{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:UVILU2CEFZSUVEJZ2HAPYVLYRX","short_pith_number":"pith:UVILU2CE","schema_version":"1.0","canonical_sha256":"a550ba68442e654a9139d1c0fc55788dedf3097a29998d3daad806e66183d1a9","source":{"kind":"arxiv","id":"2312.17322","version":3},"attestation_state":"computed","paper":{"title":"The Club Sandwich: Gapless Phases and Phase Transitions with Non-Invertible Symmetries","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.str-el","math.CT"],"primary_cat":"hep-th","authors_text":"Daniel Pajer, Lakshya Bhardwaj, Lea E. Bottini, Sakura Schafer-Nameki","submitted_at":"2023-12-28T19:00:13Z","abstract_excerpt":"We provide a generalization of the Symmetry Topological Field Theory (SymTFT) framework to characterize phase transitions and gapless phases with categorical symmetries. The central tool is the club sandwich, which extends the SymTFT setup to include an interface between two topological orders: there is a symmetry boundary, which is gapped, and a physical boundary that may be gapless, but in addition, there is also a gapped interface in the middle. The club sandwich generalizes so-called Kennedy-Tasaki (KT) transformations. Building on the results in [1, 2] on gapped phases with categorical sy"},"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":"2312.17322","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2023-12-28T19:00:13Z","cross_cats_sorted":["cond-mat.str-el","math.CT"],"title_canon_sha256":"00c30a969843d5fba0941b18af1f8fdd089f828351d79a910f7598e21e09f840","abstract_canon_sha256":"71de49a3b854208927366b94540f3a1b9953f5aa0f5ce01862bd7a4679f0eaad"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:02:10.004774Z","signature_b64":"HudzefydpIVgEMrKO5Ll16/SGIjl+ThW6omlnB9laeL/ByVkN3VNUK537qoPh+NDMq6H+JB5dinh+vjmfAP7Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a550ba68442e654a9139d1c0fc55788dedf3097a29998d3daad806e66183d1a9","last_reissued_at":"2026-07-05T11:02:10.004302Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:02:10.004302Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Club Sandwich: Gapless Phases and Phase Transitions with Non-Invertible Symmetries","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.str-el","math.CT"],"primary_cat":"hep-th","authors_text":"Daniel Pajer, Lakshya Bhardwaj, Lea E. Bottini, Sakura Schafer-Nameki","submitted_at":"2023-12-28T19:00:13Z","abstract_excerpt":"We provide a generalization of the Symmetry Topological Field Theory (SymTFT) framework to characterize phase transitions and gapless phases with categorical symmetries. The central tool is the club sandwich, which extends the SymTFT setup to include an interface between two topological orders: there is a symmetry boundary, which is gapped, and a physical boundary that may be gapless, but in addition, there is also a gapped interface in the middle. The club sandwich generalizes so-called Kennedy-Tasaki (KT) transformations. Building on the results in [1, 2] on gapped phases with categorical sy"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.17322","kind":"arxiv","version":3},"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/2312.17322/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":"2312.17322","created_at":"2026-07-05T11:02:10.004376+00:00"},{"alias_kind":"arxiv_version","alias_value":"2312.17322v3","created_at":"2026-07-05T11:02:10.004376+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.17322","created_at":"2026-07-05T11:02:10.004376+00:00"},{"alias_kind":"pith_short_12","alias_value":"UVILU2CEFZSU","created_at":"2026-07-05T11:02:10.004376+00:00"},{"alias_kind":"pith_short_16","alias_value":"UVILU2CEFZSUVEJZ","created_at":"2026-07-05T11:02:10.004376+00:00"},{"alias_kind":"pith_short_8","alias_value":"UVILU2CE","created_at":"2026-07-05T11:02:10.004376+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":12,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.05543","citing_title":"Notes