{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:LAIGUOBGSZ7CIOPS25ZGPRHZHD","short_pith_number":"pith:LAIGUOBG","schema_version":"1.0","canonical_sha256":"58106a3826967e2439f2d77267c4f938c4a2960d99fdf38ee7c76452ec7bd5b3","source":{"kind":"arxiv","id":"1905.04038","version":1},"attestation_state":"computed","paper":{"title":"Transport Proofs Of Some Discrete Variants Of The Pr{\\'e}Kopa-leindler Inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.PR","authors_text":"Cyril Roberto (LAMA), Nathael Gozlan (MAP5 - UMR 8145), Paul-Marie Samson (LAMA), Prasad Tetali (School of Mathematics)","submitted_at":"2019-05-10T09:49:06Z","abstract_excerpt":"We give a transport proof of a discrete version of the displacement convexity of entropy on integers (Z), and get, as a consequence, two discrete forms of the Pr{\\'e}kopa-Leindler Inequality : the Four Functions Theorem of Ahlswede and Daykin on the discrete hypercube [1] and a recent result on Z due to Klartag and Lehec [16]."},"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":"1905.04038","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-05-10T09:49:06Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"d7756a366390e482dfae3d5672029d5b58c8d420ca2a569306d80601791779d1","abstract_canon_sha256":"07fb21c258ef230cafcb6fbff7b402a28e451b16ad5a8c4b3f41432134c58fda"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:34.764220Z","signature_b64":"h4nWbMGTOvHiabwuRKz5H9Aod1K+axrhT7tlCw1n+Jogzv8mY6+Dvt49W0Zy3wDht717Q5HGYAn5Wsbh/EllBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"58106a3826967e2439f2d77267c4f938c4a2960d99fdf38ee7c76452ec7bd5b3","last_reissued_at":"2026-05-17T23:46:34.763494Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:34.763494Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Transport Proofs Of Some Discrete Variants Of The Pr{\\'e}Kopa-leindler Inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.PR","authors_text":"Cyril Roberto (LAMA), Nathael Gozlan (MAP5 - UMR 8145), Paul-Marie Samson (LAMA), Prasad Tetali (School of Mathematics)","submitted_at":"2019-05-10T09:49:06Z","abstract_excerpt":"We give a transport proof of a discrete version of the displacement convexity of entropy on integers (Z), and get, as a consequence, two discrete forms of the Pr{\\'e}kopa-Leindler Inequality : the Four Functions Theorem of Ahlswede and Daykin on the discrete hypercube [1] and a recent result on Z due to Klartag and Lehec [16]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.04038","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":"1905.04038","created_at":"2026-05-17T23:46:34.763605+00:00"},{"alias_kind":"arxiv_version","alias_value":"1905.04038v1","created_at":"2026-05-17T23:46:34.763605+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.04038","created_at":"2026-05-17T23:46:34.763605+00:00"},{"alias_kind":"pith_short_12","alias_value":"LAIGUOBGSZ7C","created_at":"2026-05-18T12:33:21.387695+00:00"},{"alias_kind":"pith_short_16","alias_value":"LAIGUOBGSZ7CIOPS","created_at":"2026-05-18T12:33:21.387695+00:00"},{"alias_kind":"pith_short_8","alias_value":"LAIGUOBG","created_at":"2026-05-18T12:33:21.387695+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/LAIGUOBGSZ7CIOPS25ZGPRHZHD","json":"https://pith.science/pith/LAIGUOBGSZ7CIOPS25ZGPRHZHD.json","graph_json":"https://pith.science/api/pith-number/LAIGUOBGSZ7CIOPS25ZGPRHZHD/graph.json","events_json":"https://pith.science/api/pith-number/LAIGUOBGSZ7CIOPS25ZGPRHZHD/events.json","paper":"https://pith.science/paper/LAIGUOBG"},"agent_actions":{"view_html":"https://pith.science/pith/LAIGUOBGSZ7CIOPS25ZGPRHZHD","download_json":"https://pith.science/pith/LAIGUOBGSZ7CIOPS25ZGPRHZHD.json","view_paper":"https://pith.science/paper/LAIGUOBG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1905.04038&json=true","fetch_graph":"https://pith.science/api/pith-number/LAIGUOBGSZ7CIOPS25ZGPRHZHD/graph.json","fetch_events":"https://pith.science/api/pith-number/LAIGUOBGSZ7CIOPS25ZGPRHZHD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LAIGUOBGSZ7CIOPS25ZGPRHZHD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LAIGUOBGSZ7CIOPS25ZGPRHZHD/action/storage_attestation","attest_author":"https://pith.science/pith/LAIGUOBGSZ7CIOPS25ZGPRHZHD/action/author_attestation","sign_citation":"https://pith.science/pith/LAIGUOBGSZ7CIOPS25ZGPRHZHD/action/citation_signature","submit_replication":"https://pith.science/pith/LAIGUOBGSZ7CIOPS25ZGPRHZHD/action/replication_record"}},"created_at":"2026-05-17T23:46:34.763605+00:00","updated_at":"2026-05-17T23:46:34.763605+00:00"}