{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:G7YHJIFP53BYIAK6O36N2QM6OX","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":"23cc6f3748575a3ae27cffb3875588aca6ff060d3588d576548daab1b4d9edf3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-06-08T11:31:08Z","title_canon_sha256":"2a15c237dfa2aa462754c558a1ae33b2d1e7058439279d6cb5ce5f01b04813f6"},"schema_version":"1.0","source":{"id":"1106.1539","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.1539","created_at":"2026-05-18T04:16:22Z"},{"alias_kind":"arxiv_version","alias_value":"1106.1539v1","created_at":"2026-05-18T04:16:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.1539","created_at":"2026-05-18T04:16:22Z"},{"alias_kind":"pith_short_12","alias_value":"G7YHJIFP53BY","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"G7YHJIFP53BYIAK6","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"G7YHJIFP","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:f748ac31fa36a00977d60b1b0aa32e41a74b63f297c2ddfc94c3d254cf7c6647","target":"graph","created_at":"2026-05-18T04:16:22Z","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 introduce An(1) (n=1,2,...) affine quiver matrix model by simply adopting the extended Cartan matrices as incidence matrices and study its finite N Schwinger-Dyson equations as well as their planar limit. In the case of n=1, we extend our analysis to derive the cubic planar loop equation for one-parameter family of models labelled by alpha: alpha=1 and alpha=2 correspond to the non-affine A2 case and the affine A1(1) case respectively. In the case of n=2, we derive three sets of constraint equations for the resolvents which are quadratic, cubic and quartic respectively.","authors_text":"Hiroshi Itoyama, Takeshi Oota","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-06-08T11:31:08Z","title":"An(1) Affine Quiver Matrix Model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.1539","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":"sha256:2631437f8ea13b2942d121a8c548856c532cb519b6f2fdc73d6f37086079c61c","target":"record","created_at":"2026-05-18T04:16:22Z","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":"23cc6f3748575a3ae27cffb3875588aca6ff060d3588d576548daab1b4d9edf3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-06-08T11:31:08Z","title_canon_sha256":"2a15c237dfa2aa462754c558a1ae33b2d1e7058439279d6cb5ce5f01b04813f6"},"schema_version":"1.0","source":{"id":"1106.1539","kind":"arxiv","version":1}},"canonical_sha256":"37f074a0afeec384015e76fcdd419e75db523fadc7b512c2a3ed502e01a1dc1e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"37f074a0afeec384015e76fcdd419e75db523fadc7b512c2a3ed502e01a1dc1e","first_computed_at":"2026-05-18T04:16:22.325503Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:16:22.325503Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mmeeGCAUL9cKCc+hNNDUPLLLXRzaTZ12Ml9jJFqKNgtoYrkR0SmwfNrjPbv33L1bzqtQ/XAsdK1JxB1f751pAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:16:22.326205Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.1539","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2631437f8ea13b2942d121a8c548856c532cb519b6f2fdc73d6f37086079c61c","sha256:f748ac31fa36a00977d60b1b0aa32e41a74b63f297c2ddfc94c3d254cf7c6647"],"state_sha256":"210f352e10cd9badaeffcc43bf1974b884c51e9b20315834f74f086c5c2d1317"}