{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:G3X67GPVZSNJEXJ6CLJ7SFXATD","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"b95ed3e3b1859bf04dc6cdb7b87a3b7cf9ebe9f3d3c20c7ed6301d6974cc0c34","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-04-10T09:20:12Z","title_canon_sha256":"e55ac21bb78cb66f27381d19694d14c6fa94965b6c5c18fc2664f6aef99cfb7c"},"schema_version":"1.0","source":{"id":"1804.03414","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.03414","created_at":"2026-05-18T00:18:45Z"},{"alias_kind":"arxiv_version","alias_value":"1804.03414v2","created_at":"2026-05-18T00:18:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.03414","created_at":"2026-05-18T00:18:45Z"},{"alias_kind":"pith_short_12","alias_value":"G3X67GPVZSNJ","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"G3X67GPVZSNJEXJ6","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"G3X67GPV","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:7db12cf687256a491a68d7ee97b6b9505916b12655de2d36a0fb1488273148e3","target":"graph","created_at":"2026-05-18T00:18:45Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Wangru Sun","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-04-10T09:20:12Z","title":"Dimer model, bead model and standard Young tableaux: finite cases and limit shapes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.03414","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:e223a78ed1652cc8e0db609077f438c37e367a4f49119c2ddc8f9962a068bbe0","target":"record","created_at":"2026-05-18T00:18:45Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"b95ed3e3b1859bf04dc6cdb7b87a3b7cf9ebe9f3d3c20c7ed6301d6974cc0c34","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-04-10T09:20:12Z","title_canon_sha256":"e55ac21bb78cb66f27381d19694d14c6fa94965b6c5c18fc2664f6aef99cfb7c"},"schema_version":"1.0","source":{"id":"1804.03414","kind":"arxiv","version":2}},"canonical_sha256":"36efef99f5cc9a925d3e12d3f916e098ddf878182942e4948aae6cff7215e760","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"36efef99f5cc9a925d3e12d3f916e098ddf878182942e4948aae6cff7215e760","first_computed_at":"2026-05-18T00:18:45.400273Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:45.400273Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LktvdPH70IbC5CNzB+CcGvkXhDFa7N5ytrM71VkULqAxyapXJkLBGoyTo4od3mtubeGq2jEloNRGHjVqGBntBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:45.400984Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.03414","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e223a78ed1652cc8e0db609077f438c37e367a4f49119c2ddc8f9962a068bbe0","sha256:7db12cf687256a491a68d7ee97b6b9505916b12655de2d36a0fb1488273148e3"],"state_sha256":"2fb34dfc4d3cabfb29ecf840058f35170397ce154cddefb48b71130b4b8a425e"}