{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:MOTR3U55MKUTETC34FPN767MIE","short_pith_number":"pith:MOTR3U55","schema_version":"1.0","canonical_sha256":"63a71dd3bd62a9324c5be15edffbec4110623fd174a33523023fddc9fa1567d8","source":{"kind":"arxiv","id":"2007.08515","version":1},"attestation_state":"computed","paper":{"title":"Multiple phases in a generalized Gross-Witten-Wadia matrix model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Jorge G. Russo, Miguel Tierz","submitted_at":"2020-07-16T17:59:58Z","abstract_excerpt":"We study a unitary matrix model of the Gross-Witten-Wadia type, extended with the addition of characteristic polynomial insertions. The model interpolates between solvable unitary matrix models and is the unitary counterpart of a deformed Cauchy ensemble. Exact formulas for the partition function and Wilson loops are given in terms of Toeplitz determinants and minors and large $N$ results are obtained by using Szeg\\\"o theorem with a Fisher-Hartwig singularity. In the large $N$ (planar) limit with two scaled couplings, the theory exhibits a surprisingly intricate phase structure in the two-dime"},"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":"2007.08515","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2020-07-16T17:59:58Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"76a2a3ddae34abfcf742d7bee2b63507b03b5560a2dc0b95445b4053a8966467","abstract_canon_sha256":"826ef6e7c2d52872feef0c7eb24211c71759a438ad1f00fd3c0577578d569255"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:53:09.556887Z","signature_b64":"1qVI/Qi5rzf2cNkByUAPLdCAD9wl3hpRs+aDdA4dc+nKWXqPk7x2KUNUCAHA9PvDqNGmpHZN8/0PQilUDMAWDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"63a71dd3bd62a9324c5be15edffbec4110623fd174a33523023fddc9fa1567d8","last_reissued_at":"2026-07-05T01:53:09.556400Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:53:09.556400Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multiple phases in a generalized Gross-Witten-Wadia matrix model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Jorge G. Russo, Miguel Tierz","submitted_at":"2020-07-16T17:59:58Z","abstract_excerpt":"We study a unitary matrix model of the Gross-Witten-Wadia type, extended with the addition of characteristic polynomial insertions. The model interpolates between solvable unitary matrix models and is the unitary counterpart of a deformed Cauchy ensemble. Exact formulas for the partition function and Wilson loops are given in terms of Toeplitz determinants and minors and large $N$ results are obtained by using Szeg\\\"o theorem with a Fisher-Hartwig singularity. In the large $N$ (planar) limit with two scaled couplings, the theory exhibits a surprisingly intricate phase structure in the two-dime"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.08515","kind":"arxiv","version":1},"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/2007.08515/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":"2007.08515","created_at":"2026-07-05T01:53:09.556459+00:00"},{"alias_kind":"arxiv_version","alias_value":"2007.08515v1","created_at":"2026-07-05T01:53:09.556459+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2007.08515","created_at":"2026-07-05T01:53:09.556459+00:00"},{"alias_kind":"pith_short_12","alias_value":"MOTR3U55MKUT","created_at":"2026-07-05T01:53:09.556459+00:00"},{"alias_kind":"pith_short_16","alias_value":"MOTR3U55MKUTETC3","created_at":"2026-07-05T01:53:09.556459+00:00"},{"alias_kind":"pith_short_8","alias_value":"MOTR3U55","created_at":"2026-07-05T01:53:09.556459+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2607.06384","citing_title":"Unitary matrix models, quantized symmetric functions and spin chain","ref_index":6,"is_internal_anchor":true},{"citing_arxiv_id":"2507.00689","citing_title":"Polyakov loop model with exact static quark determinant in the 't Hooft-Veneziano limit: U(N) case","ref_index":12,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MOTR3U55MKUTETC34FPN767MIE","json":"https://pith.science/pith/MOTR3U55MKUTETC34FPN767MIE.json","graph_json":"https://pith.science/api/pith-number/MOTR3U55MKUTETC34FPN767MIE/graph.json","events_json":"https://pith.science/api/pith-number/MOTR3U55MKUTETC34FPN767MIE/events.json","paper":"https://pith.science/paper/MOTR3U55"},"agent_actions":{"view_html":"https://pith.science/pith/MOTR3U55MKUTETC34FPN767MIE","download_json":"https://pith.science/pith/MOTR3U55MKUTETC34FPN767MIE.json","view_paper":"https://pith.science/paper/MOTR3U55","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2007.08515&json=true","fetch_graph":"https://pith.science/api/pith-number/MOTR3U55MKUTETC34FPN767MIE/graph.json","fetch_events":"https://pith.science/api/pith-number/MOTR3U55MKUTETC34FPN767MIE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MOTR3U55MKUTETC34FPN767MIE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MOTR3U55MKUTETC34FPN767MIE/action/storage_attestation","attest_author":"https://pith.science/pith/MOTR3U55MKUTETC34FPN767MIE/action/author_attestation","sign_citation":"https://pith.science/pith/MOTR3U55MKUTETC34FPN767MIE/action/citation_signature","submit_replication":"https://pith.science/pith/MOTR3U55MKUTETC34FPN767MIE/action/replication_record"}},"created_at":"2026-07-05T01:53:09.556459+00:00","updated_at":"2026-07-05T01:53:09.556459+00:00"}