{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:ZK3KJSZEYWS6EC23S4REGRFGAK","short_pith_number":"pith:ZK3KJSZE","canonical_record":{"source":{"id":"1507.05261","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-07-19T08:23:57Z","cross_cats_sorted":[],"title_canon_sha256":"9d521730d5a609adab9d58d742075926d12765070fd831e83eddb5648769e7b3","abstract_canon_sha256":"a4fbf01c06ceaf06a3f81fad9fce77f1631634dc65e25a63c5331d79eac0c651"},"schema_version":"1.0"},"canonical_sha256":"cab6a4cb24c5a5e20b5b97224344a602b0984c602bdae760e81acfeb0fb0d08b","source":{"kind":"arxiv","id":"1507.05261","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.05261","created_at":"2026-05-18T01:22:37Z"},{"alias_kind":"arxiv_version","alias_value":"1507.05261v1","created_at":"2026-05-18T01:22:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.05261","created_at":"2026-05-18T01:22:37Z"},{"alias_kind":"pith_short_12","alias_value":"ZK3KJSZEYWS6","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZK3KJSZEYWS6EC23","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZK3KJSZE","created_at":"2026-05-18T12:29:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:ZK3KJSZEYWS6EC23S4REGRFGAK","target":"record","payload":{"canonical_record":{"source":{"id":"1507.05261","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-07-19T08:23:57Z","cross_cats_sorted":[],"title_canon_sha256":"9d521730d5a609adab9d58d742075926d12765070fd831e83eddb5648769e7b3","abstract_canon_sha256":"a4fbf01c06ceaf06a3f81fad9fce77f1631634dc65e25a63c5331d79eac0c651"},"schema_version":"1.0"},"canonical_sha256":"cab6a4cb24c5a5e20b5b97224344a602b0984c602bdae760e81acfeb0fb0d08b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:37.767569Z","signature_b64":"rLaE26hV4/K7+RDHa6QJv6v4QBwFKqoh58IkpqfpKxHYLyizmc1SWRdeXw/3SMO2uawh9Haj/UKPej+f7JQUBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cab6a4cb24c5a5e20b5b97224344a602b0984c602bdae760e81acfeb0fb0d08b","last_reissued_at":"2026-05-18T01:22:37.767093Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:37.767093Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.05261","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:22:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hQH2ZFvfNfBKJCBtVNZdmwVz2JM2tGtAqae/ifRNrn5VGgE5BcWjjcPR7GNvfVg1XAmbaE4eNsOh8Njd4RH1Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T20:25:17.544187Z"},"content_sha256":"83ffab88854fefbbdf25d7daee1c0c33fe70f7fab428f2ba74acb7882b96ce7d","schema_version":"1.0","event_id":"sha256:83ffab88854fefbbdf25d7daee1c0c33fe70f7fab428f2ba74acb7882b96ce7d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:ZK3KJSZEYWS6EC23S4REGRFGAK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Perturbed Hankel determinant, correlation functions and Painlev\\'e equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Engui Fan, Min Chen, Yang Chen","submitted_at":"2015-07-19T08:23:57Z","abstract_excerpt":"We continue with the study of the Hankel determinant, $$ D_{n}(t,\\alpha,\\beta):=\\det\\left(\\int_{0}^{1}x^{j+k}w(x;t,\\alpha,\\beta)dx\\right)_{j,k=0}^{n-1}, $$ generated by a Pollaczek-Jacobi type weight, $$ w(x;t,\\alpha,\\beta):=x^{\\alpha}(1-x)^{\\beta}{\\rm e}^{-t/x}, \\quad x\\in [0,1], \\quad \\alpha>0, \\quad \\beta>0, \\quad t\\geq 0. $$ This reduces to the \"pure\" Jacobi weight at $t=0.$ We may take $\\alpha\\in \\mathbb{R}$, in the situation while $t$ is strictly greater than $0.$ It was shown in Chen and Dai (2010), that the logarithmic derivative of this Hankel determinant satisfies a Jimbo-Miwa-Okamot"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05261","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:22:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y40zGyHvLl9JYbmUf6f9Zk4Tfnox+2dZ4rkEpgxPMAug32641IEdivMn5tqgv8Kgd7SkoJDp/kWwmFOk2WLFDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T20:25:17.544883Z"},"content_sha256":"a89a8db3a696d48d92d86c37ba8f16437d1a64a71507c76a1334ce609319aacc","schema_version":"1.0","event_id":"sha256:a89a8db3a696d48d92d86c37ba8f16437d1a64a71507c76a1334ce609319aacc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZK3KJSZEYWS6EC23S4REGRFGAK/bundle.json","state_url":"https