{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:PZ2NQRSU7JR63SAAWPC7ZUMSVR","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":"640f5d152e41e0f45c4945ec78421322a7bfa2b6afcc281c24213fbfbfef3163","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-12-25T04:31:08Z","title_canon_sha256":"35c72743ed64e8c6c8e1b14705996f860c5865d7a7490dfc2b0f7de5d6d45498"},"schema_version":"1.0","source":{"id":"1012.5449","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.5449","created_at":"2026-05-18T04:32:23Z"},{"alias_kind":"arxiv_version","alias_value":"1012.5449v1","created_at":"2026-05-18T04:32:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.5449","created_at":"2026-05-18T04:32:23Z"},{"alias_kind":"pith_short_12","alias_value":"PZ2NQRSU7JR6","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"PZ2NQRSU7JR63SAA","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"PZ2NQRSU","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:ab04fa76712521aa58cdfe6d4d49bfea5ee0b2b09d7b108d9ea08fd3725e692b","target":"graph","created_at":"2026-05-18T04:32:23Z","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 show that for a non-degenerate dimer model, both the first consistency condition of Mozgovoy and Reineke and the properly-orderedness condition of Gulotta are equivalent to a condition on zigzag paths, which goes back to Hanany and Vegh. The last condition is used in arXiv:0905.0059 to study the behavior of a dimer model under the operation of removing a vertex from the lattice polygon and taking the convex hull of the rest.","authors_text":"Akira Ishii, Kazushi Ueda","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-12-25T04:31:08Z","title":"A note on consistency conditions on dimer models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.5449","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":"sha256:98fd2025e4ef2b1e43adcbbd78a3b81b579901947e949736d9c64b17cbcc9842","target":"record","created_at":"2026-05-18T04:32:23Z","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":"640f5d152e41e0f45c4945ec78421322a7bfa2b6afcc281c24213fbfbfef3163","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-12-25T04:31:08Z","title_canon_sha256":"35c72743ed64e8c6c8e1b14705996f860c5865d7a7490dfc2b0f7de5d6d45498"},"schema_version":"1.0","source":{"id":"1012.5449","kind":"arxiv","version":1}},"canonical_sha256":"7e74d84654fa63edc800b3c5fcd192ac619545c312f7b55d953bd1d26453c69d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7e74d84654fa63edc800b3c5fcd192ac619545c312f7b55d953bd1d26453c69d","first_computed_at":"2026-05-18T04:32:23.453009Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:32:23.453009Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"neSymMDkCxBvNfKkoXUew+NvVrCK1CYErC9yr5JBygolkGR81ckEAPwgiAD6PKP5lFdGYjr7B2PpX+8Y5FBJCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:32:23.453741Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.5449","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:98fd2025e4ef2b1e43adcbbd78a3b81b579901947e949736d9c64b17cbcc9842","sha256:ab04fa76712521aa58cdfe6d4d49bfea5ee0b2b09d7b108d9ea08fd3725e692b"],"state_sha256":"07cc12e1ccfa2170224fbde34e4eaf21299383adbcaefa666b7c345c166ff88c"}