{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:MHVO2PAJOVWVNMMAAUJNZX3OKP","short_pith_number":"pith:MHVO2PAJ","schema_version":"1.0","canonical_sha256":"61eaed3c09756d56b1800512dcdf6e53e7382fbb98f469ee522456fe7d5904fb","source":{"kind":"arxiv","id":"1011.1769","version":2},"attestation_state":"computed","paper":{"title":"The q-Gelfand-Tsetlin graph, Gibbs measures and q-Toeplitz matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR","math.QA"],"primary_cat":"math.RT","authors_text":"Vadim Gorin","submitted_at":"2010-11-08T10:59:00Z","abstract_excerpt":"The problem of the description of finite factor representations of the infinite-dimensional unitary group, investigated by Voiculescu in 1976, is equivalent to the description of all totally positive Toeplitz matrices. Vershik-Kerov showed that this problem is also equivalent to the description of the simplex of central (i.e. possessing a certain Gibbs property) measures on paths in the Gelfand-Tsetlin graph. We study a quantum version of the latter problem. We introduce a notion of a q-centrality and describe the simplex of all q-central measures on paths in the Gelfand-Tsetlin graph. Conject"},"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":"1011.1769","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-11-08T10:59:00Z","cross_cats_sorted":["math-ph","math.MP","math.PR","math.QA"],"title_canon_sha256":"7f74aaf90f8a2d86cb38e9a4433a4f38c6d7e266a266f427803aebae0707606b","abstract_canon_sha256":"23d2a9a5fa89234f9a6924df6e09d7f581d550016b2b28fbd25f38f6fd7799ff"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:48:48.284971Z","signature_b64":"bUJ3sSS/Tbw7+r5puP1Z5knLUfD9TnzqnZ0E7ESe9ozCGjykgk1yL+yFSCIlflEqoCtLYMnwpKVd4W13Fq7tBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"61eaed3c09756d56b1800512dcdf6e53e7382fbb98f469ee522456fe7d5904fb","last_reissued_at":"2026-05-18T03:48:48.284313Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:48:48.284313Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The q-Gelfand-Tsetlin graph, Gibbs measures and q-Toeplitz matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR","math.QA"],"primary_cat":"math.RT","authors_text":"Vadim Gorin","submitted_at":"2010-11-08T10:59:00Z","abstract_excerpt":"The problem of the description of finite factor representations of the infinite-dimensional unitary group, investigated by Voiculescu in 1976, is equivalent to the description of all totally positive Toeplitz matrices. Vershik-Kerov showed that this problem is also equivalent to the description of the simplex of central (i.e. possessing a certain Gibbs property) measures on paths in the Gelfand-Tsetlin graph. We study a quantum version of the latter problem. We introduce a notion of a q-centrality and describe the simplex of all q-central measures on paths in the Gelfand-Tsetlin graph. Conject"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.1769","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":""},"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":"1011.1769","created_at":"2026-05-18T03:48:48.284420+00:00"},{"alias_kind":"arxiv_version","alias_value":"1011.1769v2","created_at":"2026-05-18T03:48:48.284420+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.1769","created_at":"2026-05-18T03:48:48.284420+00:00"},{"alias_kind":"pith_short_12","alias_value":"MHVO2PAJOVWV","created_at":"2026-05-18T12:26:10.704358+00:00"},{"alias_kind":"pith_short_16","alias_value":"MHVO2PAJOVWVNMMA","created_at":"2026-05-18T12:26:10.704358+00:00"},{"alias_kind":"pith_short_8","alias_value":"MHVO2PAJ","created_at":"2026-05-18T12:26:10.704358+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MHVO2PAJOVWVNMMAAUJNZX3OKP","json":"https://pith.science/pith/MHVO2PAJOVWVNMMAAUJNZX3OKP.json","graph_json":"https://pith.science/api/pith-number/MHVO2PAJOVWVNMMAAUJNZX3OKP/graph.json","events_json":"https://pith.science/api/pith-number/MHVO2PAJOVWVNMMAAUJNZX3OKP/events.json","paper":"https://pith.science/paper/MHVO2PAJ"},"agent_actions":{"view_html":"https://pith.science/pith/MHVO2PAJOVWVNMMAAUJNZX3OKP","download_json":"https://pith.science/pith/MHVO2PAJOVWVNMMAAUJNZX3OKP.json","view_paper":"https://pith.science/paper/MHVO2PAJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1011.1769&json=true","fetch_graph":"https://pith.science/api/pith-number/MHVO2PAJOVWVNMMAAUJNZX3OKP/graph.json","fetch_events":"https://pith.science/api/pith-number/MHVO2PAJOVWVNMMAAUJNZX3OKP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MHVO2PAJOVWVNMMAAUJNZX3OKP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MHVO2PAJOVWVNMMAAUJNZX3OKP/action/storage_attestation","attest_author":"https://pith.science/pith/MHVO2PAJOVWVNMMAAUJNZX3OKP/action/author_attestation","sign_citation":"https://pith.science/pith/MHVO2PAJOVWVNMMAAUJNZX3OKP/action/citation_signature","submit_replication":"https://pith.science/pith/MHVO2PAJOVWVNMMAAUJNZX3OKP/action/replication_record"}},"created_at":"2026-05-18T03:48:48.284420+00:00","updated_at":"2026-05-18T03:48:48.284420+00:00"}