{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:PGMWID5E26VLEKYH5GEGTKJWYA","short_pith_number":"pith:PGMWID5E","schema_version":"1.0","canonical_sha256":"7999640fa4d7aab22b07e98869a936c03ef5422ce5bf6788c8dae23d1e64ee54","source":{"kind":"arxiv","id":"2405.13105","version":1},"attestation_state":"computed","paper":{"title":"Non-invertible and higher-form symmetries in 2+1d lattice gauge theories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","quant-ph"],"primary_cat":"cond-mat.str-el","authors_text":"Shu-Heng Shao, Yaman Sanghavi, Yichul Choi, Yunqin Zheng","submitted_at":"2024-05-21T18:00:00Z","abstract_excerpt":"We explore exact generalized symmetries in the standard 2+1d lattice $\\mathbb{Z}_2$ gauge theory coupled to the Ising model, and compare them with their continuum field theory counterparts. One model has a (non-anomalous) non-invertible symmetry, and we identify two distinct non-invertible symmetry protected topological phases. The non-invertible algebra involves a lattice condensation operator, which creates a toric code ground state from a product state. Another model has a mixed anomaly between a 1-form symmetry and an ordinary symmetry. This anomaly enforces a nontrivial transition in the "},"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":"2405.13105","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2024-05-21T18:00:00Z","cross_cats_sorted":["hep-th","quant-ph"],"title_canon_sha256":"8c04eaf1bcf78c3b1e95f11cab0d60d8fa1ad22abc28375f0cca813024cedea5","abstract_canon_sha256":"f55e6506de8f8adc94bbf5570f4d745a8a75fc2828dbc18809375fcfa8390327"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:00:37.166830Z","signature_b64":"lnq9SrQ2jOhaVSkrVNNYcDsKuaVcV3j22T+6YFhe5/NjbXwJ1uwO9MPo7JAyg2XiEIESHjUj7F7n7B+2I5YCCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7999640fa4d7aab22b07e98869a936c03ef5422ce5bf6788c8dae23d1e64ee54","last_reissued_at":"2026-07-05T10:00:37.166394Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:00:37.166394Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-invertible and higher-form symmetries in 2+1d lattice gauge theories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","quant-ph"],"primary_cat":"cond-mat.str-el","authors_text":"Shu-Heng Shao, Yaman Sanghavi, Yichul Choi, Yunqin Zheng","submitted_at":"2024-05-21T18:00:00Z","abstract_excerpt":"We explore exact generalized symmetries in the standard 2+1d lattice $\\mathbb{Z}_2$ gauge theory coupled to the Ising model, and compare them with their continuum field theory counterparts. One model has a (non-anomalous) non-invertible symmetry, and we identify two distinct non-invertible symmetry protected topological phases. The non-invertible algebra involves a lattice condensation operator, which creates a toric code ground state from a product state. Another model has a mixed anomaly between a 1-form symmetry and an ordinary symmetry. This anomaly enforces a nontrivial transition in the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.13105","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2405.13105/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2405.13105","created_at":"2026-07-05T10:00:37.166450+00:00"},{"alias_kind":"arxiv_version","alias_value":"2405.13105v1","created_at":"2026-07-05T10:00:37.166450+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.13105","created_at":"2026-07-05T10:00:37.166450+00:00"},{"alias_kind":"pith_short_12","alias_value":"PGMWID5E26VL","created_at":"2026-07-05T10:00:37.166450+00:00"},{"alias_kind":"pith_short_16","alias_value":"PGMWID5E26VLEKYH","created_at":"2026-07-05T10:00:37.166450+00:00"},{"alias_kind":"pith_short_8","alias_value":"PGMWID5E","created_at":"2026-07-05T10:00:37.166450+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":8,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.03582","citing_title":"Fracton Topological Holography","ref_index":57,"is_internal_anchor":false},{"citing_arxiv_id":"2605.27193","citing_title":"Algebras of order parameters in one-dimensional spin systems","ref_index":23,"is_internal_anchor":false},{"citing_arxiv_id":"2605.06287","citing_title":"Half-Spacetime Gauging of 2-Group Symmetry in 3d","ref_index":40,"is_internal_anchor":false},{"citing_arxiv_id":"2605.28688","citing_title":"Topological lattice gauge theory enriched by non-invertible symmetry","ref_index":26,"is_internal_anchor":false},{"citing_arxiv_id":"2604.02856","citing_title":"Type-IV 't Hooft Anomalies on the Lattice: Emergent Higher-Categorical Symmetries and Applications to LSM Systems","ref_index":36,"is_internal_anchor":false},{"citing_arxiv_id":"2605.06287","citing_title":"Half-Spacetime Gauging of 2-Group Symmetry in 3d","ref_index":35,"is_internal_anchor":false},{"citing_arxiv_id":"2604.06307","citing_title":"Lattice chiral symmetry from bosons in 3+1d","ref_index":111,"is_internal_anchor":false},{"citing_arxiv_id":"2604.12907","citing_title":"Hilbert Space Fragmentation from Generalized Symmetries","ref_index":58,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PGMWID5E26VLEKYH5GEGTKJWYA","json":"https://pith.science/pith/PGMWID5E26VLEKYH5GEGTKJWYA.json","graph_json":"https://pith.science/api/pith-number/PGMWID5E26VLEKYH5GEGTKJWYA/graph.json","events_json":"https://pith.science/api/pith-number/PGMWID5E26VLEKYH5GEGTKJWYA/events.json","paper":"https://pith.science/paper/PGMWID5E"},"agent_actions":{"view_html":"https://pith.science/pith/PGMWID5E26VLEKYH5GEGTKJWYA","download_json":"https://pith.science/pith/PGMWID5E26VLEKYH5GEGTKJWYA.json","view_paper":"https://pith.science/paper/PGMWID5E","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2405.13105&json=true","fetch_graph":"https://pith.science/api/pith-number/PGMWID5E26VLEKYH5GEGTKJWYA/graph.json","fetch_events":"https://pith.science/api/pith-number/PGMWID5E26VLEKYH5GEGTKJWYA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PGMWID5E26VLEKYH5GEGTKJWYA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PGMWID5E26VLEKYH5GEGTKJWYA/action/storage_attestation","attest_author":"https://pith.science/pith/PGMWID5E26VLEKYH5GEGTKJWYA/action/author_attestation","sign_citation":"https://pith.science/pith/PGMWID5E26VLEKYH5GEGTKJWYA/action/citation_signature","submit_replication":"https://pith.science/pith/PGMWID5E26VLEKYH5GEGTKJWYA/action/replication_record"}},"created_at":"2026-07-05T10:00:37.166450+00:00","updated_at":"2026-07-05T10:00:37.166450+00:00"}