{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:REC4PCQ5OLMC644XLON64JENLE","short_pith_number":"pith:REC4PCQ5","schema_version":"1.0","canonical_sha256":"8905c78a1d72d82f73975b9bee248d5924a9626037f1fa375073aceba33f0b82","source":{"kind":"arxiv","id":"2410.02715","version":2},"attestation_state":"computed","paper":{"title":"A sharp symmetrized free transport-entropy inequality for the semicircular law","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.FA","math.PR"],"primary_cat":"math.OA","authors_text":"Charles-Philippe Diez","submitted_at":"2024-10-03T17:37:48Z","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"},"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":"2410.02715","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OA","submitted_at":"2024-10-03T17:37:48Z","cross_cats_sorted":["math.FA","math.PR"],"title_canon_sha256":"df99c6813689dc6c36796e6615dd6dc5065731dc3c61ca9d3a45957c1337a228","abstract_canon_sha256":"5941b29a5ea5294e0a9d7fb29effd463bca4e13f655a5685a4eef348f7261d37"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:54:04.834306Z","signature_b64":"PPp97k2iHicy0W/kaBOvo47yWBnezMgOFVZfd2IuTcPLvZne4pUM4jkhJ6DcnQlkuLZwvQsxOQdchexPxZvbAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8905c78a1d72d82f73975b9bee248d5924a9626037f1fa375073aceba33f0b82","last_reissued_at":"2026-07-05T09:54:04.833826Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:54:04.833826Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A sharp symmetrized free transport-entropy inequality for the semicircular law","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.FA","math.PR"],"primary_cat":"math.OA","authors_text":"Charles-Philippe Diez","submitted_at":"2024-10-03T17:37:48Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.02715","kind":"arxiv","version":2},"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/2410.02715/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":"2410.02715","created_at":"2026-07-05T09:54:04.833882+00:00"},{"alias_kind":"arxiv_version","alias_value":"2410.02715v2","created_at":"2026-07-05T09:54:04.833882+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.02715","created_at":"2026-07-05T09:54:04.833882+00:00"},{"alias_kind":"pith_short_12","alias_value":"REC4PCQ5OLMC","created_at":"2026-07-05T09:54:04.833882+00:00"},{"alias_kind":"pith_short_16","alias_value":"REC4PCQ5OLMC644X","created_at":"2026-07-05T09:54:04.833882+00:00"},{"alias_kind":"pith_short_8","alias_value":"REC4PCQ5","created_at":"2026-07-05T09:54:04.833882+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.12212","citing_title":"Free information geometry and the model theory of noncommutative stochastic processes","ref_index":21,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/REC4PCQ5OLMC644XLON64JENLE","json":"https://pith.science/pith/REC4PCQ5OLMC644XLON64JENLE.json","graph_json":"https://pith.science/api/pith-number/REC4PCQ5OLMC644XLON64JENLE/graph.json","events_json":"https://pith.science/api/pith-number/REC4PCQ5OLMC644XLON64JENLE/events.json","paper":"https://pith.science/paper/REC4PCQ5"},"agent_actions":{"view_html":"https://pith.science/pith/REC4PCQ5OLMC644XLON64JENLE","download_json":"https://pith.science/pith/REC4PCQ5OLMC644XLON64JENLE.json","view_paper":"https://pith.science/paper/REC4PCQ5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2410.02715&json=true","fetch_graph":"https://pith.science/api/pith-number/REC4PCQ5OLMC644XLON64JENLE/graph.json","fetch_events":"https://pith.science/api/pith-number/REC4PCQ5OLMC644XLON64JENLE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/REC4PCQ5OLMC644XLON64JENLE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/REC4PCQ5OLMC644XLON64JENLE/action/storage_attestation","attest_author":"https://pith.science/pith/REC4PCQ5OLMC644XLON64JENLE/action/author_attestation","sign_citation":"https://pith.science/pith/REC4PCQ5OLMC644XLON64JENLE/action/citation_signature","submit_replication":"https://pith.science/pith/REC4PCQ5OLMC644XLON64JENLE/action/replication_record"}},"created_at":"2026-07-05T09:54:04.833882+00:00","updated_at":"2026-07-05T09:54:04.833882+00:00"}