{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:ZEIAI3VQPOHQ7OBOPV26INYAXI","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":"20e8bfa359a4ecdc309a481b0041a2c95ee9220c51a2e334948c6d2e6456060d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-09-07T00:24:16Z","title_canon_sha256":"dec4bf07dce21599abb3cab208d6a28e601ba31e5847e2ed241f2c6afd73247a"},"schema_version":"1.0","source":{"id":"1009.1182","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.1182","created_at":"2026-05-18T04:34:47Z"},{"alias_kind":"arxiv_version","alias_value":"1009.1182v1","created_at":"2026-05-18T04:34:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.1182","created_at":"2026-05-18T04:34:47Z"},{"alias_kind":"pith_short_12","alias_value":"ZEIAI3VQPOHQ","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"ZEIAI3VQPOHQ7OBO","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"ZEIAI3VQ","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:93b5fea88f76e05679c322b92a19ab84f3555838316b27b79648a14f4d5eb0e6","target":"graph","created_at":"2026-05-18T04:34:47Z","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 exact results on the partition function of the $q$-state Potts model on various families of graphs $G$ in a generalized external magnetic field that favors or disfavors spin values in a subset $I_s = \\{1,...,s\\}$ of the total set of possible spin values, $Z(G,q,s,v,w)$, where $v$ and $w$ are temperature- and field-dependent Boltzmann variables. We remark on differences in thermodynamic behavior between our model with a generalized external magnetic field and the Potts model with a conventional magnetic field that favors or disfavors a single spin value. Exact results are also given ","authors_text":"Robert Shrock, Yan Xu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-09-07T00:24:16Z","title":"Exact Results on Potts Model Partition Functions in a Generalized External Field and Weighted-Set Graph Colorings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.1182","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":"sha256:844f01296beae475e0fbf59f8ead3fd86be4ae5918d6c4a96b29fd9abc7da41a","target":"record","created_at":"2026-05-18T04:34:47Z","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":"20e8bfa359a4ecdc309a481b0041a2c95ee9220c51a2e334948c6d2e6456060d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-09-07T00:24:16Z","title_canon_sha256":"dec4bf07dce21599abb3cab208d6a28e601ba31e5847e2ed241f2c6afd73247a"},"schema_version":"1.0","source":{"id":"1009.1182","kind":"arxiv","version":1}},"canonical_sha256":"c910046eb07b8f0fb82e7d75e43700ba26e5717bd7cf5bb952cb2c04e67855af","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c910046eb07b8f0fb82e7d75e43700ba26e5717bd7cf5bb952cb2c04e67855af","first_computed_at":"2026-05-18T04:34:47.853932Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:34:47.853932Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XixDwUTBj6n/FFMcFVspwsLOttAvw90+A+iZhFwIbSHSsKqxXJ/sAvm0Zs3Ym3N1+vigQOenDET6otKxi0ZcAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:34:47.854402Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.1182","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:844f01296beae475e0fbf59f8ead3fd86be4ae5918d6c4a96b29fd9abc7da41a","sha256:93b5fea88f76e05679c322b92a19ab84f3555838316b27b79648a14f4d5eb0e6"],"state_sha256":"9fb5d0f0777ec62e1ad5612dd8aa5d58feb1be23f618526aa995a4736025b085"}