{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:AMLB6UQVRCHAIOVHZXYQKOOFDW","short_pith_number":"pith:AMLB6UQV","schema_version":"1.0","canonical_sha256":"03161f5215888e043aa7cdf10539c51db8ea04546474d8932f61521e0e4bab3c","source":{"kind":"arxiv","id":"1012.2417","version":1},"attestation_state":"computed","paper":{"title":"Phase transitions in Z_N gauge theory and twisted Z_N topological phases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.str-el","authors_text":"Maissam Barkeshli, Xiao-Gang Wen","submitted_at":"2010-12-11T00:25:53Z","abstract_excerpt":"We find a series of non-Abelian topological phases that are separated from the deconfined phase of Z_N gauge theory by a continuous quantum phase transition. These non-Abelian states, which we refer to as the \"twisted\" Z_N states, are described by a recently studied $U(1) \\times U(1) \\rtimes Z_2$ Chern-Simons (CS) field theory. The $U(1) \\times U(1) \\rtimes Z_2$ CS theory provides a way of gauging the global Z_2 electric-magnetic symmetry of the Abelian Z_N phases, yielding the twisted Z_N states. We introduce a parton construction to describe the Abelian Z_N phases in terms of integer quantum"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1012.2417","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2010-12-11T00:25:53Z","cross_cats_sorted":[],"title_canon_sha256":"1e10be399735eb671556e94f157c3fb6a4a490cc41124d77d0bcb32836d5de11","abstract_canon_sha256":"2936722022fa1cd8195683b9bde38df97dbf6a44d39ea8c5a1b602ea69cd93a3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:48:35.683352Z","signature_b64":"qu2IGC82E+33TsNNBkxktrCfP7cPJbQHZWmPd9UFzDYeECMHcRne6ABwo8KlfpLDKNd3J9+DdXX/GSbDC92/Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"03161f5215888e043aa7cdf10539c51db8ea04546474d8932f61521e0e4bab3c","last_reissued_at":"2026-05-18T03:48:35.682922Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:48:35.682922Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Phase transitions in Z_N gauge theory and twisted Z_N topological phases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.str-el","authors_text":"Maissam Barkeshli, Xiao-Gang Wen","submitted_at":"2010-12-11T00:25:53Z","abstract_excerpt":"We find a series of non-Abelian topological phases that are separated from the deconfined phase of Z_N gauge theory by a continuous quantum phase transition. These non-Abelian states, which we refer to as the \"twisted\" Z_N states, are described by a recently studied $U(1) \\times U(1) \\rtimes Z_2$ Chern-Simons (CS) field theory. The $U(1) \\times U(1) \\rtimes Z_2$ CS theory provides a way of gauging the global Z_2 electric-magnetic symmetry of the Abelian Z_N phases, yielding the twisted Z_N states. We introduce a parton construction to describe the Abelian Z_N phases in terms of integer quantum"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.2417","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1012.2417","created_at":"2026-05-18T03:48:35.682984+00:00"},{"alias_kind":"arxiv_version","alias_value":"1012.2417v1","created_at":"2026-05-18T03:48:35.682984+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.2417","created_at":"2026-05-18T03:48:35.682984+00:00"},{"alias_kind":"pith_short_12","alias_value":"AMLB6UQVRCHA","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_16","alias_value":"AMLB6UQVRCHAIOVH","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_8","alias_value":"AMLB6UQV","created_at":"2026-05-18T12:26:05.355336+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AMLB6UQVRCHAIOVHZXYQKOOFDW","json":"https://pith.science/pith/AMLB6UQVRCHAIOVHZXYQKOOFDW.json","graph_json":"https://pith.science/api/pith-number/AMLB6UQVRCHAIOVHZXYQKOOFDW/graph.json","events_json":"https://pith.science/api/pith-number/AMLB6UQVRCHAIOVHZXYQKOOFDW/events.json","paper":"https://pith.science/paper/AMLB6UQV"},"agent_actions":{"view_html":"https://pith.science/pith/AMLB6UQVRCHAIOVHZXYQKOOFDW","download_json":"https://pith.science/pith/AMLB6UQVRCHAIOVHZXYQKOOFDW.json","view_paper":"https://pith.science/paper/AMLB6UQV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1012.2417&json=true","fetch_graph":"https://pith.science/api/pith-number/AMLB6UQVRCHAIOVHZXYQKOOFDW/graph.json","fetch_events":"https://pith.science/api/pith-number/AMLB6UQVRCHAIOVHZXYQKOOFDW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AMLB6UQVRCHAIOVHZXYQKOOFDW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AMLB6UQVRCHAIOVHZXYQKOOFDW/action/storage_attestation","attest_author":"https://pith.science/pith/AMLB6UQVRCHAIOVHZXYQKOOFDW/action/author_attestation","sign_citation":"https://pith.science/pith/AMLB6UQVRCHAIOVHZXYQKOOFDW/action/citation_signature","submit_replication":"https://pith.science/pith/AMLB6UQVRCHAIOVHZXYQKOOFDW/action/replication_record"}},"created_at":"2026-05-18T03:48:35.682984+00:00","updated_at":"2026-05-18T03:48:35.682984+00:00"}