{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:HP35VODX2U7QXDMV6ASNFFP3KL","short_pith_number":"pith:HP35VODX","schema_version":"1.0","canonical_sha256":"3bf7dab877d53f0b8d95f024d295fb52eea1443e993c53400176c6709c820126","source":{"kind":"arxiv","id":"1809.03448","version":1},"attestation_state":"computed","paper":{"title":"CLT for fluctuations of linear statistics in the Sine-beta process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Thomas Lebl\\'e","submitted_at":"2018-09-10T16:37:43Z","abstract_excerpt":"We prove, for any $\\beta >0$, a central limit theorem for the fluctuations of linear statistics in the Sine-$\\beta$ process, which is the infinite volume limit of the random microscopic behavior in the bulk of one-dimensional log-gases at inverse temperature $\\beta$. If $\\phi$ is a compactly supported test function of class $C^4$, and $\\mathcal{C}$ is a random point configuration distributed according to Sine-$\\beta$, the integral of $\\phi(\\cdot / \\ell)$ against the random fluctuation $d\\mathcal{C} - dx$, converges in law, as $\\ell$ goes to infinity, to a centered normal random variable whose "},"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":"1809.03448","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-09-10T16:37:43Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"6382fa1a27f33b6b173b27e5828e5744befdbc35b36ae93647c235e6f3e2db15","abstract_canon_sha256":"2cf62576a968629acac11699e6506890bc475d32e21a41e6b79356650395cc50"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:06.866954Z","signature_b64":"NxeHzlpg2emOAxdOpFhfI92huGj8idiju4wBwbwdTL8hjOv5e626d/5/J/W5uHbxsv/6NtP0ua2Z0ZCEyvZGAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3bf7dab877d53f0b8d95f024d295fb52eea1443e993c53400176c6709c820126","last_reissued_at":"2026-05-18T00:06:06.866313Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:06.866313Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"CLT for fluctuations of linear statistics in the Sine-beta process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Thomas Lebl\\'e","submitted_at":"2018-09-10T16:37:43Z","abstract_excerpt":"We prove, for any $\\beta >0$, a central limit theorem for the fluctuations of linear statistics in the Sine-$\\beta$ process, which is the infinite volume limit of the random microscopic behavior in the bulk of one-dimensional log-gases at inverse temperature $\\beta$. If $\\phi$ is a compactly supported test function of class $C^4$, and $\\mathcal{C}$ is a random point configuration distributed according to Sine-$\\beta$, the integral of $\\phi(\\cdot / \\ell)$ against the random fluctuation $d\\mathcal{C} - dx$, converges in law, as $\\ell$ goes to infinity, to a centered normal random variable whose "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.03448","kind":"arxiv","version":1},"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":"1809.03448","created_at":"2026-05-18T00:06:06.866410+00:00"},{"alias_kind":"arxiv_version","alias_value":"1809.03448v1","created_at":"2026-05-18T00:06:06.866410+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.03448","created_at":"2026-05-18T00:06:06.866410+00:00"},{"alias_kind":"pith_short_12","alias_value":"HP35VODX2U7Q","created_at":"2026-05-18T12:32:28.185984+00:00"},{"alias_kind":"pith_short_16","alias_value":"HP35VODX2U7QXDMV","created_at":"2026-05-18T12:32:28.185984+00:00"},{"alias_kind":"pith_short_8","alias_value":"HP35VODX","created_at":"2026-05-18T12:32:28.185984+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/HP35VODX2U7QXDMV6ASNFFP3KL","json":"https://pith.science/pith/HP35VODX2U7QXDMV6ASNFFP3KL.json","graph_json":"https://pith.science/api/pith-number/HP35VODX2U7QXDMV6ASNFFP3KL/graph.json","events_json":"https://pith.science/api/pith-number/HP35VODX2U7QXDMV6ASNFFP3KL/events.json","paper":"https://pith.science/paper/HP35VODX"},"agent_actions":{"view_html":"https://pith.science/pith/HP35VODX2U7QXDMV6ASNFFP3KL","download_json":"https://pith.science/pith/HP35VODX2U7QXDMV6ASNFFP3KL.json","view_paper":"https://pith.science/paper/HP35VODX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1809.03448&json=true","fetch_graph":"https://pith.science/api/pith-number/HP35VODX2U7QXDMV6ASNFFP3KL/graph.json","fetch_events":"https://pith.science/api/pith-number/HP35VODX2U7QXDMV6ASNFFP3KL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HP35VODX2U7QXDMV6ASNFFP3KL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HP35VODX2U7QXDMV6ASNFFP3KL/action/storage_attestation","attest_author":"https://pith.science/pith/HP35VODX2U7QXDMV6ASNFFP3KL/action/author_attestation","sign_citation":"https://pith.science/pith/HP35VODX2U7QXDMV6ASNFFP3KL/action/citation_signature","submit_replication":"https://pith.science/pith/HP35VODX2U7QXDMV6ASNFFP3KL/action/replication_record"}},"created_at":"2026-05-18T00:06:06.866410+00:00","updated_at":"2026-05-18T00:06:06.866410+00:00"}