{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:WNLMLSBOKNLTUSUY7PRVHK5MYX","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":"44e2f4c61e0fd2ad2f889f0e81c91ba85775f5528e24704d5f940c4220cb9f34","cross_cats_sorted":["cond-mat.str-el","hep-th","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.other","submitted_at":"2012-07-26T05:03:11Z","title_canon_sha256":"2d010c5cb8fde8340d47690e372fe511f0dc7ab829c126f4e8cb9cc21f8ed6e4"},"schema_version":"1.0","source":{"id":"1207.6169","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.6169","created_at":"2026-05-18T03:38:04Z"},{"alias_kind":"arxiv_version","alias_value":"1207.6169v2","created_at":"2026-05-18T03:38:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.6169","created_at":"2026-05-18T03:38:04Z"},{"alias_kind":"pith_short_12","alias_value":"WNLMLSBOKNLT","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"WNLMLSBOKNLTUSUY","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"WNLMLSBO","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:021d9766c3358b5911ae76ba85565aed7df6a21c33cd0e07973b1383da225123","target":"graph","created_at":"2026-05-18T03:38:04Z","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 study the Levin-Wen string-net model with a $Z_N$ type fusion algebra. Solutions of the local constraints of this model correspond to $Z_N$ gauge theory and double Chern-simons theories with quantum groups. For the first time, we explicitly construct a spin-$(N-1)/2$ model with $Z_N$ gauge symmetry on a triangular lattice as an exact dual model of the string-net model with a $Z_N$ type fusion algebra on a honeycomb lattice. This exact duality exists only when the spins are coupled to a $Z_N$ gauge field living on the links of the triangular lattice. The ungauged $Z_N$ lattice spin models ar","authors_text":"Ling-Yan Hung, Yidun Wan","cross_cats":["cond-mat.str-el","hep-th","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.other","submitted_at":"2012-07-26T05:03:11Z","title":"String-Net Models with $Z_N$ Fusion Algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.6169","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":"sha256:332090d38be67075334520b09dbb49e057c8ca717ed6f8a803418c26e2925693","target":"record","created_at":"2026-05-18T03:38:04Z","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":"44e2f4c61e0fd2ad2f889f0e81c91ba85775f5528e24704d5f940c4220cb9f34","cross_cats_sorted":["cond-mat.str-el","hep-th","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.other","submitted_at":"2012-07-26T05:03:11Z","title_canon_sha256":"2d010c5cb8fde8340d47690e372fe511f0dc7ab829c126f4e8cb9cc21f8ed6e4"},"schema_version":"1.0","source":{"id":"1207.6169","kind":"arxiv","version":2}},"canonical_sha256":"b356c5c82e53573a4a98fbe353abacc5ee591426986a17a9c2e0ebc36b97f4fc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b356c5c82e53573a4a98fbe353abacc5ee591426986a17a9c2e0ebc36b97f4fc","first_computed_at":"2026-05-18T03:38:04.894957Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:04.894957Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BjhbeFCEnWpLaB49mT/OgBYSmPQCThOXWpGjl+v3/jbnhJO75muBdXIoGxh/nlCr8tAQOtrTSrtPB2GkZ8shDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:04.895447Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.6169","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:332090d38be67075334520b09dbb49e057c8ca717ed6f8a803418c26e2925693","sha256:021d9766c3358b5911ae76ba85565aed7df6a21c33cd0e07973b1383da225123"],"state_sha256":"d29f98d2a7b59f76a496090bbdef1a750495be632f2a9cb18cda8e70db31daaf"}