{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:REC4PCQ5OLMC644XLON64JENLE","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":"5941b29a5ea5294e0a9d7fb29effd463bca4e13f655a5685a4eef348f7261d37","cross_cats_sorted":["math.FA","math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OA","submitted_at":"2024-10-03T17:37:48Z","title_canon_sha256":"df99c6813689dc6c36796e6615dd6dc5065731dc3c61ca9d3a45957c1337a228"},"schema_version":"1.0","source":{"id":"2410.02715","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.02715","created_at":"2026-07-05T09:54:04Z"},{"alias_kind":"arxiv_version","alias_value":"2410.02715v2","created_at":"2026-07-05T09:54:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.02715","created_at":"2026-07-05T09:54:04Z"},{"alias_kind":"pith_short_12","alias_value":"REC4PCQ5OLMC","created_at":"2026-07-05T09:54:04Z"},{"alias_kind":"pith_short_16","alias_value":"REC4PCQ5OLMC644X","created_at":"2026-07-05T09:54:04Z"},{"alias_kind":"pith_short_8","alias_value":"REC4PCQ5","created_at":"2026-07-05T09:54:04Z"}],"graph_snapshots":[{"event_id":"sha256:1305149de6bab648e899680444ccc08ddb736a41cd58ae894cae9b1a5f4e7718","target":"graph","created_at":"2026-07-05T09:54:04Z","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/2410.02715/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, following the recent work of Fathi (2018) in the classical case, we provide by two different methods a sharp symmetrized free Talagrand inequality for the semicircular law, which improves the free TCI of Biane and Voiculescu (2000). The first proof holds only in the one-dimensional case and has the advantage of providing a connection with the machinery of free moment maps introduced by Bahr and Boschert (2023) and a free reverse Log-Sobolev inequality. This case also and sheds light on a dual formulation via the free version of the functional Blaschke-Santalo inequality. The sec","authors_text":"Charles-Philippe Diez","cross_cats":["math.FA","math.PR"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OA","submitted_at":"2024-10-03T17:37:48Z","title":"A sharp symmetrized free transport-entropy inequality for the semicircular law"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.02715","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:c662826f4a909cae7ad4d1cb497d3eb2966ed1507e1393066a43b88c3ed358c8","target":"record","created_at":"2026-07-05T09:54:04Z","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":"5941b29a5ea5294e0a9d7fb29effd463bca4e13f655a5685a4eef348f7261d37","cross_cats_sorted":["math.FA","math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OA","submitted_at":"2024-10-03T17:37:48Z","title_canon_sha256":"df99c6813689dc6c36796e6615dd6dc5065731dc3c61ca9d3a45957c1337a228"},"schema_version":"1.0","source":{"id":"2410.02715","kind":"arxiv","version":2}},"canonical_sha256":"8905c78a1d72d82f73975b9bee248d5924a9626037f1fa375073aceba33f0b82","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8905c78a1d72d82f73975b9bee248d5924a9626037f1fa375073aceba33f0b82","first_computed_at":"2026-07-05T09:54:04.833826Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:54:04.833826Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PPp97k2iHicy0W/kaBOvo47yWBnezMgOFVZfd2IuTcPLvZne4pUM4jkhJ6DcnQlkuLZwvQsxOQdchexPxZvbAA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:54:04.834306Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.02715","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c662826f4a909cae7ad4d1cb497d3eb2966ed1507e1393066a43b88c3ed358c8","sha256:1305149de6bab648e899680444ccc08ddb736a41cd58ae894cae9b1a5f4e7718"],"state_sha256":"cfb0ce31222c46f610a1b15c86994ed5feafb3352d1355367d0ce6a5890d1dd0"}