{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:LGCSU5RFVIZP2DSDJ56HIQPGWR","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":"3b3d1f30b05f2f5300f9fae8f705dfc06bf34b76d672296a78e66965b5680d12","cross_cats_sorted":["math.FA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2018-11-07T15:12:35Z","title_canon_sha256":"9d42b26a38b127ea833aecab6fabab74c562567f47e2405a1328cdb058428c35"},"schema_version":"1.0","source":{"id":"1811.02926","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.02926","created_at":"2026-05-18T00:01:20Z"},{"alias_kind":"arxiv_version","alias_value":"1811.02926v1","created_at":"2026-05-18T00:01:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.02926","created_at":"2026-05-18T00:01:20Z"},{"alias_kind":"pith_short_12","alias_value":"LGCSU5RFVIZP","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"LGCSU5RFVIZP2DSD","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"LGCSU5RF","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:bebf5b58032c240f90e99cf30d4944ceada8dc18e24c2511f1d39f145a7f1331","target":"graph","created_at":"2026-05-18T00:01:20Z","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":"Stein kernels are a way of comparing probability distributions, defined via integration by parts formulas. We provide two constructions of Stein kernels in free probability. One is given by an explicit formula, and the other via free Poincar\\'e inequalities. In particular, we show that unlike in the classical setting, free Stein kernels always exist. As corollaries, we derive new bounds on the rate of convergence in the free CLT, and a strengthening of a characterization of the semicircular law due to Biane.","authors_text":"Guillaume C\\'ebron, Max Fathi, Tobias Mai","cross_cats":["math.FA","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2018-11-07T15:12:35Z","title":"A note on existence of free Stein kernels"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.02926","kind":"arxiv","version":1},"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:e6786353180eb1b9817e3e274129106ae87d624671732b3bf2c3e9a8b3d3ed55","target":"record","created_at":"2026-05-18T00:01:20Z","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":"3b3d1f30b05f2f5300f9fae8f705dfc06bf34b76d672296a78e66965b5680d12","cross_cats_sorted":["math.FA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2018-11-07T15:12:35Z","title_canon_sha256":"9d42b26a38b127ea833aecab6fabab74c562567f47e2405a1328cdb058428c35"},"schema_version":"1.0","source":{"id":"1811.02926","kind":"arxiv","version":1}},"canonical_sha256":"59852a7625aa32fd0e434f7c7441e6b45bb9ed2b83c64048a3c8b62439c90a5e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"59852a7625aa32fd0e434f7c7441e6b45bb9ed2b83c64048a3c8b62439c90a5e","first_computed_at":"2026-05-18T00:01:20.383140Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:20.383140Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZsCpb6dJ7o8d1Y8dYPsHXB124GmnBwEIG48EG0pUICNSF4n7PM+pWYvpe+pl3ZIQZRLIKckBVrGTug2Ql/ijDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:20.383924Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.02926","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e6786353180eb1b9817e3e274129106ae87d624671732b3bf2c3e9a8b3d3ed55","sha256:bebf5b58032c240f90e99cf30d4944ceada8dc18e24c2511f1d39f145a7f1331"],"state_sha256":"3c501feb27509d189b367b88d5244e440ab0f9d7d78f739b3a78b1c0e4254dd0"}