{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:ZM3PTEDUCILM72FCZU7VLEWUSR","short_pith_number":"pith:ZM3PTEDU","canonical_record":{"source":{"id":"2210.09993","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-10-18T16:57:03Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"4d6d7db9e880c0ef081f1b4f3019bdd767384e80afc07ac66c85670f84ff75e2","abstract_canon_sha256":"e3e1f0aafde87b1c9ef86bb0c336d7df045dcfea8d16008d783ca15b638a4fce"},"schema_version":"1.0"},"canonical_sha256":"cb36f990741216cfe8a2cd3f5592d4947778c176b4592877bab456d4e6214bcd","source":{"kind":"arxiv","id":"2210.09993","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:ZM3PTEDUCILM72FCZU7VLEWUSR","target":"record","payload":{"canonical_record":{"source":{"id":"2210.09993","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-10-18T16:57:03Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"4d6d7db9e880c0ef081f1b4f3019bdd767384e80afc07ac66c85670f84ff75e2","abstract_canon_sha256":"e3e1f0aafde87b1c9ef86bb0c336d7df045dcfea8d16008d783ca15b638a4fce"},"schema_version":"1.0"},"canonical_sha256":"cb36f990741216cfe8a2cd3f5592d4947778c176b4592877bab456d4e6214bcd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:52:23.048682Z","signature_b64":"VXyVi+IFDowBy7GSLqOSpasSOFu/JMb+KFiTr6llzAAWTNCpRkNSWVzg6+AZimSLrmZz2wQZnf4YBn6W3N1LDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cb36f990741216cfe8a2cd3f5592d4947778c176b4592877bab456d4e6214bcd","last_reissued_at":"2026-07-05T05:52:23.048086Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:52:23.048086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2210.09993","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:52:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ds7N7QqDw32Qvj2h2AAFR7EulAMi6rfYKUTKtXNuuM9z5iGvl5q6ji7B6daKHpyvGNTSiWZu2gP/x8MhRgMaDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T19:24:51.454926Z"},"content_sha256":"5dc3ece4e753b6100f2a0ace3b0dccddc4238d0e6d3186334f59bb7470783132","schema_version":"1.0","event_id":"sha256:5dc3ece4e753b6100f2a0ace3b0dccddc4238d0e6d3186334f59bb7470783132"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:ZM3PTEDUCILM72FCZU7VLEWUSR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spectral curves and $W$-representations of matrix models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"A. Mironov, A. Morozov","submitted_at":"2022-10-18T16:57:03Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.09993","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2210.09993/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:52:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DtPRFydlRYXE4T8UrnalxMDyTOWtuyhkJgGIGKuzXCZe4FQmcIgVZbgiDRslNifLSmtcFLGlXZfKrA+GMc59BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T19:24:51.455427Z"},"content_sha256":"8f3160e23cd181d89f681ce3a3b3a480c3e2cb5159e1742410955fdff0708935","schema_version":"1.0","event_id":"sha256:8f3160e23cd181d89f681ce3a3b3a480c3e2cb5159e1742410955fdff0708935"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZM3PTEDUCILM72FCZU7VLEWUSR/bundle.json","state_url":"https://pith.science/pith/ZM3PTEDUCILM72FCZU7VLEWUSR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZM3PTEDUCILM72FCZU7VLEWUSR/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-04T19:24:51Z","links":{"resolver":"https://pith.science/pith/ZM3PTEDUCILM72FCZU7VLEWUSR","bundle":"https://pith.science/pith/ZM3PTEDUCILM72FCZU7VLEWUSR/bundle.json","state":"https://pith.science/pith/ZM3PTEDUCILM72FCZU7VLEWUSR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZM3PTEDUCILM72FCZU7VLEWUSR/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9tfpfJNigXLR12TE2UhCYRTQIhoGhX/9EW16ynAjgGVo2Wye3W2iBEmFYMlNMY7mue0yiuBSr4jq+/99V7u2CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T19:24:51.459442Z","bundle_sha256":"216352409c6dcc190bf09935f53594a6025ea8e1829079040ff3a687e800d01b"}}