{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:DKMCNGOARYMKC6VOBRZIZFVRLD","short_pith_number":"pith:DKMCNGOA","canonical_record":{"source":{"id":"1110.4176","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math-ph","submitted_at":"2011-10-19T04:16:23Z","cross_cats_sorted":["math.CO","math.MP","math.PR"],"title_canon_sha256":"d0ec9a5f8d631fecb27bf741405f144fee0d83e42aa8f344f2edc3958c465448","abstract_canon_sha256":"a6a3c7c992506929460af223617b01869f8ed5526ad191fb486065a34f66e9ff"},"schema_version":"1.0"},"canonical_sha256":"1a982699c08e18a17aae0c728c96b158e7172902453a56485f702c5b67a46e69","source":{"kind":"arxiv","id":"1110.4176","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.4176","created_at":"2026-05-18T00:18:41Z"},{"alias_kind":"arxiv_version","alias_value":"1110.4176v3","created_at":"2026-05-18T00:18:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.4176","created_at":"2026-05-18T00:18:41Z"},{"alias_kind":"pith_short_12","alias_value":"DKMCNGOARYMK","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"DKMCNGOARYMKC6VO","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"DKMCNGOA","created_at":"2026-05-18T12:26:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:DKMCNGOARYMKC6VOBRZIZFVRLD","target":"record","payload":{"canonical_record":{"source":{"id":"1110.4176","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math-ph","submitted_at":"2011-10-19T04:16:23Z","cross_cats_sorted":["math.CO","math.MP","math.PR"],"title_canon_sha256":"d0ec9a5f8d631fecb27bf741405f144fee0d83e42aa8f344f2edc3958c465448","abstract_canon_sha256":"a6a3c7c992506929460af223617b01869f8ed5526ad191fb486065a34f66e9ff"},"schema_version":"1.0"},"canonical_sha256":"1a982699c08e18a17aae0c728c96b158e7172902453a56485f702c5b67a46e69","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:41.995149Z","signature_b64":"GG9bTXUx7fr4ByuS7622x/SNGHl9BLAWAY/4AzmrzAEuWUG0VmIHmz9Snu/IAV9kUvxR4lJMkpXIWHwiGi1WAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1a982699c08e18a17aae0c728c96b158e7172902453a56485f702c5b67a46e69","last_reissued_at":"2026-05-18T00:18:41.994423Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:41.994423Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.4176","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":"2026-05-18T00:18:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xLAD5ZL+L3mDwdT1mzrEdhqUCCEohTQJ9yjZQFAW9wrs0Vlprd/JFw4t29DdKfV0+ltBNx0GUSZlel7eU1aWCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T19:18:40.829134Z"},"content_sha256":"68d6a9214c55e00b3a460e526e4e42e8c614e2802f0cf112e9caf83bfaba5f25","schema_version":"1.0","event_id":"sha256:68d6a9214c55e00b3a460e526e4e42e8c614e2802f0cf112e9caf83bfaba5f25"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:DKMCNGOARYMKC6VOBRZIZFVRLD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Elliptically Distributed Lozenge Tilings of a Hexagon","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.CO","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Dan Betea","submitted_at":"2011-10-19T04:16:23Z","abstract_excerpt":"We present a detailed study of a four parameter family of elliptic weights on tilings of a hexagon introduced by Borodin, Gorin and Rains, generalizing some of their results. In the process, we connect the combinatorics of the model with the theory of elliptic special functions. Using canonical coordinates for the hexagon we show how the $n$-point distribution function and transitional probabilities connect to the theory of $BC_n$-symmetric multivariate elliptic special functions and of elliptic difference operators introduced by Rains. In particular, the difference operators intrinsically cap"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.4176","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":"2026-05-18T00:18:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uDCelYgqUedB2jW06XWFkn70YwDqKttjzw3mZ4wGkmXpp965GQS/4zP2FFIvOe3HH/002ySle8kWnUwczECsAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T19:18:40.829505Z"},"content_sha256":"eabb186dc9a4badd81769cb779ac6e6d57d3970401bb5c89ce5748b804db161b","schema_version":"1.0","event_id":"sha256:eabb186dc9a4badd81769cb779ac6e6d57d3970401bb5c89ce5748b804db161b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DKMCNGOARYMKC6VOBRZIZFVRLD/bundle.json","state_url":"https://pith.science/pith/DKMCNGOARYMKC6VOBRZIZFVRLD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DKMCNGOARYMKC6VOBRZIZFVRLD/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":"2026-06-30T19:18:40Z","links":{"resolver":"https://pith.science/pith/DKMCNGOARYMKC6VOBRZIZFVRLD","bundle":"https://pith.science/pith/DKMCNGOARYMKC6VOBRZIZFVRLD/bundle.json","state":"https://pith.science/pith/DKMCNGOARYMKC6VOBRZIZFVRLD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DKMCNGOARYMKC6VOBRZIZFVRLD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:DKMCNGOARYMKC6VOBRZIZFVRLD","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":"a6a3c7c992506929460af223617b01869f8ed5526ad191fb486065a34f66e9ff","cross_cats_sorted":["math.CO","math.MP","math.PR"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math-ph","submitted_at":"2011-10-19T04:16:23Z","title_canon_sha256":"d0ec9a5f8d631fecb27bf741405f144fee0d83e42aa8f344f2edc3958c465448"},"schema_version":"1.0","source":{"id":"1110.4176","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.4176","created_at":"2026-05-18T00:18:41Z"},{"alias_kind":"arxiv_version","alias_value":"1110.4176v3","created_at":"2026-05-18T00:18:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.4176","created_at":"2026-05-18T00:18:41Z"},{"alias_kind":"pith_short_12","alias_value":"DKMCNGOARYMK","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"DKMCNGOARYMKC6VO","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"DKMCNGOA","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:eabb186dc9a4badd81769cb779ac6e6d57d3970401bb5c89ce5748b804db161b","target":"graph","created_at":"2026-05-18T00:18:41Z","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 present a detailed study of a four parameter family of elliptic weights on tilings of a hexagon introduced by Borodin, Gorin and Rains, generalizing some of their results. In the process, we connect the combinatorics of the model with the theory of elliptic special functions. Using canonical coordinates for the hexagon we show how the $n$-point distribution function and transitional probabilities connect to the theory of $BC_n$-symmetric multivariate elliptic special functions and of elliptic difference operators introduced by Rains. In particular, the difference operators intrinsically cap","authors_text":"Dan Betea","cross_cats":["math.CO","math.MP","math.PR"],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math-ph","submitted_at":"2011-10-19T04:16:23Z","title":"Elliptically Distributed Lozenge Tilings of a Hexagon"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.4176","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":"sha256:68d6a9214c55e00b3a460e526e4e42e8c614e2802f0cf112e9caf83bfaba5f25","target":"record","created_at":"2026-05-18T00:18:41Z","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":"a6a3c7c992506929460af223617b01869f8ed5526ad191fb486065a34f66e9ff","cross_cats_sorted":["math.CO","math.MP","math.PR"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math-ph","submitted_at":"2011-10-19T04:16:23Z","title_canon_sha256":"d0ec9a5f8d631fecb27bf741405f144fee0d83e42aa8f344f2edc3958c465448"},"schema_version":"1.0","source":{"id":"1110.4176","kind":"arxiv","version":3}},"canonical_sha256":"1a982699c08e18a17aae0c728c96b158e7172902453a56485f702c5b67a46e69","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1a982699c08e18a17aae0c728c96b158e7172902453a56485f702c5b67a46e69","first_computed_at":"2026-05-18T00:18:41.994423Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:41.994423Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GG9bTXUx7fr4ByuS7622x/SNGHl9BLAWAY/4AzmrzAEuWUG0VmIHmz9Snu/IAV9kUvxR4lJMkpXIWHwiGi1WAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:41.995149Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.4176","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:68d6a9214c55e00b3a460e526e4e42e8c614e2802f0cf112e9caf83bfaba5f25","sha256:eabb186dc9a4badd81769cb779ac6e6d57d3970401bb5c89ce5748b804db161b"],"state_sha256":"0e83c91870cb32f3506aec040466548f0ee5a7ed32e55dce988f1b485db42560"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8JCtDXJTKPN3pKb9bx1RgKFZ1+SyOr5uuFEESoM8OXfwXsSBfZYyZfZRrFSyk+PfCZAIutkBnftVHXvhKLvGDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T19:18:40.831504Z","bundle_sha256":"fe69a76d1538ecef16207bde2a16a38226fca68bc9dbd4ff8c014fcddd8ee0af"}}