{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:KY7NIL2CVG25ROJJQNCVLGQNTA","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":"9671f4c8d4e218ed12c23cfe1f91baa250ba3fe8eb691f571c3783ec729027f6","cross_cats_sorted":["math.CO","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-04-24T20:30:00Z","title_canon_sha256":"4d637a073d42e9570eb7cd9eab1d82fbbcf5764816f1ea03164d245bd8b10378"},"schema_version":"1.0","source":{"id":"1704.07454","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.07454","created_at":"2026-05-18T00:40:28Z"},{"alias_kind":"arxiv_version","alias_value":"1704.07454v2","created_at":"2026-05-18T00:40:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.07454","created_at":"2026-05-18T00:40:28Z"},{"alias_kind":"pith_short_12","alias_value":"KY7NIL2CVG25","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"KY7NIL2CVG25ROJJ","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"KY7NIL2C","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:73a73b81e109eaf2411ebb0bd31a2292b212be450f5f6554543609b6c34d3fdd","target":"graph","created_at":"2026-05-18T00:40:28Z","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":"In this paper, we describe a general setting for dimer models on cylinders over Dynkin diagrams which in type A reduces to the well studied case of dimer models on a disc. We prove that all Berenstein--Fomin--Zelevinsky quivers for Schubert cells in a symmetric Kac--Moody algebra give rise to dimer models on the cylinder over the corresponding Dynkin diagram. We also give an independent proof of a result of Buan, Iyama, Reiten and Smith that the corresponding superpotentials are rigid using the dimer model structure of the quivers.","authors_text":"Maitreyee C. Kulkarni","cross_cats":["math.CO","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-04-24T20:30:00Z","title":"Dimer models on cylinders over Dynkin diagrams and cluster algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.07454","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":"sha256:4991e62bf4f027954871b7b2d5abf84ae841883658d70ad0d3939440b0f03aae","target":"record","created_at":"2026-05-18T00:40:28Z","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":"9671f4c8d4e218ed12c23cfe1f91baa250ba3fe8eb691f571c3783ec729027f6","cross_cats_sorted":["math.CO","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-04-24T20:30:00Z","title_canon_sha256":"4d637a073d42e9570eb7cd9eab1d82fbbcf5764816f1ea03164d245bd8b10378"},"schema_version":"1.0","source":{"id":"1704.07454","kind":"arxiv","version":2}},"canonical_sha256":"563ed42f42a9b5d8b9298345559a0d9805abc975371f4773cc13e3e044ce6397","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"563ed42f42a9b5d8b9298345559a0d9805abc975371f4773cc13e3e044ce6397","first_computed_at":"2026-05-18T00:40:28.429132Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:28.429132Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qGilhiw4yXnJfe+XqB8ZytLlAk2FaK8JTVLXdcLXEwMFrRHOw62kdiujnfDELBer8/BXKnMxFzv51GkZRLEFBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:28.429839Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.07454","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4991e62bf4f027954871b7b2d5abf84ae841883658d70ad0d3939440b0f03aae","sha256:73a73b81e109eaf2411ebb0bd31a2292b212be450f5f6554543609b6c34d3fdd"],"state_sha256":"269010eb5dc1f0c3ac780e9525106e764d8b6304ad72b35376361a8e6d50b669"}