":"TTKOC3SDA3VA","created_at":"2026-07-05T00:58:36.735043+00:00"},{"alias_kind":"pith_short_16","alias_value":"TTKOC3SDA3VAGC7Z","created_at":"2026-07-05T00:58:36.735043+00:00"},{"alias_kind":"pith_short_8","alias_value":"TTKOC3SD","created_at":"2026-07-05T00:58:36.735043+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.08933","citing_title":"The complete classification of empty lattice $4$-simplices","ref_index":17,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TTKOC3SDA3VAGC7ZQRQAGH4CXP","json":"https://pith.science/pith/TTKOC3SDA3VAGC7ZQRQAGH4CXP.json","graph_json":"https://pith.science/api/pith-number/TTKOC3SDA3VAGC7ZQRQAGH4CXP/graph.json","events_json":"https://pith.science/api/pith-number/TTKOC3SDA3VAGC7ZQRQAGH4CXP/events.json","paper":"https://pith.science/paper/TTKOC3SD"},"agent_actions":{"view_html":"https://pith.science/pith/TTKOC3SDA3VAGC7ZQRQAGH4CXP","download_json":"https://pith.science/pith/TTKOC3SDA3VAGC7ZQRQAGH4CXP.json","view_paper":"https://pith.science/paper/TTKOC3SD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.06426&json=true","fetch_graph":"https://pith.science/api/pith-number/TTKOC3SDA3VAGC7ZQRQAGH4CXP/graph.json","fetch_events":"https://pith.science/api/pith-number/TTKOC3SDA3VAGC7ZQRQAGH4CXP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TTKOC3SDA3VAGC7ZQRQAGH4CXP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TTKOC3SDA3VAGC7ZQRQAGH4CXP/action/storage_attestation","attest_author":"https://pith.science/pith/TTKOC3SDA3VAGC7ZQRQAGH4CXP/action/author_attestation","sign_citation":"https://pith.science/pith/TTKOC3SDA3VAGC7ZQRQAGH4CXP/action/citation_signature","submit_replication":"https://pith.science/pith/TTKOC3SDA3VAGC7ZQRQAGH4CXP/action/replication_record"}},"created_at":"2026-07-05T00:58:36.735043+00:00","updated_at":"2026-07-05T00:58:36.735043+00:00"}