{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:R5IF4K6PAYEVZQM7ZIUBV6SL2S","short_pith_number":"pith:R5IF4K6P","canonical_record":{"source":{"id":"1604.01491","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-04-06T05:28:19Z","cross_cats_sorted":["math-ph","math.CO","math.MP"],"title_canon_sha256":"3090fa43fde101eb188db62eb36dd601e4dbcc3c756fdfb164e844c794033591","abstract_canon_sha256":"a1aefca586dba6199d014df2e2db2aa037d3c57bcb8537bda5b30f57743f5b63"},"schema_version":"1.0"},"canonical_sha256":"8f505e2bcf06095cc19fca281afa4bd494c3c43ee6a1456f0d9d699d5a99c12a","source":{"kind":"arxiv","id":"1604.01491","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.01491","created_at":"2026-05-18T00:41:53Z"},{"alias_kind":"arxiv_version","alias_value":"1604.01491v3","created_at":"2026-05-18T00:41:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.01491","created_at":"2026-05-18T00:41:53Z"},{"alias_kind":"pith_short_12","alias_value":"R5IF4K6PAYEV","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"R5IF4K6PAYEVZQM7","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"R5IF4K6P","created_at":"2026-05-18T12:30:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:R5IF4K6PAYEVZQM7ZIUBV6SL2S","target":"record","payload":{"canonical_record":{"source":{"id":"1604.01491","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-04-06T05:28:19Z","cross_cats_sorted":["math-ph","math.CO","math.MP"],"title_canon_sha256":"3090fa43fde101eb188db62eb36dd601e4dbcc3c756fdfb164e844c794033591","abstract_canon_sha256":"a1aefca586dba6199d014df2e2db2aa037d3c57bcb8537bda5b30f57743f5b63"},"schema_version":"1.0"},"canonical_sha256":"8f505e2bcf06095cc19fca281afa4bd494c3c43ee6a1456f0d9d699d5a99c12a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:53.666410Z","signature_b64":"FXT9Xoliiz8AOlbBW5tdLefQR7sja0wPf58B+J8mH8rwyr1ps7KKEWUjc7FAND8FQRtbykjmvq3XhjrUYyLACQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8f505e2bcf06095cc19fca281afa4bd494c3c43ee6a1456f0d9d699d5a99c12a","last_reissued_at":"2026-05-18T00:41:53.665707Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:53.665707Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.01491","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:41:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GXBADJZwr21ohr5q3ENDblDH4vSq9/EWj3Rd0J2HMLcy8ODJhdq9DQVwkcH91ob3TIP4yo15ACIbq/BcLuvfCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T17:44:11.892389Z"},"content_sha256":"7e88c0a71ad0fa693e361337c5ba3a7c2f7fc636a8555a6da452dd0bee30dc8c","schema_version":"1.0","event_id":"sha256:7e88c0a71ad0fa693e361337c5ba3a7c2f7fc636a8555a6da452dd0bee30dc8c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:R5IF4K6PAYEVZQM7ZIUBV6SL2S","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotics of random domino tilings of rectangular Aztec diamonds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CO","math.MP"],"primary_cat":"math.PR","authors_text":"Alexey Bufetov, Alisa Knizel","submitted_at":"2016-04-06T05:28:19Z","abstract_excerpt":"We consider asymtotics of a domino tiling model on a class of domains which we call rectangular Aztec diamonds. We prove the Law of Large Numbers for the corresponding height functions and provide explicit formulas for the limit. For a special class of examples, the explicit parametrization of the frozen boundary is given. It turns out to be an algebraic curve with very special properties. Moreover, we establish the convergence of the fluctuations to the Gaussian Free Field in appropriate coordinates. Our main tool is a recently developed moment method for discrete particle systems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.01491","kind":"arxiv","version":3},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:41:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7Ew829Xc6BXpbuNJ7ycGMo9IJvEqVLESYxiWVasXgGdEU+BQVWbM624qUYkzJZOaAfFanBEtaEJTFhqmNum6Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T17:44:11.893085Z"},"content_sha256":"2c6fed6cb28cf8e4fa91b5a83a2d2e626d6f2bd5520cf8cd6cb9ee8b591efd8a","schema_version":"1.0","event_id":"sha256:2c6fed6cb28cf8e4fa91b5a83a2d2e626d6f2bd5520cf8cd6cb9ee8b591efd8a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/R5IF4K6PAYEVZQM7ZIUBV6SL2S/bundle.json","state_url":"https://pith.science/pith/R5IF4K6PAYEVZQM7ZIUBV6SL2S/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/R5IF4K6PAYEVZQM7ZIUBV6SL2S/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-28T17:44:11Z","links":{"resolver":"https://pith.science/pith/R5IF4K6PAYEVZQM7ZIUBV6SL2S","bundle":"https://pith.science/pith/R5IF4K6PAYEVZQM7ZIUBV6SL2S/bundle.json","state":"https://pith.science/pith/R5IF4K6PAYEVZQM7ZIUBV6SL2S/state.json","well_known_bundle":"https://pith.science/.well-known/pith/R5IF4K6PAYEVZQM7ZIUBV6SL2S/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:R5IF4K6PAYEVZQM7ZIUBV6SL2S","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":"a1aefca586dba6199d014df2e2db2aa037d3c57bcb8537bda5b30f57743f5b63","cross_cats_sorted":["math-ph","math.CO","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-04-06T05:28:19Z","title_canon_sha256":"3090fa43fde101eb188db62eb36dd601e4dbcc3c756fdfb164e844c794033591"},"schema_version":"1.0","source":{"id":"1604.01491","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.01491","created_at":"2026-05-18T00:41:53Z"},{"alias_kind":"arxiv_version","alias_value":"1604.01491v3","created_at":"2026-05-18T00:41:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.01491","created_at":"2026-05-18T00:41:53Z"},{"alias_kind":"pith_short_12","alias_value":"R5IF4K6PAYEV","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"R5IF4K6PAYEVZQM7","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"R5IF4K6P","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:2c6fed6cb28cf8e4fa91b5a83a2d2e626d6f2bd5520cf8cd6cb9ee8b591efd8a","target":"graph","created_at":"2026-05-18T00:41:53Z","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":"We consider asymtotics of a domino tiling model on a class of domains which we call rectangular Aztec diamonds. We prove the Law of Large Numbers for the corresponding height functions and provide explicit formulas for the limit. For a special class of examples, the explicit parametrization of the frozen boundary is given. It turns out to be an algebraic curve with very special properties. Moreover, we establish the convergence of the fluctuations to the Gaussian Free Field in appropriate coordinates. Our main tool is a recently developed moment method for discrete particle systems.","authors_text":"Alexey Bufetov, Alisa Knizel","cross_cats":["math-ph","math.CO","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-04-06T05:28:19Z","title":"Asymptotics of random domino tilings of rectangular Aztec diamonds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.01491","kind":"arxiv","version":3},"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":"sha256:7e88c0a71ad0fa693e361337c5ba3a7c2f7fc636a8555a6da452dd0bee30dc8c","target":"record","created_at":"2026-05-18T00:41:53Z","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":"a1aefca586dba6199d014df2e2db2aa037d3c57bcb8537bda5b30f57743f5b63","cross_cats_sorted":["math-ph","math.CO","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-04-06T05:28:19Z","title_canon_sha256":"3090fa43fde101eb188db62eb36dd601e4dbcc3c756fdfb164e844c794033591"},"schema_version":"1.0","source":{"id":"1604.01491","kind":"arxiv","version":3}},"canonical_sha256":"8f505e2bcf06095cc19fca281afa4bd494c3c43ee6a1456f0d9d699d5a99c12a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8f505e2bcf06095cc19fca281afa4bd494c3c43ee6a1456f0d9d699d5a99c12a","first_computed_at":"2026-05-18T00:41:53.665707Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:53.665707Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FXT9Xoliiz8AOlbBW5tdLefQR7sja0wPf58B+J8mH8rwyr1ps7KKEWUjc7FAND8FQRtbykjmvq3XhjrUYyLACQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:53.666410Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.01491","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7e88c0a71ad0fa693e361337c5ba3a7c2f7fc636a8555a6da452dd0bee30dc8c","sha256:2c6fed6cb28cf8e4fa91b5a83a2d2e626d6f2bd5520cf8cd6cb9ee8b591efd8a"],"state_sha256":"8fa9bf7e2e309b042d8e25335d96bb20878a8fecaee4d93850574a151fe98c56"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3AaJ7XOQ1RQ9BmCZQKE9f7a7fshQceBFsCkSEQpibHWKQL04bQEN+Ezn6KCPD2bEnBSJvtdCI3TTDFLU8qDMBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T17:44:11.897042Z","bundle_sha256":"6fdf6a407732bbaaa50c58b15dddc33798334a319f2b43cf9cc9962015b84813"}}