{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:Z2JIFAVGL5JZCLEJRW7CXVGPA4","short_pith_number":"pith:Z2JIFAVG","schema_version":"1.0","canonical_sha256":"ce928282a65f53912c898dbe2bd4cf071488a38fd4b828bd460382a939602b14","source":{"kind":"arxiv","id":"0910.1636","version":2},"attestation_state":"computed","paper":{"title":"Arctic circles, domino tilings and square Young tableaux","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Dan Romik","submitted_at":"2009-10-09T00:12:38Z","abstract_excerpt":"The arctic circle theorem of Jockusch, Propp, and Shor asserts that uniformly random domino tilings of an Aztec diamond of high order are frozen with asymptotically high probability outside the \"arctic circle\" inscribed within the diamond. A similar arctic circle phenomenon has been observed in the limiting behavior of random square Young tableaux. In this paper, we show that random domino tilings of the Aztec diamond are asymptotically related to random square Young tableaux in a more refined sense that looks also at the behavior inside the arctic circle. This is done by giving a new derivati"},"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":"0910.1636","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-10-09T00:12:38Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"6026653633901d6077aabc22f3fc3b36d67aa9390c213e38e0a559e1d4e20278","abstract_canon_sha256":"7f7495ea2ed94d48b249bfaa882f899e2d3303c3a6071c2c93a8dd6331686b8a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:58:14.298893Z","signature_b64":"inNCzXZ+1NKx0c/LXABGlH1AClEmkKqUt+Y9RfSH1b8P/2CYpRQGJEJmiHdJFRudhIvDLmEF6XU1MwnsRdW9Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ce928282a65f53912c898dbe2bd4cf071488a38fd4b828bd460382a939602b14","last_reissued_at":"2026-05-18T03:58:14.297111Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:58:14.297111Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Arctic circles, domino tilings and square Young tableaux","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Dan Romik","submitted_at":"2009-10-09T00:12:38Z","abstract_excerpt":"The arctic circle theorem of Jockusch, Propp, and Shor asserts that uniformly random domino tilings of an Aztec diamond of high order are frozen with asymptotically high probability outside the \"arctic circle\" inscribed within the diamond. A similar arctic circle phenomenon has been observed in the limiting behavior of random square Young tableaux. In this paper, we show that random domino tilings of the Aztec diamond are asymptotically related to random square Young tableaux in a more refined sense that looks also at the behavior inside the arctic circle. This is done by giving a new derivati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.1636","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":"0910.1636","created_at":"2026-05-18T03:58:14.297254+00:00"},{"alias_kind":"arxiv_version","alias_value":"0910.1636v2","created_at":"2026-05-18T03:58:14.297254+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.1636","created_at":"2026-05-18T03:58:14.297254+00:00"},{"alias_kind":"pith_short_12","alias_value":"Z2JIFAVGL5JZ","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_16","alias_value":"Z2JIFAVGL5JZCLEJ","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_8","alias_value":"Z2JIFAVG","created_at":"2026-05-18T12:26:02.257875+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/Z2JIFAVGL5JZCLEJRW7CXVGPA4","json":"https://pith.science/pith/Z2JIFAVGL5JZCLEJRW7CXVGPA4.json","graph_json":"https://pith.science/api/pith-number/Z2JIFAVGL5JZCLEJRW7CXVGPA4/graph.json","events_json":"https://pith.science/api/pith-number/Z2JIFAVGL5JZCLEJRW7CXVGPA4/events.json","paper":"https://pith.science/paper/Z2JIFAVG"},"agent_actions":{"view_html":"https://pith.science/pith/Z2JIFAVGL5JZCLEJRW7CXVGPA4","download_json":"https://pith.science/pith/Z2JIFAVGL5JZCLEJRW7CXVGPA4.json","view_paper":"https://pith.science/paper/Z2JIFAVG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0910.1636&json=true","fetch_graph":"https://pith.science/api/pith-number/Z2JIFAVGL5JZCLEJRW7CXVGPA4/graph.json","fetch_events":"https://pith.science/api/pith-number/Z2JIFAVGL5JZCLEJRW7CXVGPA4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Z2JIFAVGL5JZCLEJRW7CXVGPA4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Z2JIFAVGL5JZCLEJRW7CXVGPA4/action/storage_attestation","attest_author":"https://pith.science/pith/Z2JIFAVGL5JZCLEJRW7CXVGPA4/action/author_attestation","sign_citation":"https://pith.science/pith/Z2JIFAVGL5JZCLEJRW7CXVGPA4/action/citation_signature","submit_replication":"https://pith.science/pith/Z2JIFAVGL5JZCLEJRW7CXVGPA4/action/replication_record"}},"created_at":"2026-05-18T03:58:14.297254+00:00","updated_at":"2026-05-18T03:58:14.297254+00:00"}