{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:CJK7W4ZNTPR4OBBR323X73VHVK","short_pith_number":"pith:CJK7W4ZN","schema_version":"1.0","canonical_sha256":"1255fb732d9be3c70431deb77feea7aa9d130c7a66120a9a4e48faf83eae4786","source":{"kind":"arxiv","id":"1011.1650","version":1},"attestation_state":"computed","paper":{"title":"Difference system for Selberg correlation integrals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Masahiko Ito, Peter J. Forrester","submitted_at":"2010-11-07T16:39:46Z","abstract_excerpt":"The Selberg correlation integrals are averages of the products $\\prod_{s=1}^m\\prod_{l=1}^n (x_s - z_l)^{\\mu_s}$ with respect to the Selberg density. Our interest is in the case $m=1$, $\\mu_1 = \\mu$, when this corresponds to the $\\mu$-th moment of the corresponding characteristic polynomial. We give the explicit form of a $(n+1) \\times (n+1)$ matrix linear difference system in the variable $\\mu$ which determines the average, and we give the Gauss decomposition of the corresponding $(n+1) \\times (n+1)$ matrix. For $\\mu$ a positive integer the difference system can be used to efficiently compute "},"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":"1011.1650","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-11-07T16:39:46Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"a34345502ea49bafc92343539ce151b43684a41de268170e0e5870ed0be392a1","abstract_canon_sha256":"75dfecb6d300f66a0e45d992ab052fb4cc9d98ede746b4793d5dc12350e10756"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:04:50.667506Z","signature_b64":"i3/cAIJDBErptBtNd97JCQOmkWY6sEj2ZxqQzzw99KIh88v7fg0d5/Byd04CU4uMdbJSACSYTxHSyiYxCz6UCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1255fb732d9be3c70431deb77feea7aa9d130c7a66120a9a4e48faf83eae4786","last_reissued_at":"2026-05-18T02:04:50.666948Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:04:50.666948Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Difference system for Selberg correlation integrals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Masahiko Ito, Peter J. Forrester","submitted_at":"2010-11-07T16:39:46Z","abstract_excerpt":"The Selberg correlation integrals are averages of the products $\\prod_{s=1}^m\\prod_{l=1}^n (x_s - z_l)^{\\mu_s}$ with respect to the Selberg density. Our interest is in the case $m=1$, $\\mu_1 = \\mu$, when this corresponds to the $\\mu$-th moment of the corresponding characteristic polynomial. We give the explicit form of a $(n+1) \\times (n+1)$ matrix linear difference system in the variable $\\mu$ which determines the average, and we give the Gauss decomposition of the corresponding $(n+1) \\times (n+1)$ matrix. For $\\mu$ a positive integer the difference system can be used to efficiently compute "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.1650","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":"1011.1650","created_at":"2026-05-18T02:04:50.667019+00:00"},{"alias_kind":"arxiv_version","alias_value":"1011.1650v1","created_at":"2026-05-18T02:04:50.667019+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.1650","created_at":"2026-05-18T02:04:50.667019+00:00"},{"alias_kind":"pith_short_12","alias_value":"CJK7W4ZNTPR4","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_16","alias_value":"CJK7W4ZNTPR4OBBR","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_8","alias_value":"CJK7W4ZN","created_at":"2026-05-18T12:26:06.534383+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/CJK7W4ZNTPR4OBBR323X73VHVK","json":"https://pith.science/pith/CJK7W4ZNTPR4OBBR323X73VHVK.json","graph_json":"https://pith.science/api/pith-number/CJK7W4ZNTPR4OBBR323X73VHVK/graph.json","events_json":"https://pith.science/api/pith-number/CJK7W4ZNTPR4OBBR323X73VHVK/events.json","paper":"https://pith.science/paper/CJK7W4ZN"},"agent_actions":{"view_html":"https://pith.science/pith/CJK7W4ZNTPR4OBBR323X73VHVK","download_json":"https://pith.science/pith/CJK7W4ZNTPR4OBBR323X73VHVK.json","view_paper":"https://pith.science/paper/CJK7W4ZN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1011.1650&json=true","fetch_graph":"https://pith.science/api/pith-number/CJK7W4ZNTPR4OBBR323X73VHVK/graph.json","fetch_events":"https://pith.science/api/pith-number/CJK7W4ZNTPR4OBBR323X73VHVK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CJK7W4ZNTPR4OBBR323X73VHVK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CJK7W4ZNTPR4OBBR323X73VHVK/action/storage_attestation","attest_author":"https://pith.science/pith/CJK7W4ZNTPR4OBBR323X73VHVK/action/author_attestation","sign_citation":"https://pith.science/pith/CJK7W4ZNTPR4OBBR323X73VHVK/action/citation_signature","submit_replication":"https://pith.science/pith/CJK7W4ZNTPR4OBBR323X73VHVK/action/replication_record"}},"created_at":"2026-05-18T02:04:50.667019+00:00","updated_at":"2026-05-18T02:04:50.667019+00:00"}