{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:G3X67GPVZSNJEXJ6CLJ7SFXATD","short_pith_number":"pith:G3X67GPV","schema_version":"1.0","canonical_sha256":"36efef99f5cc9a925d3e12d3f916e098ddf878182942e4948aae6cff7215e760","source":{"kind":"arxiv","id":"1804.03414","version":2},"attestation_state":"computed","paper":{"title":"Dimer model, bead model and standard Young tableaux: finite cases and limit shapes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Wangru Sun","submitted_at":"2018-04-10T09:20:12Z","abstract_excerpt":"The bead model is a random point field on $\\mathbb{Z}\\times\\mathbb{R}$ which can be viewed as a scaling limit of dimer model. We prove that, in the scaling limit, the normalized height function of a uniformly chosen random bead configuration lies in an arbitrarily small neighborhood of a surface $h_0$ that maximizes some functional which we call as entropy. We also prove that the limit shape $h_0$ is a scaling limit of the limit shapes of a properly chosen sequence of dimer models. There is a map from bead configurations to standard tableaux of a (skew) Young diagram, and the map preserves uni"},"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":"1804.03414","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-04-10T09:20:12Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"e55ac21bb78cb66f27381d19694d14c6fa94965b6c5c18fc2664f6aef99cfb7c","abstract_canon_sha256":"b95ed3e3b1859bf04dc6cdb7b87a3b7cf9ebe9f3d3c20c7ed6301d6974cc0c34"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:45.400984Z","signature_b64":"LktvdPH70IbC5CNzB+CcGvkXhDFa7N5ytrM71VkULqAxyapXJkLBGoyTo4od3mtubeGq2jEloNRGHjVqGBntBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"36efef99f5cc9a925d3e12d3f916e098ddf878182942e4948aae6cff7215e760","last_reissued_at":"2026-05-18T00:18:45.400273Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:45.400273Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dimer model, bead model and standard Young tableaux: finite cases and limit shapes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Wangru Sun","submitted_at":"2018-04-10T09:20:12Z","abstract_excerpt":"The bead model is a random point field on $\\mathbb{Z}\\times\\mathbb{R}$ which can be viewed as a scaling limit of dimer model. We prove that, in the scaling limit, the normalized height function of a uniformly chosen random bead configuration lies in an arbitrarily small neighborhood of a surface $h_0$ that maximizes some functional which we call as entropy. We also prove that the limit shape $h_0$ is a scaling limit of the limit shapes of a properly chosen sequence of dimer models. There is a map from bead configurations to standard tableaux of a (skew) Young diagram, and the map preserves uni"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.03414","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":"1804.03414","created_at":"2026-05-18T00:18:45.400394+00:00"},{"alias_kind":"arxiv_version","alias_value":"1804.03414v2","created_at":"2026-05-18T00:18:45.400394+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.03414","created_at":"2026-05-18T00:18:45.400394+00:00"},{"alias_kind":"pith_short_12","alias_value":"G3X67GPVZSNJ","created_at":"2026-05-18T12:32:25.280505+00:00"},{"alias_kind":"pith_short_16","alias_value":"G3X67GPVZSNJEXJ6","created_at":"2026-05-18T12:32:25.280505+00:00"},{"alias_kind":"pith_short_8","alias_value":"G3X67GPV","created_at":"2026-05-18T12:32:25.280505+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.18601","citing_title":"Global fluctuations for standard Young tableaux","ref_index":74,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/G3X67GPVZSNJEXJ6CLJ7SFXATD","json":"https://pith.science/pith/G3X67GPVZSNJEXJ6CLJ7SFXATD.json","graph_json":"https://pith.science/api/pith-number/G3X67GPVZSNJEXJ6CLJ7SFXATD/graph.json","events_json":"https://pith.science/api/pith-number/G3X67GPVZSNJEXJ6CLJ7SFXATD/events.json","paper":"https://pith.science/paper/G3X67GPV"},"agent_actions":{"view_html":"https://pith.science/pith/G3X67GPVZSNJEXJ6CLJ7SFXATD","download_json":"https://pith.science/pith/G3X67GPVZSNJEXJ6CLJ7SFXATD.json","view_paper":"https://pith.science/paper/G3X67GPV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1804.03414&json=true","fetch_graph":"https://pith.science/api/pith-number/G3X67GPVZSNJEXJ6CLJ7SFXATD/graph.json","fetch_events":"https://pith.science/api/pith-number/G3X67GPVZSNJEXJ6CLJ7SFXATD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/G3X67GPVZSNJEXJ6CLJ7SFXATD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/G3X67GPVZSNJEXJ6CLJ7SFXATD/action/storage_attestation","attest_author":"https://pith.science/pith/G3X67GPVZSNJEXJ6CLJ7SFXATD/action/author_attestation","sign_citation":"https://pith.science/pith/G3X67GPVZSNJEXJ6CLJ7SFXATD/action/citation_signature","submit_replication":"https://pith.science/pith/G3X67GPVZSNJEXJ6CLJ7SFXATD/action/replication_record"}},"created_at":"2026-05-18T00:18:45.400394+00:00","updated_at":"2026-05-18T00:18:45.400394+00:00"}