{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:2YTMNS75H4EGDOOUJUUL2GJ3ZK","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":"5580dbaf4421073af573557d68180c08330cfbe04a6f42f2ebdce840b3e528b7","cross_cats_sorted":["hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-09-29T21:20:49Z","title_canon_sha256":"6c3096a2ea328850e300dafe64c96ffbaf0a7db2fb08df7189ff8081efc10eed"},"schema_version":"1.0","source":{"id":"1009.6007","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.6007","created_at":"2026-05-18T04:24:52Z"},{"alias_kind":"arxiv_version","alias_value":"1009.6007v1","created_at":"2026-05-18T04:24:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.6007","created_at":"2026-05-18T04:24:52Z"},{"alias_kind":"pith_short_12","alias_value":"2YTMNS75H4EG","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"2YTMNS75H4EGDOOU","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"2YTMNS75","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:bb1eb08917103baea0898c3ffd093770e4ee7bd36c93ee1571e3fb7ff8287455","target":"graph","created_at":"2026-05-18T04:24:52Z","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 solve the loop equations of the $\\beta$-ensemble model analogously to the solution found for the Hermitian matrices $\\beta=1$. For \\beta=1$, the solution was expressed using the algebraic spectral curve of equation $y^2=U(x)$. For arbitrary $\\beta$, the spectral curve converts into a Schr\\\"odinger equation $((\\hbar\\partial)^2-U(x))\\psi(x)=0$ with $\\hbar\\propto (\\sqrt\\beta-1/\\sqrt\\beta)/N$. This paper is similar to the sister paper~I, in particular, all the main ingredients specific for the algebraic solution of the problem remain the same, but here we present the second approach to finding ","authors_text":"B. Eynard, L. O. Chekhov, O. Marchal","cross_cats":["hep-th","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-09-29T21:20:49Z","title":"Topological expansion of beta-ensemble model and quantum algebraic geometry in the sectorwise approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.6007","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:e2405f839a686c53928e89b084ce81e25ab2e81a95bfbff5a9bd52c9fa858ed8","target":"record","created_at":"2026-05-18T04:24:52Z","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":"5580dbaf4421073af573557d68180c08330cfbe04a6f42f2ebdce840b3e528b7","cross_cats_sorted":["hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-09-29T21:20:49Z","title_canon_sha256":"6c3096a2ea328850e300dafe64c96ffbaf0a7db2fb08df7189ff8081efc10eed"},"schema_version":"1.0","source":{"id":"1009.6007","kind":"arxiv","version":1}},"canonical_sha256":"d626c6cbfd3f0861b9d44d28bd193bcaa1a4d4e59b179584cba66d8eb13da886","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d626c6cbfd3f0861b9d44d28bd193bcaa1a4d4e59b179584cba66d8eb13da886","first_computed_at":"2026-05-18T04:24:52.902329Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:24:52.902329Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pJ1U+jbmvzAhTYBxTrj0fQZ+HxITRoEHrbkdtIG5TKZF7benBOA2PVa24RjGnWPUoINvqffH3FhnQ8EVM5ueBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:24:52.902941Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.6007","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e2405f839a686c53928e89b084ce81e25ab2e81a95bfbff5a9bd52c9fa858ed8","sha256:bb1eb08917103baea0898c3ffd093770e4ee7bd36c93ee1571e3fb7ff8287455"],"state_sha256":"096abbcd65deb238db29a4990d322bfa8838a1e9ddbba6af84255c0274594e88"}