{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:47JBO456SAJRDZQ3KOU63LKQNH","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":"09e03dc355cf092dab0269209ef83ef8c1890cf44af4d8d0190bbc7d9645734b","cross_cats_sorted":["cond-mat.str-el","math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2023-09-11T08:25:31Z","title_canon_sha256":"d31eb5ae3e519659231457a7aa2daeab693a7c8ee5a0454bf3a03aa1da087e2e"},"schema_version":"1.0","source":{"id":"2309.05294","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.05294","created_at":"2026-07-05T07:38:30Z"},{"alias_kind":"arxiv_version","alias_value":"2309.05294v3","created_at":"2026-07-05T07:38:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.05294","created_at":"2026-07-05T07:38:30Z"},{"alias_kind":"pith_short_12","alias_value":"47JBO456SAJR","created_at":"2026-07-05T07:38:30Z"},{"alias_kind":"pith_short_16","alias_value":"47JBO456SAJRDZQ3","created_at":"2026-07-05T07:38:30Z"},{"alias_kind":"pith_short_8","alias_value":"47JBO456","created_at":"2026-07-05T07:38:30Z"}],"graph_snapshots":[{"event_id":"sha256:ae649274cbb5573bce6cf693878f07444d1960cc25a5fe925953632fbdb04536","target":"graph","created_at":"2026-07-05T07:38:30Z","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/2309.05294/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study non-invertible duality symmetries by gauging a diagonal subgroup of a non-anomalous U(1) $\\times$ U(1) global symmetry. In particular, we employ the half-space gauging to $c=2$ bosonic torus conformal field theory (CFT) in two dimensions and pure U(1) $\\times$ U(1) gauge theory in four dimensions. In $c=2$ bosonic torus CFT, we show that the non-invertible symmetry obtained from the diagonal gauging becomes emergent on an irrational CFT point. We also calculate the fusion rules concerning the duality defect. We find out that the fusion algebra is non-commutative. We also obtain a simi","authors_text":"Soichiro Shimamori, Yuta Nagoya","cross_cats":["cond-mat.str-el","math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2023-09-11T08:25:31Z","title":"Non-invertible duality defect and non-commutative fusion algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.05294","kind":"arxiv","version":3},"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":"sha256:1c90c9f2e9476ffa7f77a588084c8095282a1409d3ca2169cfe7a4d16c79da41","target":"record","created_at":"2026-07-05T07:38:30Z","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":"09e03dc355cf092dab0269209ef83ef8c1890cf44af4d8d0190bbc7d9645734b","cross_cats_sorted":["cond-mat.str-el","math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2023-09-11T08:25:31Z","title_canon_sha256":"d31eb5ae3e519659231457a7aa2daeab693a7c8ee5a0454bf3a03aa1da087e2e"},"schema_version":"1.0","source":{"id":"2309.05294","kind":"arxiv","version":3}},"canonical_sha256":"e7d21773be901311e61b53a9edad5069cfbc9012300fb16f09b296e23085eea8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e7d21773be901311e61b53a9edad5069cfbc9012300fb16f09b296e23085eea8","first_computed_at":"2026-07-05T07:38:30.475920Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:38:30.475920Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jHXHWiRkG1pWljXyhwjfecvBq4NoNIcjU8jArnNoe58KdeEoCyKCXZvd97kn59IW6yy0X2eDNjCzvKIHSMG2Bw==","signature_status":"signed_v1","signed_at":"2026-07-05T07:38:30.476347Z","signed_message":"canonical_sha256_bytes"},"source_id":"2309.05294","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1c90c9f2e9476ffa7f77a588084c8095282a1409d3ca2169cfe7a4d16c79da41","sha256:ae649274cbb5573bce6cf693878f07444d1960cc25a5fe925953632fbdb04536"],"state_sha256":"3928710e8fae3c8c6203475d90f84a675c2c88f29be2f3dae06602adefb5cd77"}