{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:672UY44K6TWJPAQHTFOHJCUQIE","short_pith_number":"pith:672UY44K","schema_version":"1.0","canonical_sha256":"f7f54c738af4ec978207995c748a90413772376fec9b661f990476627c483e13","source":{"kind":"arxiv","id":"1303.1130","version":1},"attestation_state":"computed","paper":{"title":"Universality and critical behavior in the chiral two-matrix model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.CA","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Dries Geudens, Lun Zhang, Steven Delvaux","submitted_at":"2013-03-05T18:32:27Z","abstract_excerpt":"We study the chiral two-matrix model with polynomial potential functions $V$ and $W$, which was introduced by Akemann, Damgaard, Osborn and Splittorff. We show that the squared singular values of each of the individual matrices in this model form a determinantal point process with correlation kernel determined by a matrix-valued Riemann-Hilbert problem. The size of the Riemann-Hilbert matrix depends on the degree of the potential function $W$ (or $V$ respectively). In this way we obtain the chiral analogue of a result of Kuijlaars-McLaughlin for the non-chiral two-matrix model. The Gaussian ca"},"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":"1303.1130","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-03-05T18:32:27Z","cross_cats_sorted":["hep-th","math.CA","math.MP","math.PR"],"title_canon_sha256":"8d99775d2e906a1832096b95f7bfeb13fc42c0f993bda165e17fa0514838ce93","abstract_canon_sha256":"da2bbaab411e0f25cfbff4735b71fbc456516cf236cf688d703a1e6cefcec9e9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:51:16.696083Z","signature_b64":"fGd0DaDJVPXHjlCg6wrBB4myGqFxo2Aaq/4SDIDuhdUmmQ8ZK7dvtbRXLmVzKJCzGVt9A5WABbCD1QXvVriuBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f7f54c738af4ec978207995c748a90413772376fec9b661f990476627c483e13","last_reissued_at":"2026-05-18T01:51:16.695587Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:51:16.695587Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Universality and critical behavior in the chiral two-matrix model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.CA","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Dries Geudens, Lun Zhang, Steven Delvaux","submitted_at":"2013-03-05T18:32:27Z","abstract_excerpt":"We study the chiral two-matrix model with polynomial potential functions $V$ and $W$, which was introduced by Akemann, Damgaard, Osborn and Splittorff. We show that the squared singular values of each of the individual matrices in this model form a determinantal point process with correlation kernel determined by a matrix-valued Riemann-Hilbert problem. The size of the Riemann-Hilbert matrix depends on the degree of the potential function $W$ (or $V$ respectively). In this way we obtain the chiral analogue of a result of Kuijlaars-McLaughlin for the non-chiral two-matrix model. The Gaussian ca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.1130","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":"1303.1130","created_at":"2026-05-18T01:51:16.695673+00:00"},{"alias_kind":"arxiv_version","alias_value":"1303.1130v1","created_at":"2026-05-18T01:51:16.695673+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.1130","created_at":"2026-05-18T01:51:16.695673+00:00"},{"alias_kind":"pith_short_12","alias_value":"672UY44K6TWJ","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_16","alias_value":"672UY44K6TWJPAQH","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_8","alias_value":"672UY44K","created_at":"2026-05-18T12:27:36.564083+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/672UY44K6TWJPAQHTFOHJCUQIE","json":"https://pith.science/pith/672UY44K6TWJPAQHTFOHJCUQIE.json","graph_json":"https://pith.science/api/pith-number/672UY44K6TWJPAQHTFOHJCUQIE/graph.json","events_json":"https://pith.science/api/pith-number/672UY44K6TWJPAQHTFOHJCUQIE/events.json","paper":"https://pith.science/paper/672UY44K"},"agent_actions":{"view_html":"https://pith.science/pith/672UY44K6TWJPAQHTFOHJCUQIE","download_json":"https://pith.science/pith/672UY44K6TWJPAQHTFOHJCUQIE.json","view_paper":"https://pith.science/paper/672UY44K","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1303.1130&json=true","fetch_graph":"https://pith.science/api/pith-number/672UY44K6TWJPAQHTFOHJCUQIE/graph.json","fetch_events":"https://pith.science/api/pith-number/672UY44K6TWJPAQHTFOHJCUQIE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/672UY44K6TWJPAQHTFOHJCUQIE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/672UY44K6TWJPAQHTFOHJCUQIE/action/storage_attestation","attest_author":"https://pith.science/pith/672UY44K6TWJPAQHTFOHJCUQIE/action/author_attestation","sign_citation":"https://pith.science/pith/672UY44K6TWJPAQHTFOHJCUQIE/action/citation_signature","submit_replication":"https://pith.science/pith/672UY44K6TWJPAQHTFOHJCUQIE/action/replication_record"}},"created_at":"2026-05-18T01:51:16.695673+00:00","updated_at":"2026-05-18T01:51:16.695673+00:00"}