{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:RKAVOOCMEXH73NWSNWFGFXI2AC","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":"b5dd49b9a32ec1e9a31e66e7c7b56ace568ed3aedc2a7ac911d49a2e8365bafc","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-lat","submitted_at":"2016-04-01T16:24:59Z","title_canon_sha256":"57dd2d45ab86ea8583c70858339938118776aa9450478b1b20d710a12607f129"},"schema_version":"1.0","source":{"id":"1604.00315","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.00315","created_at":"2026-05-18T00:57:44Z"},{"alias_kind":"arxiv_version","alias_value":"1604.00315v2","created_at":"2026-05-18T00:57:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.00315","created_at":"2026-05-18T00:57:44Z"},{"alias_kind":"pith_short_12","alias_value":"RKAVOOCMEXH7","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RKAVOOCMEXH73NWS","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RKAVOOCM","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:ee8cf939411327121c98b5293dd514bdd5b0d63b7c922674987f0ad8be56d1dd","target":"graph","created_at":"2026-05-18T00:57:44Z","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":"The Wegner $Z_2$ gauge theory-$Z_2$ Ising spin model duality in $(2+1)$ dimensions is revisited and derived through a series of canonical transformations. The Kramers-Wannier duality is similarly obtained. The Wegner $Z_2$ gauge-spin duality is directly generalized to SU(N) lattice gauge theory in $(2+1)$ dimensions to obtain the SU(N) spin model in terms of the SU(N) magnetic fields and their conjugate SU(N) electric scalar potentials. The exact and complete solutions of the $Z_2, U(1), SU(N)$ Gauss law constraints in terms of the corresponding spin or dual potential operators are given. The ","authors_text":"Manu Mathur, T. P. Sreeraj","cross_cats":["hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-lat","submitted_at":"2016-04-01T16:24:59Z","title":"Lattice Gauge Theories and Spin Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.00315","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:b7661c9408b19382800520fa26fb306c2ebd26308a6ce68ad2b0da011ccfaf59","target":"record","created_at":"2026-05-18T00:57:44Z","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":"b5dd49b9a32ec1e9a31e66e7c7b56ace568ed3aedc2a7ac911d49a2e8365bafc","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-lat","submitted_at":"2016-04-01T16:24:59Z","title_canon_sha256":"57dd2d45ab86ea8583c70858339938118776aa9450478b1b20d710a12607f129"},"schema_version":"1.0","source":{"id":"1604.00315","kind":"arxiv","version":2}},"canonical_sha256":"8a8157384c25cffdb6d26d8a62dd1a009318696c9e9f9beefdc3a6ad001994b3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8a8157384c25cffdb6d26d8a62dd1a009318696c9e9f9beefdc3a6ad001994b3","first_computed_at":"2026-05-18T00:57:44.081368Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:57:44.081368Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CyQLMxCzaZojZWw9H1G3N6gUyKS+F15L/r35j5fS+uK+x8naTDCs9tpqKq8Z0IXZ1g30/LZdRtvrCO4Hi8eTAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:57:44.082014Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.00315","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b7661c9408b19382800520fa26fb306c2ebd26308a6ce68ad2b0da011ccfaf59","sha256:ee8cf939411327121c98b5293dd514bdd5b0d63b7c922674987f0ad8be56d1dd"],"state_sha256":"0ae7f94ddcde760fe4a4bb1bd3fcaf4e55f1dbd7e5d8c86e1915c4c3c0dd88ff"}