{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:65ZZDNAG4ILY4CJIHROZQ5GZJD","short_pith_number":"pith:65ZZDNAG","schema_version":"1.0","canonical_sha256":"f77391b406e2178e09283c5d9874d948ef38cfb915d85d737fa34902a5d559ea","source":{"kind":"arxiv","id":"1412.0102","version":2},"attestation_state":"computed","paper":{"title":"Singular linear statistics of the Laguerre Unitary Ensemble and Painlev\\'e III (${\\rm P_{III}}$): Double scaling analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Min Chen, Yang Chen","submitted_at":"2014-11-29T12:49:04Z","abstract_excerpt":"We continue with the study of the Hankel determinant, $$ D_{n}(t,\\alpha):=\\det\\left(\\int_{0}^{\\infty}x^{j+k}w(x;t,\\alpha)dx\\right)_{j,k=0 }^{n-1}, $$ generated by singularly perturbed Laguerre weight, $$ w(x;t,\\alpha):=x^{\\alpha}{\\rm e}^{-x}\\:{\\rm e}^{-t/x}, \\quad 0\\leq x<\\infty,\\;\\;\\;\\alpha>0,\\;\\;\\;\\;t>0, $$ obtained through a deformation of the Laguerre weight function, $$ w(x;0,\\alpha):=x^{\\alpha}{\\rm e}^{-x},\\quad 0\\leq x<\\infty,\\;\\; \\alpha>0, $$ via the multiplicative factor ${\\rm e}^{-t/x}$. \\\\ An earlier investigation was made on the finite $n$ aspect of the problem, this has appeared i"},"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":"1412.0102","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-11-29T12:49:04Z","cross_cats_sorted":[],"title_canon_sha256":"600d789ea63023a69cda822d1316279b8884279a58f4731ed5b9f86ad5807734","abstract_canon_sha256":"8d5a13975533f7f4ec1605cb5d93e7a6ff0a92376ae4ba036914eb6319e604ba"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:19:16.450603Z","signature_b64":"ohm/YgxSLK9kfnhW+KBJ/X9YtzHTKSiCfFXjH3+iFvfvc747fxJGcO8piaeGHwV3X1AYJ4eWu+key5BlWFFVAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f77391b406e2178e09283c5d9874d948ef38cfb915d85d737fa34902a5d559ea","last_reissued_at":"2026-05-18T02:19:16.450045Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:19:16.450045Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Singular linear statistics of the Laguerre Unitary Ensemble and Painlev\\'e III (${\\rm P_{III}}$): Double scaling analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Min Chen, Yang Chen","submitted_at":"2014-11-29T12:49:04Z","abstract_excerpt":"We continue with the study of the Hankel determinant, $$ D_{n}(t,\\alpha):=\\det\\left(\\int_{0}^{\\infty}x^{j+k}w(x;t,\\alpha)dx\\right)_{j,k=0 }^{n-1}, $$ generated by singularly perturbed Laguerre weight, $$ w(x;t,\\alpha):=x^{\\alpha}{\\rm e}^{-x}\\:{\\rm e}^{-t/x}, \\quad 0\\leq x<\\infty,\\;\\;\\;\\alpha>0,\\;\\;\\;\\;t>0, $$ obtained through a deformation of the Laguerre weight function, $$ w(x;0,\\alpha):=x^{\\alpha}{\\rm e}^{-x},\\quad 0\\leq x<\\infty,\\;\\; \\alpha>0, $$ via the multiplicative factor ${\\rm e}^{-t/x}$. \\\\ An earlier investigation was made on the finite $n$ aspect of the problem, this has appeared i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.0102","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":"1412.0102","created_at":"2026-05-18T02:19:16.450113+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.0102v2","created_at":"2026-05-18T02:19:16.450113+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.0102","created_at":"2026-05-18T02:19:16.450113+00:00"},{"alias_kind":"pith_short_12","alias_value":"65ZZDNAG4ILY","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_16","alias_value":"65ZZDNAG4ILY4CJI","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_8","alias_value":"65ZZDNAG","created_at":"2026-05-18T12:28:16.859392+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/65ZZDNAG4ILY4CJIHROZQ5GZJD","json":"https://pith.science/pith/65ZZDNAG4ILY4CJIHROZQ5GZJD.json","graph_json":"https://pith.science/api/pith-number/65ZZDNAG4ILY4CJIHROZQ5GZJD/graph.json","events_json":"https://pith.science/api/pith-number/65ZZDNAG4ILY4CJIHROZQ5GZJD/events.json","paper":"https://pith.science/paper/65ZZDNAG"},"agent_actions":{"view_html":"https://pith.science/pith/65ZZDNAG4ILY4CJIHROZQ5GZJD","download_json":"https://pith.science/pith/65ZZDNAG4ILY4CJIHROZQ5GZJD.json","view_paper":"https://pith.science/paper/65ZZDNAG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.0102&json=true","fetch_graph":"https://pith.science/api/pith-number/65ZZDNAG4ILY4CJIHROZQ5GZJD/graph.json","fetch_events":"https://pith.science/api/pith-number/65ZZDNAG4ILY4CJIHROZQ5GZJD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/65ZZDNAG4ILY4CJIHROZQ5GZJD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/65ZZDNAG4ILY4CJIHROZQ5GZJD/action/storage_attestation","attest_author":"https://pith.science/pith/65ZZDNAG4ILY4CJIHROZQ5GZJD/action/author_attestation","sign_citation":"https://pith.science/pith/65ZZDNAG4ILY4CJIHROZQ5GZJD/action/citation_signature","submit_replication":"https://pith.science/pith/65ZZDNAG4ILY4CJIHROZQ5GZJD/action/replication_record"}},"created_at":"2026-05-18T02:19:16.450113+00:00","updated_at":"2026-05-18T02:19:16.450113+00:00"}