{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:WNVIDUHJBCURQK2T63TNAURZ4V","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":"3c541beaac27f21677074e3827e6a5a2eabed846320f090f70acae1974885d5a","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2024-09-09T12:02:33Z","title_canon_sha256":"7bb8e8a4ebbcb0fc2c9c060fe4d3ca488502b87583d314fdeb5b2ff4665a8853"},"schema_version":"1.0","source":{"id":"2409.05541","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.05541","created_at":"2026-07-05T10:09:47Z"},{"alias_kind":"arxiv_version","alias_value":"2409.05541v2","created_at":"2026-07-05T10:09:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.05541","created_at":"2026-07-05T10:09:47Z"},{"alias_kind":"pith_short_12","alias_value":"WNVIDUHJBCUR","created_at":"2026-07-05T10:09:47Z"},{"alias_kind":"pith_short_16","alias_value":"WNVIDUHJBCURQK2T","created_at":"2026-07-05T10:09:47Z"},{"alias_kind":"pith_short_8","alias_value":"WNVIDUHJ","created_at":"2026-07-05T10:09:47Z"}],"graph_snapshots":[{"event_id":"sha256:5ddfe80fa72b83b73e132b5aa3e58adad8ef3cc17853ad3119f63b7438fb865d","target":"graph","created_at":"2026-07-05T10:09:47Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2409.05541/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Nakamura and Tsuji recently obtained an integral inequality involving a Laplace transform of even functions that implies, at the limit, the Blaschke-Santal\\'o inequality in its functional form. Inspired by their method, based on the Fokker-Planck semi-group, we extend the inequality to non-even functions. We consider a well-chosen centering procedure by studying the infimum over translations in a double Laplace transform. This requires a new look on the existing methods and leads to several observations of independent interest on the geometry of the Laplace transform. Application to reverse hy","authors_text":"Dario Cordero-Erausquin, Dylan Langharst, Matthieu Fradelizi","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2024-09-09T12:02:33Z","title":"On a Santal\\'o point for Nakamura-Tsuji's Laplace transform inequality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.05541","kind":"arxiv","version":2},"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:b6ad6a550c0799b044b07349e72e3f6e4f631bb858f105379c6aede9bdcfa99b","target":"record","created_at":"2026-07-05T10:09:47Z","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":"3c541beaac27f21677074e3827e6a5a2eabed846320f090f70acae1974885d5a","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2024-09-09T12:02:33Z","title_canon_sha256":"7bb8e8a4ebbcb0fc2c9c060fe4d3ca488502b87583d314fdeb5b2ff4665a8853"},"schema_version":"1.0","source":{"id":"2409.05541","kind":"arxiv","version":2}},"canonical_sha256":"b36a81d0e908a9182b53f6e6d05239e551ffe9b97546a5cfa08ec881bfa0a5a9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b36a81d0e908a9182b53f6e6d05239e551ffe9b97546a5cfa08ec881bfa0a5a9","first_computed_at":"2026-07-05T10:09:47.570383Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:09:47.570383Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5/YLlTFmjurKkVlSNJownIsLyt3ErYUTbHogiZissOXwuYJGSaDGO8jzJEpu1CJ0hQlIL43lHAW3IR5ytaJ2Aw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:09:47.570902Z","signed_message":"canonical_sha256_bytes"},"source_id":"2409.05541","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b6ad6a550c0799b044b07349e72e3f6e4f631bb858f105379c6aede9bdcfa99b","sha256:5ddfe80fa72b83b73e132b5aa3e58adad8ef3cc17853ad3119f63b7438fb865d"],"state_sha256":"be3eb8b8ca8063182e7ab9cac03e87bb4b698f9056c56aae13842571a9adbb04"}