on (-2)-form symmetries","ref_index":57,"is_internal_anchor":false},{"citing_arxiv_id":"2605.07734","citing_title":"Characterizing gapped phases by smeared boundary conformal field theories: Duality in unusual ordering with spontaneously broken generalized symmetries","ref_index":82,"is_internal_anchor":false},{"citing_arxiv_id":"2605.31601","citing_title":"Twin Phases: Intrinsic Deconfined Quantum Criticality","ref_index":33,"is_internal_anchor":false},{"citing_arxiv_id":"2605.31602","citing_title":"Twin Algebras: Condensable Algebras beyond Anyons","ref_index":35,"is_internal_anchor":false},{"citing_arxiv_id":"2405.05964","citing_title":"Lattice Models for Phases and Transitions with Non-Invertible Symmetries","ref_index":32,"is_internal_anchor":false},{"citing_arxiv_id":"2408.01490","citing_title":"Defect Charges, Gapped Boundary Conditions, and the Symmetry TFT","ref_index":86,"is_internal_anchor":false},{"citing_arxiv_id":"2605.07734","citing_title":"Characterizing gapped phases by smeared boundary conformal field theories: Duality in unusual ordering with spontaneously broken generalized symmetries","ref_index":89,"is_internal_anchor":false},{"citing_arxiv_id":"2511.11059","citing_title":"Generalizing quantum dimensions: Symmetry-based classification of local pseudo-Hermitian systems and the corresponding domain walls","ref_index":127,"is_internal_anchor":false},{"citing_arxiv_id":"2602.09105","citing_title":"Generalized Families of QFTs","ref_index":53,"is_internal_anchor":false},{"citing_arxiv_id":"2605.15194","citing_title":"Non-Invertible Symmetries on Tensor-Product Hilbert Spaces and Quantum Cellular Automata","ref_index":23,"is_internal_anchor":false},{"citing_arxiv_id":"2604.25821","citing_title":"Categorical Symmetries via Operator Algebras","ref_index":22,"is_internal_anchor":false},{"citing_arxiv_id":"2605.07734","citing_title":"Characterizing gapped phases by smeared boundary conformal field theories: Duality in unusual ordering with spontaneously broken generalized symmetries","ref_index":89,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/UVILU2CEFZSUVEJZ2HAPYVLYRX","json":"https://pith.science/pith/UVILU2CEFZSUVEJZ2HAPYVLYRX.json","graph_json":"https://pith.science/api/pith-number/UVILU2CEFZSUVEJZ2HAPYVLYRX/graph.json","events_json":"https://pith.science/api/pith-number/UVILU2CEFZSUVEJZ2HAPYVLYRX/events.json","paper":"https://pith.science/paper/UVILU2CE"},"agent_actions":{"view_html":"https://pith.science/pith/UVILU2CEFZSUVEJZ2HAPYVLYRX","download_json":"https://pith.science/pith/UVILU2CEFZSUVEJZ2HAPYVLYRX.json","view_paper":"https://pith.science/paper/UVILU2CE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2312.17322&json=true","fetch_graph":"https://pith.science/api/pith-number/UVILU2CEFZSUVEJZ2HAPYVLYRX/graph.json","fetch_events":"https://pith.science/api/pith-number/UVILU2CEFZSUVEJZ2HAPYVLYRX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UVILU2CEFZSUVEJZ2HAPYVLYRX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UVILU2CEFZSUVEJZ2HAPYVLYRX/action/storage_attestation","attest_author":"https://pith.science/pith/UVILU2CEFZSUVEJZ2HAPYVLYRX/action/author_attestation","sign_citation":"https://pith.science/pith/UVILU2CEFZSUVEJZ2HAPYVLYRX/action/citation_signature","submit_replication":"https://pith.science/pith/UVILU2CEFZSUVEJZ2HAPYVLYRX/action/replication_record"}},"created_at":"2026-07-05T11:02:10.004376+00:00","updated_at":"2026-07-05T11:02:10.004376+00:00"}