{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:ABJ4XJY2ZOXVWTAS7LH2O6KMYP","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":"8386bf3f579c8cb15257e85b19726d23ce527599d3e9523576e502f911e8c9f7","cross_cats_sorted":["cond-mat.mes-hall"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2009-09-26T18:17:45Z","title_canon_sha256":"dae0fe2669675c76a5797a1e2a01ad24ddc35a55bb15d991ee2eca2dea483b11"},"schema_version":"1.0","source":{"id":"0909.4882","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.4882","created_at":"2026-05-18T03:54:06Z"},{"alias_kind":"arxiv_version","alias_value":"0909.4882v1","created_at":"2026-05-18T03:54:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.4882","created_at":"2026-05-18T03:54:06Z"},{"alias_kind":"pith_short_12","alias_value":"ABJ4XJY2ZOXV","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"ABJ4XJY2ZOXVWTAS","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"ABJ4XJY2","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:9e3d1b50421724b01afa798c8a57b997962d5720f61a5ce37a0854ca6a6516cb","target":"graph","created_at":"2026-05-18T03:54:06Z","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 $U(1) \\times U(1) \\rtimes Z_2$ Chern-Simons theory with integral coupling constants (k,l) and its relation to certain non-Abelian fractional quantum Hall (FQH) states. For the $U(1) \\times U(1) \\rtimes Z_2$ Chern-Simons theory, we show how to compute the dimension of its Hilbert space on genus g surfaces and how this yields the quantum dimensions of topologically distinct excitations. We find that Z_2 vortices in the $U(1) \\times U(1)\\rtimes Z_2$ Chern-Simons theory carry non-Abelian statistics and we show how to compute the dimension of the Hilbert space in the presence of n pairs of","authors_text":"Maissam Barkeshli, Xiao-Gang Wen","cross_cats":["cond-mat.mes-hall"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2009-09-26T18:17:45Z","title":"$U(1) \\times U(1) \\rtimes Z_2$ Chern-Simons Theory and Z_4 Parafermion Fractional Quantum Hall States"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.4882","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:f88228ca2ec43656a76497519ea876f9ea2d61a00408c2c75238f6fd3a3a4aac","target":"record","created_at":"2026-05-18T03:54:06Z","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":"8386bf3f579c8cb15257e85b19726d23ce527599d3e9523576e502f911e8c9f7","cross_cats_sorted":["cond-mat.mes-hall"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2009-09-26T18:17:45Z","title_canon_sha256":"dae0fe2669675c76a5797a1e2a01ad24ddc35a55bb15d991ee2eca2dea483b11"},"schema_version":"1.0","source":{"id":"0909.4882","kind":"arxiv","version":1}},"canonical_sha256":"0053cba71acbaf5b4c12facfa7794cc3c313b55cc1ba1b4cf002df5e61dd368e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0053cba71acbaf5b4c12facfa7794cc3c313b55cc1ba1b4cf002df5e61dd368e","first_computed_at":"2026-05-18T03:54:06.358363Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:54:06.358363Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8Vml3P0qH1IuDy29O2TXeOYb7YxLGlVf5eh+/mcj/3xb1FwPNRjbJS1D+JQYGDl/jq6zKoxHN+CR8YhxQZckBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:54:06.359022Z","signed_message":"canonical_sha256_bytes"},"source_id":"0909.4882","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f88228ca2ec43656a76497519ea876f9ea2d61a00408c2c75238f6fd3a3a4aac","sha256:9e3d1b50421724b01afa798c8a57b997962d5720f61a5ce37a0854ca6a6516cb"],"state_sha256":"e5bfd1b628fe57b747fd8b1d62138b3ad8221372554db6ae5d45c1a48e79c72c"}