{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:CBSP4N4JGZGZEC3B6ATWDIUOTO","short_pith_number":"pith:CBSP4N4J","schema_version":"1.0","canonical_sha256":"1064fe3789364d920b61f02761a28e9bb405109f96e032edcdededc9cfb98a99","source":{"kind":"arxiv","id":"1407.7578","version":2},"attestation_state":"computed","paper":{"title":"Lozenge tilings and Hurwitz numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Jonathan Novak","submitted_at":"2014-07-28T21:49:09Z","abstract_excerpt":"We give a new proof of the fact that, near a turning point of the frozen boundary, the vertical tiles in a uniformly random lozenge tiling of a large sawtooth domain are distributed like the eigenvalues of a GUE random matrix. Our argument uses none of the standard tools of integrable probability. In their place, it uses a combinatorial interpretation of the Harish-Chandra/Itzykson-Zuber integral as a generating function for desymmetrized Hurwitz numbers."},"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":"1407.7578","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-07-28T21:49:09Z","cross_cats_sorted":["math.CO","math.MP","math.PR"],"title_canon_sha256":"928d3a8179d10f6e8a833d6cfdcd618021d57dbd778c6bce23fee63eef36d0d1","abstract_canon_sha256":"f3b8a496b1378023b813ac44db7b88c1e1f748fa64605fbb6ec89c7709704270"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:29:05.472821Z","signature_b64":"jYF5jr/T2Au/3SFvWqBlgRwGRDloQb/9bY+ve8QPnXaZaPXtNoOWVPM1nyoSgaucGM2V7HxZ8aHEr/CQgta6CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1064fe3789364d920b61f02761a28e9bb405109f96e032edcdededc9cfb98a99","last_reissued_at":"2026-05-18T01:29:05.472113Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:29:05.472113Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lozenge tilings and Hurwitz numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Jonathan Novak","submitted_at":"2014-07-28T21:49:09Z","abstract_excerpt":"We give a new proof of the fact that, near a turning point of the frozen boundary, the vertical tiles in a uniformly random lozenge tiling of a large sawtooth domain are distributed like the eigenvalues of a GUE random matrix. Our argument uses none of the standard tools of integrable probability. In their place, it uses a combinatorial interpretation of the Harish-Chandra/Itzykson-Zuber integral as a generating function for desymmetrized Hurwitz numbers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.7578","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":"1407.7578","created_at":"2026-05-18T01:29:05.472229+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.7578v2","created_at":"2026-05-18T01:29:05.472229+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.7578","created_at":"2026-05-18T01:29:05.472229+00:00"},{"alias_kind":"pith_short_12","alias_value":"CBSP4N4JGZGZ","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_16","alias_value":"CBSP4N4JGZGZEC3B","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_8","alias_value":"CBSP4N4J","created_at":"2026-05-18T12:28:22.404517+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/CBSP4N4JGZGZEC3B6ATWDIUOTO","json":"https://pith.science/pith/CBSP4N4JGZGZEC3B6ATWDIUOTO.json","graph_json":"https://pith.science/api/pith-number/CBSP4N4JGZGZEC3B6ATWDIUOTO/graph.json","events_json":"https://pith.science/api/pith-number/CBSP4N4JGZGZEC3B6ATWDIUOTO/events.json","paper":"https://pith.science/paper/CBSP4N4J"},"agent_actions":{"view_html":"https://pith.science/pith/CBSP4N4JGZGZEC3B6ATWDIUOTO","download_json":"https://pith.science/pith/CBSP4N4JGZGZEC3B6ATWDIUOTO.json","view_paper":"https://pith.science/paper/CBSP4N4J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.7578&json=true","fetch_graph":"https://pith.science/api/pith-number/CBSP4N4JGZGZEC3B6ATWDIUOTO/graph.json","fetch_events":"https://pith.science/api/pith-number/CBSP4N4JGZGZEC3B6ATWDIUOTO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CBSP4N4JGZGZEC3B6ATWDIUOTO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CBSP4N4JGZGZEC3B6ATWDIUOTO/action/storage_attestation","attest_author":"https://pith.science/pith/CBSP4N4JGZGZEC3B6ATWDIUOTO/action/author_attestation","sign_citation":"https://pith.science/pith/CBSP4N4JGZGZEC3B6ATWDIUOTO/action/citation_signature","submit_replication":"https://pith.science/pith/CBSP4N4JGZGZEC3B6ATWDIUOTO/action/replication_record"}},"created_at":"2026-05-18T01:29:05.472229+00:00","updated_at":"2026-05-18T01:29:05.472229+00:00"}