{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:S57O6QM3LLPEIIGLH65J7MZNVK","short_pith_number":"pith:S57O6QM3","schema_version":"1.0","canonical_sha256":"977eef419b5ade4420cb3fba9fb32daaa4aa531c5d3d2ce5b5519a557a5c4844","source":{"kind":"arxiv","id":"1512.02883","version":1},"attestation_state":"computed","paper":{"title":"On the asymptotic behavior of a log gas in the bulk scaling limit in the presence of a varying external potential II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.MP","math.PR","nlin.SI"],"primary_cat":"math-ph","authors_text":"Alexander Its, Igor Krasovsky, Percy Deift, Thomas Bothner","submitted_at":"2015-12-09T14:51:21Z","abstract_excerpt":"In this paper we continue our analysis \\cite{BDIK} of the determinant $\\det(I-\\gamma K_s),\\gamma\\in(0,1)$ where $K_s$ is the trace class operator acting in $L^2(-1,1)$ with kernel $K_s(\\lambda,\\mu)=\\frac{\\sin s(\\lambda-\\mu)}{\\pi(\\lambda-\\mu)}$. In \\cite{BDIK} various key asymptotic results were stated and utilized, but without proof: Here we provide the proofs (see Theorem 1.2 and Proposition 1.3 below)."},"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":"1512.02883","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-12-09T14:51:21Z","cross_cats_sorted":["math.CA","math.MP","math.PR","nlin.SI"],"title_canon_sha256":"5925be94becf96287b6a6ed7ae7e47b439ecd03a5300d8be4c4e77f2d59f4245","abstract_canon_sha256":"91f2ea66a3ee690ffa3b67a92368adb395bca00e80bd65409a573665f63783fb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:39.266643Z","signature_b64":"qVpZegNJk/atNl3s9rA0Rc9W4LLJzrQyoIKEk44FJkupJ+ivz/v6vHR5iLUVVo54f5peVaylZblC98zXjG0NBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"977eef419b5ade4420cb3fba9fb32daaa4aa531c5d3d2ce5b5519a557a5c4844","last_reissued_at":"2026-05-18T01:24:39.266281Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:39.266281Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the asymptotic behavior of a log gas in the bulk scaling limit in the presence of a varying external potential II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.MP","math.PR","nlin.SI"],"primary_cat":"math-ph","authors_text":"Alexander Its, Igor Krasovsky, Percy Deift, Thomas Bothner","submitted_at":"2015-12-09T14:51:21Z","abstract_excerpt":"In this paper we continue our analysis \\cite{BDIK} of the determinant $\\det(I-\\gamma K_s),\\gamma\\in(0,1)$ where $K_s$ is the trace class operator acting in $L^2(-1,1)$ with kernel $K_s(\\lambda,\\mu)=\\frac{\\sin s(\\lambda-\\mu)}{\\pi(\\lambda-\\mu)}$. In \\cite{BDIK} various key asymptotic results were stated and utilized, but without proof: Here we provide the proofs (see Theorem 1.2 and Proposition 1.3 below)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.02883","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":"1512.02883","created_at":"2026-05-18T01:24:39.266345+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.02883v1","created_at":"2026-05-18T01:24:39.266345+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.02883","created_at":"2026-05-18T01:24:39.266345+00:00"},{"alias_kind":"pith_short_12","alias_value":"S57O6QM3LLPE","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_16","alias_value":"S57O6QM3LLPEIIGL","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_8","alias_value":"S57O6QM3","created_at":"2026-05-18T12:29:39.896362+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/S57O6QM3LLPEIIGLH65J7MZNVK","json":"https://pith.science/pith/S57O6QM3LLPEIIGLH65J7MZNVK.json","graph_json":"https://pith.science/api/pith-number/S57O6QM3LLPEIIGLH65J7MZNVK/graph.json","events_json":"https://pith.science/api/pith-number/S57O6QM3LLPEIIGLH65J7MZNVK/events.json","paper":"https://pith.science/paper/S57O6QM3"},"agent_actions":{"view_html":"https://pith.science/pith/S57O6QM3LLPEIIGLH65J7MZNVK","download_json":"https://pith.science/pith/S57O6QM3LLPEIIGLH65J7MZNVK.json","view_paper":"https://pith.science/paper/S57O6QM3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.02883&json=true","fetch_graph":"https://pith.science/api/pith-number/S57O6QM3LLPEIIGLH65J7MZNVK/graph.json","fetch_events":"https://pith.science/api/pith-number/S57O6QM3LLPEIIGLH65J7MZNVK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S57O6QM3LLPEIIGLH65J7MZNVK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S57O6QM3LLPEIIGLH65J7MZNVK/action/storage_attestation","attest_author":"https://pith.science/pith/S57O6QM3LLPEIIGLH65J7MZNVK/action/author_attestation","sign_citation":"https://pith.science/pith/S57O6QM3LLPEIIGLH65J7MZNVK/action/citation_signature","submit_replication":"https://pith.science/pith/S57O6QM3LLPEIIGLH65J7MZNVK/action/replication_record"}},"created_at":"2026-05-18T01:24:39.266345+00:00","updated_at":"2026-05-18T01:24:39.266345+00:00"}