{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:6CDXDB7NCI34QYFNJAUFQLBHRU","short_pith_number":"pith:6CDXDB7N","canonical_record":{"source":{"id":"1712.08396","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-12-22T11:24:04Z","cross_cats_sorted":["math.MP","math.PR"],"title_canon_sha256":"e9466da2e98cc63c16703dd6d19bd193cef13dc52c8a965cf28dfd5f3261274a","abstract_canon_sha256":"eeac7a27435536ad787b45f5324325e1a4f6561b5a2cec7abf727dc4ff58ed37"},"schema_version":"1.0"},"canonical_sha256":"f0877187ed1237c860ad4828582c278d1bb8dc2086da69c32168e2e6c2d68cd5","source":{"kind":"arxiv","id":"1712.08396","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.08396","created_at":"2026-05-18T00:27:23Z"},{"alias_kind":"arxiv_version","alias_value":"1712.08396v1","created_at":"2026-05-18T00:27:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.08396","created_at":"2026-05-18T00:27:23Z"},{"alias_kind":"pith_short_12","alias_value":"6CDXDB7NCI34","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6CDXDB7NCI34QYFN","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6CDXDB7N","created_at":"2026-05-18T12:31:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:6CDXDB7NCI34QYFNJAUFQLBHRU","target":"record","payload":{"canonical_record":{"source":{"id":"1712.08396","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-12-22T11:24:04Z","cross_cats_sorted":["math.MP","math.PR"],"title_canon_sha256":"e9466da2e98cc63c16703dd6d19bd193cef13dc52c8a965cf28dfd5f3261274a","abstract_canon_sha256":"eeac7a27435536ad787b45f5324325e1a4f6561b5a2cec7abf727dc4ff58ed37"},"schema_version":"1.0"},"canonical_sha256":"f0877187ed1237c860ad4828582c278d1bb8dc2086da69c32168e2e6c2d68cd5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:23.582670Z","signature_b64":"OH/jTmlMjbEuQisZBo5PWoJL6iQ381iEPkGIQto9uIWUaTJi3HIo4KSq4NM/Ncqqi2DLg5JVvLBnP5WrBp4GAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f0877187ed1237c860ad4828582c278d1bb8dc2086da69c32168e2e6c2d68cd5","last_reissued_at":"2026-05-18T00:27:23.582095Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:23.582095Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.08396","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:27:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gMPJpQ860GgnwBTLhyodHVZGANWEplNuit8wdxTvWubuBx60c/h/KgdYpMzxlpae4YLC+6VCVc0U0gzpvGlKAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T16:38:26.217455Z"},"content_sha256":"f18cda1f1cdee1acb626fb155f75767df2b053548df75fef7f28fad57c37c77d","schema_version":"1.0","event_id":"sha256:f18cda1f1cdee1acb626fb155f75767df2b053548df75fef7f28fad57c37c77d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:6CDXDB7NCI34QYFNJAUFQLBHRU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Limit shapes for the dimer model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Nikolai Kuchumov","submitted_at":"2017-12-22T11:24:04Z","abstract_excerpt":"We prove the existence of a limit shape for the dimer model on planar periodic bipartite graphs with an arbitrary fundamental domain and arbitrary periodic weights. This proof is based on a variational principle that uses the locality of the model and the compactness of the space of states."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.08396","kind":"arxiv","version":1},"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":"2026-05-18T00:27:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TN5n4WbtzvWAPQqv7ZFRQ1VeqIWD3yD+yCq0vY739kcUgrGD76K3S+DV5t92/p2C/lqxEwpipxR/Yv8VTCJoAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T16:38:26.217956Z"},"content_sha256":"cc2cfae74e5d251736b124d4b58d1d417863fc407a23a6183449513298bbdbd6","schema_version":"1.0","event_id":"sha256:cc2cfae74e5d251736b124d4b58d1d417863fc407a23a6183449513298bbdbd6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6CDXDB7NCI34QYFNJAUFQLBHRU/bundle.json","state_url":"https://pith.science/pith/