{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:BS6RS3FR377FQ3BBJH44BDPZKK","short_pith_number":"pith:BS6RS3FR","schema_version":"1.0","canonical_sha256":"0cbd196cb1dffe586c2149f9c08df952948f82e7f02bdbb49975559d59c23808","source":{"kind":"arxiv","id":"1905.09566","version":3},"attestation_state":"computed","paper":{"title":"Condensations in higher categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.str-el","hep-th","math.QA"],"primary_cat":"math.CT","authors_text":"Davide Gaiotto, Theo Johnson-Freyd","submitted_at":"2019-05-23T10:07:25Z","abstract_excerpt":"We present a higher-categorical generalization of the \"Karoubi envelope\" construction from ordinary category theory, and prove that, like the ordinary Karoubi envelope, our higher Karoubi envelope is the closure for absolute limits. Our construction replaces the idempotents in the ordinary version with a notion that we call \"condensations.\" The name is justified by the direct physical interpretation of the notion of condensation: it encodes a general class of constructions which produce a new topological phase of matter by turning on a commuting projector Hamiltonian on a lattice of defects wi"},"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":"1905.09566","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2019-05-23T10:07:25Z","cross_cats_sorted":["cond-mat.str-el","hep-th","math.QA"],"title_canon_sha256":"29dfedd31d9edbd4085fbb1d4ab3b505cc1276d9bca2a3c22454464ccfa186d3","abstract_canon_sha256":"6f573b1a3142a4c3f99f73a5ce0814a00fa5fa9b70e96a143d801d2ff0ea42b3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:44:10.191855Z","signature_b64":"s2bwSt6YkKz+d3CGT0cQ3PhMArCM+D4jseIsxUhsBNJu28HnqknmCnHsbONdzGY5NZSpltJMTtoP3DUhyn3CBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0cbd196cb1dffe586c2149f9c08df952948f82e7f02bdbb49975559d59c23808","last_reissued_at":"2026-07-05T10:44:10.191339Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:44:10.191339Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Condensations in higher categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.str-el","hep-th","math.QA"],"primary_cat":"math.CT","authors_text":"Davide Gaiotto, Theo Johnson-Freyd","submitted_at":"2019-05-23T10:07:25Z","abstract_excerpt":"We present a higher-categorical generalization of the \"Karoubi envelope\" construction from ordinary category theory, and prove that, like the ordinary Karoubi envelope, our higher Karoubi envelope is the closure for absolute limits. Our construction replaces the idempotents in the ordinary version with a notion that we call \"condensations.\" The name is justified by the direct physical interpretation of the notion of condensation: it encodes a general class of constructions which produce a new topological phase of matter by turning on a commuting projector Hamiltonian on a lattice of defects wi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.09566","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/1905.09566/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":"1905.09566","created_at":"2026-07-05T10:44:10.191404+00:00"},{"alias_kind":"arxiv_version","alias_value":"1905.09566v3","created_at":"2026-07-05T10:44:10.191404+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.09566","created_at":"2026-07-05T10:44:10.191404+00:00"},{"alias_kind":"pith_short_12","alias_value":"BS6RS3FR377F","created_at":"2026-07-05T10:44:10.191404+00:00"},{"alias_kind":"pith_short_16","alias_value":"BS6RS3FR377FQ3BB","created_at":"2026-07-05T10:44:10.191404+00:00"},{"alias_kind":"pith_short_8","alias_value":"BS6RS3FR","created_at":"2026-07-05T10:44:10.191404+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":17,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2607.01322","citing_title":"Wormholes as red herrings: reflection positivity and the reconstruction