{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:K2RPPOSGZHULAGLEK4NXVTYVQJ","short_pith_number":"pith:K2RPPOSG","schema_version":"1.0","canonical_sha256":"56a2f7ba46c9e8b01964571b7acf15826d85089f87c472f684300d656cb3dfa8","source":{"kind":"arxiv","id":"1110.0119","version":2},"attestation_state":"computed","paper":{"title":"On the Variance of the Index for the Gaussian Unitary Ensemble","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.CA","authors_text":"N. S. Witte, P.J. Forrester","submitted_at":"2011-10-01T19:08:48Z","abstract_excerpt":"We derive simple linear, inhomogeneous recurrences for the variance of the index by utilising the fact that the generating function for the distribution of the number of positive eigenvalues of a Gaussian unitary ensemble is a $\\tau$-function of the fourth Painlev\\'e equation. From this we deduce a simple summation formula, several integral representations and finally an exact hypergeometric function evaluation for the variance."},"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":"1110.0119","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-10-01T19:08:48Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"2e0390656a8924dd8639f5c02dffea27f3780390e46bc489f2e4803849b2880d","abstract_canon_sha256":"39c4a735970d6c5e7d796367dd241520959a270c60a731fa3ba48308325bc74c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:11:40.437002Z","signature_b64":"gPdY7GPwarV7j2eQDOAzos7G36JzbU6/gfgpH75zwNlhcXwc8xyGcgPejWqdKFevGbxOicnnEb5lmZxPoV9wAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"56a2f7ba46c9e8b01964571b7acf15826d85089f87c472f684300d656cb3dfa8","last_reissued_at":"2026-05-18T04:11:40.436583Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:11:40.436583Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Variance of the Index for the Gaussian Unitary Ensemble","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.CA","authors_text":"N. S. Witte, P.J. Forrester","submitted_at":"2011-10-01T19:08:48Z","abstract_excerpt":"We derive simple linear, inhomogeneous recurrences for the variance of the index by utilising the fact that the generating function for the distribution of the number of positive eigenvalues of a Gaussian unitary ensemble is a $\\tau$-function of the fourth Painlev\\'e equation. From this we deduce a simple summation formula, several integral representations and finally an exact hypergeometric function evaluation for the variance."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.0119","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":"1110.0119","created_at":"2026-05-18T04:11:40.436645+00:00"},{"alias_kind":"arxiv_version","alias_value":"1110.0119v2","created_at":"2026-05-18T04:11:40.436645+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.0119","created_at":"2026-05-18T04:11:40.436645+00:00"},{"alias_kind":"pith_short_12","alias_value":"K2RPPOSGZHUL","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_16","alias_value":"K2RPPOSGZHULAGLE","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_8","alias_value":"K2RPPOSG","created_at":"2026-05-18T12:26:32.869790+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/K2RPPOSGZHULAGLEK4NXVTYVQJ","json":"https://pith.science/pith/K2RPPOSGZHULAGLEK4NXVTYVQJ.json","graph_json":"https://pith.science/api/pith-number/K2RPPOSGZHULAGLEK4NXVTYVQJ/graph.json","events_json":"https://pith.science/api/pith-number/K2RPPOSGZHULAGLEK4NXVTYVQJ/events.json","paper":"https://pith.science/paper/K2RPPOSG"},"agent_actions":{"view_html":"https://pith.science/pith/K2RPPOSGZHULAGLEK4NXVTYVQJ","download_json":"https://pith.science/pith/K2RPPOSGZHULAGLEK4NXVTYVQJ.json","view_paper":"https://pith.science/paper/K2RPPOSG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1110.0119&json=true","fetch_graph":"https://pith.science/api/pith-number/K2RPPOSGZHULAGLEK4NXVTYVQJ/graph.json","fetch_events":"https://pith.science/api/pith-number/K2RPPOSGZHULAGLEK4NXVTYVQJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/K2RPPOSGZHULAGLEK4NXVTYVQJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/K2RPPOSGZHULAGLEK4NXVTYVQJ/action/storage_attestation","attest_author":"https://pith.science/pith/K2RPPOSGZHULAGLEK4NXVTYVQJ/action/author_attestation","sign_citation":"https://pith.science/pith/K2RPPOSGZHULAGLEK4NXVTYVQJ/action/citation_signature","submit_replication":"https://pith.science/pith/K2RPPOSGZHULAGLEK4NXVTYVQJ/action/replication_record"}},"created_at":"2026-05-18T04:11:40.436645+00:00","updated_at":"2026-05-18T04:11:40.436645+00:00"}