6CDXDB7NCI34QYFNJAUFQLBHRU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6CDXDB7NCI34QYFNJAUFQLBHRU/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":"2026-08-09T16:38:26Z","links":{"resolver":"https://pith.science/pith/6CDXDB7NCI34QYFNJAUFQLBHRU","bundle":"https://pith.science/pith/6CDXDB7NCI34QYFNJAUFQLBHRU/bundle.json","state":"https://pith.science/pith/6CDXDB7NCI34QYFNJAUFQLBHRU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6CDXDB7NCI34QYFNJAUFQLBHRU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:6CDXDB7NCI34QYFNJAUFQLBHRU","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":"eeac7a27435536ad787b45f5324325e1a4f6561b5a2cec7abf727dc4ff58ed37","cross_cats_sorted":["math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-12-22T11:24:04Z","title_canon_sha256":"e9466da2e98cc63c16703dd6d19bd193cef13dc52c8a965cf28dfd5f3261274a"},"schema_version":"1.0","source":{"id":"1712.08396","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.08396","created_at":"2026-05-18T00:27:23Z"},{"alias_kind":"arxiv_version","alias_value":"1712.08396v1","created_at":"2026-05-18T00:27:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.08396","created_at":"2026-05-18T00:27:23Z"},{"alias_kind":"pith_short_12","alias_value":"6CDXDB7NCI34","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6CDXDB7NCI34QYFN","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6CDXDB7N","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:cc2cfae74e5d251736b124d4b58d1d417863fc407a23a6183449513298bbdbd6","target":"graph","created_at":"2026-05-18T00:27:23Z","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 prove the existence of a limit shape for the dimer model on planar periodic bipartite graphs with an arbitrary fundamental domain and arbitrary periodic weights. This proof is based on a variational principle that uses the locality of the model and the compactness of the space of states.","authors_text":"Nikolai Kuchumov","cross_cats":["math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-12-22T11:24:04Z","title":"Limit shapes for the dimer model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.08396","kind":"arxiv","version":1},"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:f18cda1f1cdee1acb626fb155f75767df2b053548df75fef7f28fad57c37c77d","target":"record","created_at":"2026-05-18T00:27:23Z","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":"eeac7a27435536ad787b45f5324325e1a4f6561b5a2cec7abf727dc4ff58ed37","cross_cats_sorted":["math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-12-22T11:24:04Z","title_canon_sha256":"e9466da2e98cc63c16703dd6d19bd193cef13dc52c8a965cf28dfd5f3261274a"},"schema_version":"1.0","source":{"id":"1712.08396","kind":"arxiv","version":1}},"canonical_sha256":"f0877187ed1237c860ad4828582c278d1bb8dc2086da69c32168e2e6c2d68cd5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f0877187ed1237c860ad4828582c278d1bb8dc2086da69c32168e2e6c2d68cd5","first_computed_at":"2026-05-18T00:27:23.582095Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:27:23.582095Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OH/jTmlMjbEuQisZBo5PWoJL6iQ381iEPkGIQto9uIWUaTJi3HIo4KSq4NM/Ncqqi2DLg5JVvLBnP5WrBp4GAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:27:23.582670Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.08396","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f18cda1f1cdee1acb626fb155f75767df2b053548df75fef7f28fad57c37c77d","sha256:cc2cfae74e5d251736b124d4b58d1d417863fc407a23a6183449513298bbdbd6"],"state_sha256":"8b1fc5aafbc19bea194f14c78d539f80b2eaaa103738c953da6402a2ed058055"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TTUNTmHCN8gnPR68P2SOPU9z0OGHrEGH+CTp5IlBjPynIvzzT/kYV9A8O4WYwdyEhbL1NtJrEzGt5a/XxZyfDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T16:38:26.221485Z","bundle_sha256":"21a0f7c346b0fac93fef7029d47c896c927c02f92925d8094c7df5dc7b70cfd4"}}