{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:PIYR4BTTSKSCK4NGJTPKPRLPMV","short_pith_number":"pith:PIYR4BTT","schema_version":"1.0","canonical_sha256":"7a311e067392a42571a64cdea7c56f6577567a6c7dce5d694cb6ac2f99fa688b","source":{"kind":"arxiv","id":"1407.7334","version":2},"attestation_state":"computed","paper":{"title":"Painlev\\'e III asymptotics of Hankel determinants for a singularly perturbed Laguerre weight","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Dan Dai, Shuai-Xia Xu, Yu-Qiu Zhao","submitted_at":"2014-07-28T06:47:07Z","abstract_excerpt":"In this paper, we consider the Hankel determinants associated with the singularly perturbed Laguerre weight $w(x)=x^\\alpha e^{-x-t/x}$, $x\\in (0, \\infty)$, $t>0$ and $\\alpha>0$. When the matrix size $n\\to\\infty$, we obtain an asymptotic formula for the Hankel determinants, valid uniformly for $t\\in (0, d]$, $d>0$ fixed. A particular Painlev\\'{e} III transcendent is involved in the approximation, as well as in the large-$n$ asymptotics of the leading coefficients and recurrence coefficients for the corresponding perturbed Laguerre polynomials. The derivation is based on the asymptotic results 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":"1407.7334","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-07-28T06:47:07Z","cross_cats_sorted":[],"title_canon_sha256":"426d578ffeef3bbfb06dbce94efe93794144f96c7eac0fca2172c3c807c982a1","abstract_canon_sha256":"6b97eb2040e3d067ce4aba64e4240bc78f4aab8b3b0a92426e152a9f017ba135"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:36.695668Z","signature_b64":"iFh5FAVzzKYXwpWPeNi4ffb6E4k7P/AC+ecVq3iwAzDVWaJ4ks6jrqnR5LcswMFrA6oNVJ6BVL3TslPLshK3CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7a311e067392a42571a64cdea7c56f6577567a6c7dce5d694cb6ac2f99fa688b","last_reissued_at":"2026-05-18T02:38:36.695138Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:36.695138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Painlev\\'e III asymptotics of Hankel determinants for a singularly perturbed Laguerre weight","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Dan Dai, Shuai-Xia Xu, Yu-Qiu Zhao","submitted_at":"2014-07-28T06:47:07Z","abstract_excerpt":"In this paper, we consider the Hankel determinants associated with the singularly perturbed Laguerre weight $w(x)=x^\\alpha e^{-x-t/x}$, $x\\in (0, \\infty)$, $t>0$ and $\\alpha>0$. When the matrix size $n\\to\\infty$, we obtain an asymptotic formula for the Hankel determinants, valid uniformly for $t\\in (0, d]$, $d>0$ fixed. A particular Painlev\\'{e} III transcendent is involved in the approximation, as well as in the large-$n$ asymptotics of the leading coefficients and recurrence coefficients for the corresponding perturbed Laguerre polynomials. The derivation is based on the asymptotic results i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.7334","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":"1407.7334","created_at":"2026-05-18T02:38:36.695220+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.7334v2","created_at":"2026-05-18T02:38:36.695220+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.7334","created_at":"2026-05-18T02:38:36.695220+00:00"},{"alias_kind":"pith_short_12","alias_value":"PIYR4BTTSKSC","created_at":"2026-05-18T12:28:43.426989+00:00"},{"alias_kind":"pith_short_16","alias_value":"PIYR4BTTSKSCK4NG","created_at":"2026-05-18T12:28:43.426989+00:00"},{"alias_kind":"pith_short_8","alias_value":"PIYR4BTT","created_at":"2026-05-18T12:28:43.426989+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/PIYR4BTTSKSCK4NGJTPKPRLPMV","json":"https://pith.science/pith/PIYR4BTTSKSCK4NGJTPKPRLPMV.json","graph_json":"https://pith.science/api/pith-number/PIYR4BTTSKSCK4NGJTPKPRLPMV/graph.json","events_json":"https://pith.science/api/pith-number/PIYR4BTTSKSCK4NGJTPKPRLPMV/events.json","paper":"https://pith.science/paper/PIYR4BTT"},"agent_actions":{"view_html":"https://pith.science/pith/PIYR4BTTSKSCK4NGJTPKPRLPMV","download_json":"https://pith.science/pith/PIYR4BTTSKSCK4NGJTPKPRLPMV.json","view_paper":"https://pith.science/paper/PIYR4BTT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.7334&json=true","fetch_graph":"https://pith.science/api/pith-number/PIYR4BTTSKSCK4NGJTPKPRLPMV/graph.json","fetch_events":"https://pith.science/api/pith-number/PIYR4BTTSKSCK4NGJTPKPRLPMV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PIYR4BTTSKSCK4NGJTPKPRLPMV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PIYR4BTTSKSCK4NGJTPKPRLPMV/action/storage_attestation","attest_author":"https://pith.science/pith/PIYR4BTTSKSCK4NGJTPKPRLPMV/action/author_attestation","sign_citation":"https://pith.science/pith/PIYR4BTTSKSCK4NGJTPKPRLPMV/action/citation_signature","submit_replication":"https://pith.science/pith/PIYR4BTTSKSCK4NGJTPKPRLPMV/action/replication_record"}},"created_at":"2026-05-18T02:38:36.695220+00:00","updated_at":"2026-05-18T02:38:36.695220+00:00"}