{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:GJ74JFBKVJPQ7KSHRA2PAUTX77","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":"e21f3d695c56be20bf1a7edea722164315083af45d734aaabb1f3821cb17d101","cross_cats_sorted":["math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-06-29T10:24:21Z","title_canon_sha256":"27f2ceb93472d6683840acd16ba7aef960305833463f1e8599c5d472c8ec5b86"},"schema_version":"1.0","source":{"id":"1706.09663","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.09663","created_at":"2026-05-18T00:24:10Z"},{"alias_kind":"arxiv_version","alias_value":"1706.09663v2","created_at":"2026-05-18T00:24:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.09663","created_at":"2026-05-18T00:24:10Z"},{"alias_kind":"pith_short_12","alias_value":"GJ74JFBKVJPQ","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"GJ74JFBKVJPQ7KSH","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"GJ74JFBK","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:48f27e8a9cc77d4445d9f68ef3bef5d6ba0be767c6f1d9662d7b7a8a22fc0917","target":"graph","created_at":"2026-05-18T00:24:10Z","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":"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.","authors_text":"Florent Bekerman, Sylvia Serfaty, Thomas Lebl\\'e","cross_cats":["math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-06-29T10:24:21Z","title":"CLT for fluctuations of $\\beta$-ensembles with general potential"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.09663","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":"sha256:5e57e7fcd947737169593ee96b298840d72478cbad9c7b0e7d28df2e4b996ac6","target":"record","created_at":"2026-05-18T00:24:10Z","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":"e21f3d695c56be20bf1a7edea722164315083af45d734aaabb1f3821cb17d101","cross_cats_sorted":["math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-06-29T10:24:21Z","title_canon_sha256":"27f2ceb93472d6683840acd16ba7aef960305833463f1e8599c5d472c8ec5b86"},"schema_version":"1.0","source":{"id":"1706.09663","kind":"arxiv","version":2}},"canonical_sha256":"327fc4942aaa5f0faa478834f05277ffd184638c25db20824ed93422fad90d16","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"327fc4942aaa5f0faa478834f05277ffd184638c25db20824ed93422fad90d16","first_computed_at":"2026-05-18T00:24:10.062660Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:10.062660Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jkEzCEwtyiVO+QEY0BzdydBTwx/EjcMgTsTwbbac8N3d+A8PlNvhbHFjqwwLMxvP5prg6G7n+ejXo05FfaBNAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:10.063331Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.09663","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5e57e7fcd947737169593ee96b298840d72478cbad9c7b0e7d28df2e4b996ac6","sha256:48f27e8a9cc77d4445d9f68ef3bef5d6ba0be767c6f1d9662d7b7a8a22fc0917"],"state_sha256":"5b9eb450a05b4f93a1e2266dd95e823870977f0dcd03670c5583395fae2d2aa9"}