{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1999:BBIDNVPMV4PSI2S6R5LVHLB6FE","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":"35e4a71f026f91520c84d6c902b6ff37092c0f18c97f065ac8a7276bbe48ea8b","cross_cats_sorted":["hep-lat","math.CO"],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"1999-08-24T01:50:32Z","title_canon_sha256":"ff88ddc21b346049a11c0a9f9efe42bcdca92e4e08495b8e888ff78ff4217649"},"schema_version":"1.0","source":{"id":"cond-mat/9908323","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/9908323","created_at":"2026-07-04T16:13:11Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/9908323v1","created_at":"2026-07-04T16:13:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/9908323","created_at":"2026-07-04T16:13:11Z"},{"alias_kind":"pith_short_12","alias_value":"BBIDNVPMV4PS","created_at":"2026-07-04T16:13:11Z"},{"alias_kind":"pith_short_16","alias_value":"BBIDNVPMV4PSI2S6","created_at":"2026-07-04T16:13:11Z"},{"alias_kind":"pith_short_8","alias_value":"BBIDNVPM","created_at":"2026-07-04T16:13:11Z"}],"graph_snapshots":[{"event_id":"sha256:083dc661e532618577fa38e3b93658c68a5dd12be7a819f1fe64af76ee7809df","target":"graph","created_at":"2026-07-04T16:13:11Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/cond-mat/9908323/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present exact calculations of the zero-temperature partition function of the $q$-state Potts antiferromagnet (equivalently the chromatic polynomial) for Moebius strips, with width $L_y=2$ or 3, of regular lattices and homeomorphic expansions thereof. These are compared with the corresponding partition functions for strip graphs with (untwisted) periodic longitudinal boundary conditions.","authors_text":"Robert Shrock","cross_cats":["hep-lat","math.CO"],"headline":"","license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"1999-08-24T01:50:32Z","title":"T=0 Partition Functions for Potts Antiferromagnets on Moebius Strips and Effects of Graph Topology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/9908323","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:b0a1fa9d977b464dedf36820dfd06773bc1f9365513dc3ba52c4232abba0a6c0","target":"record","created_at":"2026-07-04T16:13:11Z","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":"35e4a71f026f91520c84d6c902b6ff37092c0f18c97f065ac8a7276bbe48ea8b","cross_cats_sorted":["hep-lat","math.CO"],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"1999-08-24T01:50:32Z","title_canon_sha256":"ff88ddc21b346049a11c0a9f9efe42bcdca92e4e08495b8e888ff78ff4217649"},"schema_version":"1.0","source":{"id":"cond-mat/9908323","kind":"arxiv","version":1}},"canonical_sha256":"085036d5ecaf1f246a5e8f5753ac3e29352a95f4a117c1d1a6ef8d19f2b7097b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"085036d5ecaf1f246a5e8f5753ac3e29352a95f4a117c1d1a6ef8d19f2b7097b","first_computed_at":"2026-07-04T16:13:11.151296Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:13:11.151296Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O8gh/ZMnPK3aLj9WEf6CSAiyliDpdleWh6nWBwWiz1iApi++Gi9bJKI9rnpu1bFEIDaL0gc2rnojsfvhU7nYCA==","signature_status":"signed_v1","signed_at":"2026-07-04T16:13:11.151720Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/9908323","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b0a1fa9d977b464dedf36820dfd06773bc1f9365513dc3ba52c4232abba0a6c0","sha256:083dc661e532618577fa38e3b93658c68a5dd12be7a819f1fe64af76ee7809df"],"state_sha256":"472e1afe439402d6fa808a6b30fdb82b0baacd003149e82daba283fe0a5c59cb"}