{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:2742QIZ53VTIMEXG4BUT7QSS2P","short_pith_number":"pith:2742QIZ5","schema_version":"1.0","canonical_sha256":"d7f9a8233ddd668612e6e0693fc252d3ea9deb3a4fb44b7c2c2229d32813ba40","source":{"kind":"arxiv","id":"1506.07117","version":1},"attestation_state":"computed","paper":{"title":"Overcrowding asymptotics for 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":"Benedek Valk\\'o, Diane Holcomb","submitted_at":"2015-06-23T18:05:17Z","abstract_excerpt":"We give overcrowding estimates for the Sine_beta process, the bulk point process limit of the Gaussian beta-ensemble. We show that the probability of having at least n points in a fixed interval is given by $e^{-\\frac{\\beta}{2} n^2 \\log(n)+O(n^2)}$ as $n\\to \\infty$. We also identify the next order term in the exponent if the size of the interval goes to zero."},"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":"1506.07117","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-23T18:05:17Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"8f261f903919de3784f26f6a845820be9034d0b2e3c4186e15a8b0bd799d9480","abstract_canon_sha256":"03f970adf885bb2d01a890aee19c1394ba6f28e12ea08a99224fe318553f9fa9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:40:55.113337Z","signature_b64":"3xiz3nx8uOv2voFqvkDHVQk8LdNJPFVLG1nWLQv7bkuoYA8RyYRgQ8LdzxMYwYsTSXXY2z1jAG8Wh/W1BXPeBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d7f9a8233ddd668612e6e0693fc252d3ea9deb3a4fb44b7c2c2229d32813ba40","last_reissued_at":"2026-05-18T01:40:55.112519Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:40:55.112519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Overcrowding asymptotics for 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":"Benedek Valk\\'o, Diane Holcomb","submitted_at":"2015-06-23T18:05:17Z","abstract_excerpt":"We give overcrowding estimates for the Sine_beta process, the bulk point process limit of the Gaussian beta-ensemble. We show that the probability of having at least n points in a fixed interval is given by $e^{-\\frac{\\beta}{2} n^2 \\log(n)+O(n^2)}$ as $n\\to \\infty$. We also identify the next order term in the exponent if the size of the interval goes to zero."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.07117","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":"1506.07117","created_at":"2026-05-18T01:40:55.112654+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.07117v1","created_at":"2026-05-18T01:40:55.112654+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.07117","created_at":"2026-05-18T01:40:55.112654+00:00"},{"alias_kind":"pith_short_12","alias_value":"2742QIZ53VTI","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_16","alias_value":"2742QIZ53VTIMEXG","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_8","alias_value":"2742QIZ5","created_at":"2026-05-18T12:28:59.999130+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/2742QIZ53VTIMEXG4BUT7QSS2P","json":"https://pith.science/pith/2742QIZ53VTIMEXG4BUT7QSS2P.json","graph_json":"https://pith.science/api/pith-number/2742QIZ53VTIMEXG4BUT7QSS2P/graph.json","events_json":"https://pith.science/api/pith-number/2742QIZ53VTIMEXG4BUT7QSS2P/events.json","paper":"https://pith.science/paper/2742QIZ5"},"agent_actions":{"view_html":"https://pith.science/pith/2742QIZ53VTIMEXG4BUT7QSS2P","download_json":"https://pith.science/pith/2742QIZ53VTIMEXG4BUT7QSS2P.json","view_paper":"https://pith.science/paper/2742QIZ5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.07117&json=true","fetch_graph":"https://pith.science/api/pith-number/2742QIZ53VTIMEXG4BUT7QSS2P/graph.json","fetch_events":"https://pith.science/api/pith-number/2742QIZ53VTIMEXG4BUT7QSS2P/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2742QIZ53VTIMEXG4BUT7QSS2P/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2742QIZ53VTIMEXG4BUT7QSS2P/action/storage_attestation","attest_author":"https://pith.science/pith/2742QIZ53VTIMEXG4BUT7QSS2P/action/author_attestation","sign_citation":"https://pith.science/pith/2742QIZ53VTIMEXG4BUT7QSS2P/action/citation_signature","submit_replication":"https://pith.science/pith/2742QIZ53VTIMEXG4BUT7QSS2P/action/replication_record"}},"created_at":"2026-05-18T01:40:55.112654+00:00","updated_at":"2026-05-18T01:40:55.112654+00:00"}