{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:46MM5SAKPSJW537UJ4GFBUELYZ","short_pith_number":"pith:46MM5SAK","schema_version":"1.0","canonical_sha256":"e798cec80a7c936eeff44f0c50d08bc65e446300b38b36f65c5ac13ba2371426","source":{"kind":"arxiv","id":"1010.1210","version":4},"attestation_state":"computed","paper":{"title":"The uses of the refined matrix model recursion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Andrea Brini, Marcos Marino, Sebastien Stevan","submitted_at":"2010-10-06T17:27:31Z","abstract_excerpt":"We study matrix models in the beta ensemble by building on the refined recursion relation proposed by Chekhov and Eynard. We present explicit results for the first beta-deformed corrections in the one-cut and the two-cut cases, as well as two applications to supersymmetric gauge theories: the calculation of superpotentials in N=1 gauge theories, and the calculation of vevs of surface operators in superconformal N=2 theories and their Liouville duals. Finally, we study the beta deformation of the Chern-Simons matrix model. Our results indicate that this model does not provide an appropriate des"},"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":"1010.1210","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2010-10-06T17:27:31Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"76369f5811610a77eff0f8754301e8a9a3c69ad3b094e1245e7d4fbdccea5a0d","abstract_canon_sha256":"6a580e0bdb0830b4b16ceaa41ee241d8b37fc37b562cbc13dbd8eb0c177148bf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:50:01.137553Z","signature_b64":"OVKTBtmOvQgmdldQHwsUgCtbSRJ5O6LpQQWwj2DmFtlwVk/NjdaIMDbPorhoFZBXNSxNdbX1TTYwReA4+HOoCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e798cec80a7c936eeff44f0c50d08bc65e446300b38b36f65c5ac13ba2371426","last_reissued_at":"2026-05-18T02:50:01.137062Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:50:01.137062Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The uses of the refined matrix model recursion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Andrea Brini, Marcos Marino, Sebastien Stevan","submitted_at":"2010-10-06T17:27:31Z","abstract_excerpt":"We study matrix models in the beta ensemble by building on the refined recursion relation proposed by Chekhov and Eynard. We present explicit results for the first beta-deformed corrections in the one-cut and the two-cut cases, as well as two applications to supersymmetric gauge theories: the calculation of superpotentials in N=1 gauge theories, and the calculation of vevs of surface operators in superconformal N=2 theories and their Liouville duals. Finally, we study the beta deformation of the Chern-Simons matrix model. Our results indicate that this model does not provide an appropriate des"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.1210","kind":"arxiv","version":4},"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":"1010.1210","created_at":"2026-05-18T02:50:01.137148+00:00"},{"alias_kind":"arxiv_version","alias_value":"1010.1210v4","created_at":"2026-05-18T02:50:01.137148+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.1210","created_at":"2026-05-18T02:50:01.137148+00:00"},{"alias_kind":"pith_short_12","alias_value":"46MM5SAKPSJW","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_16","alias_value":"46MM5SAKPSJW537U","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_8","alias_value":"46MM5SAK","created_at":"2026-05-18T12:26:03.138858+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":2,"sample":[{"citing_arxiv_id":"2509.18916","citing_title":"Dynamical Triangulations for 2D Pure Gravity and Topological Recursion","ref_index":27,"is_internal_anchor":true},{"citing_arxiv_id":"2512.10519","citing_title":"Multicritical Dynamical Triangulations and Topological Recursion","ref_index":22,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/46MM5SAKPSJW537UJ4GFBUELYZ","json":"https://pith.science/pith/46MM5SAKPSJW537UJ4GFBUELYZ.json","graph_json":"https://pith.science/api/pith-number/46MM5SAKPSJW537UJ4GFBUELYZ/graph.json","events_json":"https://pith.science/api/pith-number/46MM5SAKPSJW537UJ4GFBUELYZ/events.json","paper":"https://pith.science/paper/46MM5SAK"},"agent_actions":{"view_html":"https://pith.science/pith/46MM5SAKPSJW537UJ4GFBUELYZ","download_json":"https://pith.science/pith/46MM5SAKPSJW537UJ4GFBUELYZ.json","view_paper":"https://pith.science/paper/46MM5SAK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1010.1210&json=true","fetch_graph":"https://pith.science/api/pith-number/46MM5SAKPSJW537UJ4GFBUELYZ/graph.json","fetch_events":"https://pith.science/api/pith-number/46MM5SAKPSJW537UJ4GFBUELYZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/46MM5SAKPSJW537UJ4GFBUELYZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/46MM5SAKPSJW537UJ4GFBUELYZ/action/storage_attestation","attest_author":"https://pith.science/pith/46MM5SAKPSJW537UJ4GFBUELYZ/action/author_attestation","sign_citation":"https://pith.science/pith/46MM5SAKPSJW537UJ4GFBUELYZ/action/citation_signature","submit_replication":"https://pith.science/pith/46MM5SAKPSJW537UJ4GFBUELYZ/action/replication_record"}},"created_at":"2026-05-18T02:50:01.137148+00:00","updated_at":"2026-05-18T02:50:01.137148+00:00"}