://pith.science/pith/ZK3KJSZEYWS6EC23S4REGRFGAK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZK3KJSZEYWS6EC23S4REGRFGAK/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-08T20:25:17Z","links":{"resolver":"https://pith.science/pith/ZK3KJSZEYWS6EC23S4REGRFGAK","bundle":"https://pith.science/pith/ZK3KJSZEYWS6EC23S4REGRFGAK/bundle.json","state":"https://pith.science/pith/ZK3KJSZEYWS6EC23S4REGRFGAK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZK3KJSZEYWS6EC23S4REGRFGAK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ZK3KJSZEYWS6EC23S4REGRFGAK","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a4fbf01c06ceaf06a3f81fad9fce77f1631634dc65e25a63c5331d79eac0c651","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-07-19T08:23:57Z","title_canon_sha256":"9d521730d5a609adab9d58d742075926d12765070fd831e83eddb5648769e7b3"},"schema_version":"1.0","source":{"id":"1507.05261","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.05261","created_at":"2026-05-18T01:22:37Z"},{"alias_kind":"arxiv_version","alias_value":"1507.05261v1","created_at":"2026-05-18T01:22:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.05261","created_at":"2026-05-18T01:22:37Z"},{"alias_kind":"pith_short_12","alias_value":"ZK3KJSZEYWS6","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZK3KJSZEYWS6EC23","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZK3KJSZE","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:a89a8db3a696d48d92d86c37ba8f16437d1a64a71507c76a1334ce609319aacc","target":"graph","created_at":"2026-05-18T01:22:37Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We continue with the study of the Hankel determinant, $$ D_{n}(t,\\alpha,\\beta):=\\det\\left(\\int_{0}^{1}x^{j+k}w(x;t,\\alpha,\\beta)dx\\right)_{j,k=0}^{n-1}, $$ generated by a Pollaczek-Jacobi type weight, $$ w(x;t,\\alpha,\\beta):=x^{\\alpha}(1-x)^{\\beta}{\\rm e}^{-t/x}, \\quad x\\in [0,1], \\quad \\alpha>0, \\quad \\beta>0, \\quad t\\geq 0. $$ This reduces to the \"pure\" Jacobi weight at $t=0.$ We may take $\\alpha\\in \\mathbb{R}$, in the situation while $t$ is strictly greater than $0.$ It was shown in Chen and Dai (2010), that the logarithmic derivative of this Hankel determinant satisfies a Jimbo-Miwa-Okamot","authors_text":"Engui Fan, Min Chen, Yang Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-07-19T08:23:57Z","title":"Perturbed Hankel determinant, correlation functions and Painlev\\'e equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05261","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:83ffab88854fefbbdf25d7daee1c0c33fe70f7fab428f2ba74acb7882b96ce7d","target":"record","created_at":"2026-05-18T01:22:37Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"a4fbf01c06ceaf06a3f81fad9fce77f1631634dc65e25a63c5331d79eac0c651","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-07-19T08:23:57Z","title_canon_sha256":"9d521730d5a609adab9d58d742075926d12765070fd831e83eddb5648769e7b3"},"schema_version":"1.0","source":{"id":"1507.05261","kind":"arxiv","version":1}},"canonical_sha256":"cab6a4cb24c5a5e20b5b97224344a602b0984c602bdae760e81acfeb0fb0d08b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cab6a4cb24c5a5e20b5b97224344a602b0984c602bdae760e81acfeb0fb0d08b","first_computed_at":"2026-05-18T01:22:37.767093Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:37.767093Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rLaE26hV4/K7+RDHa6QJv6v4QBwFKqoh58IkpqfpKxHYLyizmc1SWRdeXw/3SMO2uawh9Haj/UKPej+f7JQUBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:37.767569Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.05261","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:83ffab88854fefbbdf25d7daee1c0c33fe70f7fab428f2ba74acb7882b96ce7d","sha256:a89a8db3a696d48d92d86c37ba8f16437d1a64a71507c76a1334ce609319aacc"],"state_sha256":"927b560c495571e972ed9c5e01333e170b96bfe30f8a531e1fd9c9ec99ddd1c1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VPbXuMtNAmoWPKppWqgWx64IX6le8FCe5g7VP1rKzhai+TPe4wiIJ5u7XpzFHv5O8Zf3DDFILFmEFmA4uxIYAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T20:25:17.548841Z","bundle_sha256":"703fd89274c8dd9f77d528d3f405df3fcf6c51df89cc00fe7dee165fe9754fdf"}}