{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:GJ74JFBKVJPQ7KSHRA2PAUTX77","short_pith_number":"pith:GJ74JFBK","schema_version":"1.0","canonical_sha256":"327fc4942aaa5f0faa478834f05277ffd184638c25db20824ed93422fad90d16","source":{"kind":"arxiv","id":"1706.09663","version":2},"attestation_state":"computed","paper":{"title":"CLT for fluctuations of $\\beta$-ensembles with general potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Florent Bekerman, Sylvia Serfaty, Thomas Lebl\\'e","submitted_at":"2017-06-29T10:24:21Z","abstract_excerpt":"We prove a central limit theorem for the linear statistics of one-dimensional log-gases, or $\\beta$-ensembles. We use a method based on a change of variables which allows to treat fairly general situations, including multi-cut and, for the first time, critical cases, and generalizes the previously known results of Johansson, Borot-Guionnet and Shcherbina. In the one-cut regular case, our approach also allows to retrieve a rate of convergence as well as previously known expansions of the free energy to arbitrary order."},"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":"1706.09663","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-06-29T10:24:21Z","cross_cats_sorted":["math.MP","math.PR"],"title_canon_sha256":"27f2ceb93472d6683840acd16ba7aef960305833463f1e8599c5d472c8ec5b86","abstract_canon_sha256":"e21f3d695c56be20bf1a7edea722164315083af45d734aaabb1f3821cb17d101"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:10.063331Z","signature_b64":"jkEzCEwtyiVO+QEY0BzdydBTwx/EjcMgTsTwbbac8N3d+A8PlNvhbHFjqwwLMxvP5prg6G7n+ejXo05FfaBNAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"327fc4942aaa5f0faa478834f05277ffd184638c25db20824ed93422fad90d16","last_reissued_at":"2026-05-18T00:24:10.062660Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:10.062660Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"CLT for fluctuations of $\\beta$-ensembles with general potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Florent Bekerman, Sylvia Serfaty, Thomas Lebl\\'e","submitted_at":"2017-06-29T10:24:21Z","abstract_excerpt":"We prove a central limit theorem for the linear statistics of one-dimensional log-gases, or $\\beta$-ensembles. We use a method based on a change of variables which allows to treat fairly general situations, including multi-cut and, for the first time, critical cases, and generalizes the previously known results of Johansson, Borot-Guionnet and Shcherbina. In the one-cut regular case, our approach also allows to retrieve a rate of convergence as well as previously known expansions of the free energy to arbitrary order."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.09663","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":""},"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":"1706.09663","created_at":"2026-05-18T00:24:10.062770+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.09663v2","created_at":"2026-05-18T00:24:10.062770+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.09663","created_at":"2026-05-18T00:24:10.062770+00:00"},{"alias_kind":"pith_short_12","alias_value":"GJ74JFBKVJPQ","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_16","alias_value":"GJ74JFBKVJPQ7KSH","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_8","alias_value":"GJ74JFBK","created_at":"2026-05-18T12:31:18.294218+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GJ74JFBKVJPQ7KSHRA2PAUTX77","json":"https://pith.science/pith/GJ74JFBKVJPQ7KSHRA2PAUTX77.json","graph_json":"https://pith.science/api/pith-number/GJ74JFBKVJPQ7KSHRA2PAUTX77/graph.json","events_json":"https://pith.science/api/pith-number/GJ74JFBKVJPQ7KSHRA2PAUTX77/events.json","paper":"https://pith.science/paper/GJ74JFBK"},"agent_actions":{"view_html":"https://pith.science/pith/GJ74JFBKVJPQ7KSHRA2PAUTX77","download_json":"https://pith.science/pith/GJ74JFBKVJPQ7KSHRA2PAUTX77.json","view_paper":"https://pith.science/paper/GJ74JFBK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.09663&json=true","fetch_graph":"https://pith.science/api/pith-number/GJ74JFBKVJPQ7KSHRA2PAUTX77/graph.json","fetch_events":"https://pith.science/api/pith-number/GJ74JFBKVJPQ7KSHRA2PAUTX77/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GJ74JFBKVJPQ7KSHRA2PAUTX77/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GJ74JFBKVJPQ7KSHRA2PAUTX77/action/storage_attestation","attest_author":"https://pith.science/pith/GJ74JFBKVJPQ7KSHRA2PAUTX77/action/author_attestation","sign_citation":"https://pith.science/pith/GJ74JFBKVJPQ7KSHRA2PAUTX77/action/citation_signature","submit_replication":"https://pith.science/pith/GJ74JFBKVJPQ7KSHRA2PAUTX77/action/replication_record"}},"created_at":"2026-05-18T00:24:10.062770+00:00","updated_at":"2026-05-18T00:24:10.062770+00:00"}