{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:ZM3PTEDUCILM72FCZU7VLEWUSR","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":"e3e1f0aafde87b1c9ef86bb0c336d7df045dcfea8d16008d783ca15b638a4fce","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-10-18T16:57:03Z","title_canon_sha256":"4d6d7db9e880c0ef081f1b4f3019bdd767384e80afc07ac66c85670f84ff75e2"},"schema_version":"1.0","source":{"id":"2210.09993","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2210.09993","created_at":"2026-07-05T05:52:23Z"},{"alias_kind":"arxiv_version","alias_value":"2210.09993v3","created_at":"2026-07-05T05:52:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2210.09993","created_at":"2026-07-05T05:52:23Z"},{"alias_kind":"pith_short_12","alias_value":"ZM3PTEDUCILM","created_at":"2026-07-05T05:52:23Z"},{"alias_kind":"pith_short_16","alias_value":"ZM3PTEDUCILM72FC","created_at":"2026-07-05T05:52:23Z"},{"alias_kind":"pith_short_8","alias_value":"ZM3PTEDU","created_at":"2026-07-05T05:52:23Z"}],"graph_snapshots":[{"event_id":"sha256:8f3160e23cd181d89f681ce3a3b3a480c3e2cb5159e1742410955fdff0708935","target":"graph","created_at":"2026-07-05T05:52:23Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2210.09993/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We explain how the spectral curve can be extracted from the ${\\cal W}$-representation of a matrix model. It emerges from the part of the ${\\cal W}$-operator, which is linear in time-variables. A possibility of extracting the spectral curve in this way is important because there are models where matrix integrals are not yet available, and still they possess all their important features. We apply this reasoning to the family of WLZZ models and discuss additional peculiarities which appear for the non-negative value of the family parameter $n$, when the model depends on additional couplings (dual","authors_text":"A. Mironov, A. Morozov","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-10-18T16:57:03Z","title":"Spectral curves and $W$-representations of matrix models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.09993","kind":"arxiv","version":3},"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":"sha256:5dc3ece4e753b6100f2a0ace3b0dccddc4238d0e6d3186334f59bb7470783132","target":"record","created_at":"2026-07-05T05:52:23Z","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":"e3e1f0aafde87b1c9ef86bb0c336d7df045dcfea8d16008d783ca15b638a4fce","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-10-18T16:57:03Z","title_canon_sha256":"4d6d7db9e880c0ef081f1b4f3019bdd767384e80afc07ac66c85670f84ff75e2"},"schema_version":"1.0","source":{"id":"2210.09993","kind":"arxiv","version":3}},"canonical_sha256":"cb36f990741216cfe8a2cd3f5592d4947778c176b4592877bab456d4e6214bcd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cb36f990741216cfe8a2cd3f5592d4947778c176b4592877bab456d4e6214bcd","first_computed_at":"2026-07-05T05:52:23.048086Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:52:23.048086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VXyVi+IFDowBy7GSLqOSpasSOFu/JMb+KFiTr6llzAAWTNCpRkNSWVzg6+AZimSLrmZz2wQZnf4YBn6W3N1LDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T05:52:23.048682Z","signed_message":"canonical_sha256_bytes"},"source_id":"2210.09993","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5dc3ece4e753b6100f2a0ace3b0dccddc4238d0e6d3186334f59bb7470783132","sha256:8f3160e23cd181d89f681ce3a3b3a480c3e2cb5159e1742410955fdff0708935"],"state_sha256":"dda0069c83a8a7e0c387b6f1b81c62ff7ddac0d347b4a41b6cb7e23f544adec8"}