{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:4SWWSHELUTJG3Y3BAA2UXEUE2V","short_pith_number":"pith:4SWWSHEL","schema_version":"1.0","canonical_sha256":"e4ad691c8ba4d26de36100354b9284d54c63420fe1ecc3ca9042009a88380ae4","source":{"kind":"arxiv","id":"2301.12763","version":2},"attestation_state":"computed","paper":{"title":"$W$-representations for multi-character partition functions and their $\\beta$-deformations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"A. Popolitov, Fan Liu, Lu-Yao Wang, Rui Wang, V. Mishnyakov","submitted_at":"2023-01-30T10:17:01Z","abstract_excerpt":"In this letter we continue the development of $W$-representations. We propose several generalizations of the known models, such as the hypergeometric Hurwitz $\\tau$-functions. We construct $W$-representations for multi-character expansions, which involve a generic number of sets of time variables. We propose integral representations for such kind of partition functions which are given by tensor models and multi-matrix models with multi-trace couplings. We further propose the $\\beta$-deformation of the discussed $W$-representation for the Hurwitz case for two sets of times as well as for the mu"},"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":"2301.12763","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2023-01-30T10:17:01Z","cross_cats_sorted":[],"title_canon_sha256":"4b0b03ab34e7b1a75ecfddfab12a59395f7f0113c32bc7b0b41fb5d1806ab2ba","abstract_canon_sha256":"e1a8147e96c33cbd3604a3a4b9b9e64c415025e3d2e94d631d593fd7f9861b10"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:37:12.414687Z","signature_b64":"YDD/H7Czhuwt/qzM/Hl1xS3Ad+Y8FJf+QCpyzB5rrTNpP8b9qyx0iPnbOlODkbLTe2HAGamlS0PfHwl6BIsqAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e4ad691c8ba4d26de36100354b9284d54c63420fe1ecc3ca9042009a88380ae4","last_reissued_at":"2026-07-05T05:37:12.414304Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:37:12.414304Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$W$-representations for multi-character partition functions and their $\\beta$-deformations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"A. Popolitov, Fan Liu, Lu-Yao Wang, Rui Wang, V. Mishnyakov","submitted_at":"2023-01-30T10:17:01Z","abstract_excerpt":"In this letter we continue the development of $W$-representations. We propose several generalizations of the known models, such as the hypergeometric Hurwitz $\\tau$-functions. We construct $W$-representations for multi-character expansions, which involve a generic number of sets of time variables. We propose integral representations for such kind of partition functions which are given by tensor models and multi-matrix models with multi-trace couplings. We further propose the $\\beta$-deformation of the discussed $W$-representation for the Hurwitz case for two sets of times as well as for the mu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2301.12763","kind":"arxiv","version":2},"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/2301.12763/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2301.12763","created_at":"2026-07-05T05:37:12.414369+00:00"},{"alias_kind":"arxiv_version","alias_value":"2301.12763v2","created_at":"2026-07-05T05:37:12.414369+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2301.12763","created_at":"2026-07-05T05:37:12.414369+00:00"},{"alias_kind":"pith_short_12","alias_value":"4SWWSHELUTJG","created_at":"2026-07-05T05:37:12.414369+00:00"},{"alias_kind":"pith_short_16","alias_value":"4SWWSHELUTJG3Y3B","created_at":"2026-07-05T05:37:12.414369+00:00"},{"alias_kind":"pith_short_8","alias_value":"4SWWSHEL","created_at":"2026-07-05T05:37:12.414369+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2505.08132","citing_title":"Correlators in two rainbow tensor and complex multi-matrix models","ref_index":37,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4SWWSHELUTJG3Y3BAA2UXEUE2V","json":"https://pith.science/pith/4SWWSHELUTJG3Y3BAA2UXEUE2V.json","graph_json":"https://pith.science/api/pith-number/4SWWSHELUTJG3Y3BAA2UXEUE2V/graph.json","events_json":"https://pith.science/api/pith-number/4SWWSHELUTJG3Y3BAA2UXEUE2V/events.json","paper":"https://pith.science/paper/4SWWSHEL"},"agent_actions":{"view_html":"https://pith.science/pith/4SWWSHELUTJG3Y3BAA2UXEUE2V","download_json":"https://pith.science/pith/4SWWSHELUTJG3Y3BAA2UXEUE2V.json","view_paper":"https://pith.science/paper/4SWWSHEL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2301.12763&json=true","fetch_graph":"https://pith.science/api/pith-number/4SWWSHELUTJG3Y3BAA2UXEUE2V/graph.json","fetch_events":"https://pith.science/api/pith-number/4SWWSHELUTJG3Y3BAA2UXEUE2V/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4SWWSHELUTJG3Y3BAA2UXEUE2V/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4SWWSHELUTJG3Y3BAA2UXEUE2V/action/storage_attestation","attest_author":"https://pith.science/pith/4SWWSHELUTJG3Y3BAA2UXEUE2V/action/author_attestation","sign_citation":"https://pith.science/pith/4SWWSHELUTJG3Y3BAA2UXEUE2V/action/citation_signature","submit_replication":"https://pith.science/pith/4SWWSHELUTJG3Y3BAA2UXEUE2V/action/replication_record"}},"created_at":"2026-07-05T05:37:12.414369+00:00","updated_at":"2026-07-05T05:37:12.414369+00:00"}