{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:Y6TA2N23BDBPXBPI5XGXREJ2ZI","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":"0188bccdf87f0517ec49972f1b1f34a064172d7edb3f448ecb6c310af9cc30c3","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-12-16T11:28:53Z","title_canon_sha256":"d34b771afad1f460d267aa7a95d0483c82e1da31aee605aeee533c0488e365e8"},"schema_version":"1.0","source":{"id":"1512.05131","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.05131","created_at":"2026-05-18T01:01:28Z"},{"alias_kind":"arxiv_version","alias_value":"1512.05131v3","created_at":"2026-05-18T01:01:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.05131","created_at":"2026-05-18T01:01:28Z"},{"alias_kind":"pith_short_12","alias_value":"Y6TA2N23BDBP","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"Y6TA2N23BDBPXBPI","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"Y6TA2N23","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:d4da8444e5157a99bafd954cf483bc3a23277456c6f57c26612ac06798c99365","target":"graph","created_at":"2026-05-18T01:01:28Z","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":"We present an abstract form of the Pr\\'ekopa-Leindler inequality that includes several known -and a few new- related functional inequalities on Euclidean spaces. The method of proof and also the formulation of the new inequalities are based on Christer Borell's stochastic approach to Brunn-Minkowski type inequalities.","authors_text":"Bernard Maurey, Dario Cordero-Erausquin","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-12-16T11:28:53Z","title":"Some extensions of the Pr\\'ekopa-Leindler inequality using Borell's stochastic approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.05131","kind":"arxiv","version":3},"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:fff7b7bde17882d74478ab3019c1f7af83e68db1b5b93a851839c15c3f33cf42","target":"record","created_at":"2026-05-18T01:01:28Z","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":"0188bccdf87f0517ec49972f1b1f34a064172d7edb3f448ecb6c310af9cc30c3","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-12-16T11:28:53Z","title_canon_sha256":"d34b771afad1f460d267aa7a95d0483c82e1da31aee605aeee533c0488e365e8"},"schema_version":"1.0","source":{"id":"1512.05131","kind":"arxiv","version":3}},"canonical_sha256":"c7a60d375b08c2fb85e8edcd78913aca335e7a9e85c8e036c5d57746afca01fa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c7a60d375b08c2fb85e8edcd78913aca335e7a9e85c8e036c5d57746afca01fa","first_computed_at":"2026-05-18T01:01:28.871736Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:01:28.871736Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xdHTPzIH363PPYIlk5ir3P1hTo9zxrLpW597ECQZHNX0D35I0fIc24iD3iFM9/ycB1F1GUEwr9si8Xs75eeJBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:01:28.872189Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.05131","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fff7b7bde17882d74478ab3019c1f7af83e68db1b5b93a851839c15c3f33cf42","sha256:d4da8444e5157a99bafd954cf483bc3a23277456c6f57c26612ac06798c99365"],"state_sha256":"f8ef4a6188299f7e6af2a6726a6e4da8ce2cf22cb62be709c4dcda7de9027605"}