of unitary quantum field theories","ref_index":204,"is_internal_anchor":false},{"citing_arxiv_id":"2606.05543","citing_title":"Notes on (-2)-form symmetries","ref_index":66,"is_internal_anchor":false},{"citing_arxiv_id":"2606.02046","citing_title":"Frobenius Algebras and Dual Bimodules in Monoidal 2-Categories","ref_index":9,"is_internal_anchor":false},{"citing_arxiv_id":"2605.06287","citing_title":"Half-Spacetime Gauging of 2-Group Symmetry in 3d","ref_index":68,"is_internal_anchor":false},{"citing_arxiv_id":"2204.02407","citing_title":"Higher Gauging and Non-invertible Condensation Defects","ref_index":57,"is_internal_anchor":false},{"citing_arxiv_id":"2111.01139","citing_title":"Non-Invertible Duality Defects in 3+1 Dimensions","ref_index":54,"is_internal_anchor":false},{"citing_arxiv_id":"2308.00747","citing_title":"What's Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries","ref_index":236,"is_internal_anchor":false},{"citing_arxiv_id":"2312.16317","citing_title":"Non-Invertible Anyon Condensation and Level-Rank Dualities","ref_index":50,"is_internal_anchor":false},{"citing_arxiv_id":"2205.09545","citing_title":"Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond","ref_index":44,"is_internal_anchor":false},{"citing_arxiv_id":"2605.06661","citing_title":"Pro-Tensor Network","ref_index":46,"is_internal_anchor":false},{"citing_arxiv_id":"2305.18296","citing_title":"ICTP Lectures on (Non-)Invertible Generalized Symmetries","ref_index":68,"is_internal_anchor":false},{"citing_arxiv_id":"2602.03926","citing_title":"The Line, the Strip and the Duality Defect","ref_index":34,"is_internal_anchor":false},{"citing_arxiv_id":"2603.09903","citing_title":"Homotopy Posets, Postnikov Towers, and Hypercompletions of $\\infty$-Categories","ref_index":8,"is_internal_anchor":false},{"citing_arxiv_id":"2605.03891","citing_title":"Parameterized Families of Toric Code Phase: $em$-duality family and higher-order anyon pumping","ref_index":96,"is_internal_anchor":false},{"citing_arxiv_id":"2604.24847","citing_title":"The Classification of Pauli Stabilizer Codes: A Lattice and Continuum Treatise","ref_index":24,"is_internal_anchor":false},{"citing_arxiv_id":"2605.06287","citing_title":"Half-Spacetime Gauging of 2-Group Symmetry in 3d","ref_index":63,"is_internal_anchor":false},{"citing_arxiv_id":"2604.14275","citing_title":"Generalized Complexity Distances and Non-Invertible Symmetries","ref_index":15,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BS6RS3FR377FQ3BBJH44BDPZKK","json":"https://pith.science/pith/BS6RS3FR377FQ3BBJH44BDPZKK.json","graph_json":"https://pith.science/api/pith-number/BS6RS3FR377FQ3BBJH44BDPZKK/graph.json","events_json":"https://pith.science/api/pith-number/BS6RS3FR377FQ3BBJH44BDPZKK/events.json","paper":"https://pith.science/paper/BS6RS3FR"},"agent_actions":{"view_html":"https://pith.science/pith/BS6RS3FR377FQ3BBJH44BDPZKK","download_json":"https://pith.science/pith/BS6RS3FR377FQ3BBJH44BDPZKK.json","view_paper":"https://pith.science/paper/BS6RS3FR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1905.09566&json=true","fetch_graph":"https://pith.science/api/pith-number/BS6RS3FR377FQ3BBJH44BDPZKK/graph.json","fetch_events":"https://pith.science/api/pith-number/BS6RS3FR377FQ3BBJH44BDPZKK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BS6RS3FR377FQ3BBJH44BDPZKK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BS6RS3FR377FQ3BBJH44BDPZKK/action/storage_attestation","attest_author":"https://pith.science/pith/BS6RS3FR377FQ3BBJH44BDPZKK/action/author_attestation","sign_citation":"https://pith.science/pith/BS6RS3FR377FQ3BBJH44BDPZKK/action/citation_signature","submit_replication":"https://pith.science/pith/BS6RS3FR377FQ3BBJH44BDPZKK/action/replication_record"}},"created_at":"2026-07-05T10:44:10.191404+00:00","updated_at":"2026-07-05T10:44:10.191404+00:00"}