{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:WUFWF3AUKTV3EJTUDCIVLL4JOO","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":"49164c49d72883ab798e410c833b354ae240d7d244b57bbd0280a7c3dde29bbd","cross_cats_sorted":["math.CO","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-08-02T09:02:06Z","title_canon_sha256":"779b59a4c97ffd8bd399582393e68e7bc08b05d11d52d682809ea3e240dfaa03"},"schema_version":"1.0","source":{"id":"1608.00741","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.00741","created_at":"2026-05-18T00:57:26Z"},{"alias_kind":"arxiv_version","alias_value":"1608.00741v2","created_at":"2026-05-18T00:57:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.00741","created_at":"2026-05-18T00:57:26Z"},{"alias_kind":"pith_short_12","alias_value":"WUFWF3AUKTV3","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"WUFWF3AUKTV3EJTU","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"WUFWF3AU","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:cef799fc22db16f7742daf97a8519ffbc287680c2d97c845ce11c0b264fcd2df","target":"graph","created_at":"2026-05-18T00:57:26Z","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":"Given a weighted graph $G$ embedded in a non-orientable surface $\\Sigma$, one can consider the corresponding weighted graph $\\widetilde{G}$ embedded in the so-called orientation cover $\\widetilde\\Sigma$ of $\\Sigma$. We prove identities relating twisted partition functions of the dimer model on these two graphs. When $\\Sigma$ is the M\\\"obius strip or the Klein bottle, then $\\widetilde\\Sigma$ is the cylinder or the torus, respectively, and under some natural assumptions, these identities imply relations between the genuine dimer partition functions $Z(G)$ and $Z(\\widetilde{G})$. For example, we ","authors_text":"Anh Minh Pham, David Cimasoni","cross_cats":["math.CO","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-08-02T09:02:06Z","title":"Identities between dimer partition functions on different surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.00741","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:d730387f142ed853b643442a0a8aba658b39f0ed748ebd9d8dd77e321da5a23e","target":"record","created_at":"2026-05-18T00:57:26Z","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":"49164c49d72883ab798e410c833b354ae240d7d244b57bbd0280a7c3dde29bbd","cross_cats_sorted":["math.CO","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-08-02T09:02:06Z","title_canon_sha256":"779b59a4c97ffd8bd399582393e68e7bc08b05d11d52d682809ea3e240dfaa03"},"schema_version":"1.0","source":{"id":"1608.00741","kind":"arxiv","version":2}},"canonical_sha256":"b50b62ec1454ebb22674189155af8973a017f442c50e255098e340c4a86028a2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b50b62ec1454ebb22674189155af8973a017f442c50e255098e340c4a86028a2","first_computed_at":"2026-05-18T00:57:26.610953Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:57:26.610953Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pcBEpXwIxFuv+Eg8sUDDQuK2JTo4NqSmFR7LMUZbJ5LpEHztqgnYLmVDqs/G4ZcTiAOZZ7sBFNz+u4TbssWbBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:57:26.611480Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.00741","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d730387f142ed853b643442a0a8aba658b39f0ed748ebd9d8dd77e321da5a23e","sha256:cef799fc22db16f7742daf97a8519ffbc287680c2d97c845ce11c0b264fcd2df"],"state_sha256":"95f75799b9f101dfe5b5b93f621cd0a7567b741479d86619c32d40f38ac857d5"}