{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:V37SHE3MNPS66E65Q6K3HF7AM4","short_pith_number":"pith:V37SHE3M","schema_version":"1.0","canonical_sha256":"aeff23936c6be5ef13dd8795b397e0670d1fc08079b1403f862b34762f76cd27","source":{"kind":"arxiv","id":"2003.06663","version":5},"attestation_state":"computed","paper":{"title":"On the classification of topological orders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.str-el","math.QA"],"primary_cat":"math.CT","authors_text":"Theo Johnson-Freyd","submitted_at":"2020-03-14T15:56:45Z","abstract_excerpt":"We axiomatize the extended operators in topological orders (possibly gravitationally anomalous, possibly with degenerate ground states) in terms of monoidal Karoubi-complete $n$-categories which are mildly dualizable and have trivial centre. Dualizability encodes the word \"topological,\" and we take it as the definition of \"(separable) multifusion $n$-category\"; triviality of the centre implements the physical principle of \"remote detectability.\" We show that such $n$-categorical algebras are Morita-invertible (in the appropriate higher Morita category), thereby identifying topological orders w"},"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":"2003.06663","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2020-03-14T15:56:45Z","cross_cats_sorted":["cond-mat.str-el","math.QA"],"title_canon_sha256":"5b39d8f78957e7275420e366cb42361d46baf7d4a5e667260286ae79ed7bac94","abstract_canon_sha256":"5f5c35aec586ad4adcc8d3fd932227d159c1a8650bf0a3caf4575b6af591bf9f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:31:19.472991Z","signature_b64":"7HZQ2cHW3kvsRvX2HWtXFNAyoVGi/ioBinsvBj8AzeJ67oEr14ND78NIcmsz8dCTeWwRwtrqfU3dgWaEKrmzDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aeff23936c6be5ef13dd8795b397e0670d1fc08079b1403f862b34762f76cd27","last_reissued_at":"2026-07-05T04:31:19.472497Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:31:19.472497Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the classification of topological orders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.str-el","math.QA"],"primary_cat":"math.CT","authors_text":"Theo Johnson-Freyd","submitted_at":"2020-03-14T15:56:45Z","abstract_excerpt":"We axiomatize the extended operators in topological orders (possibly gravitationally anomalous, possibly with degenerate ground states) in terms of monoidal Karoubi-complete $n$-categories which are mildly dualizable and have trivial centre. Dualizability encodes the word \"topological,\" and we take it as the definition of \"(separable) multifusion $n$-category\"; triviality of the centre implements the physical principle of \"remote detectability.\" We show that such $n$-categorical algebras are Morita-invertible (in the appropriate higher Morita category), thereby identifying topological orders w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2003.06663","kind":"arxiv","version":5},"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/2003.06663/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":"2003.06663","created_at":"2026-07-05T04:31:19.472557+00:00"},{"alias_kind":"arxiv_version","alias_value":"2003.06663v5","created_at":"2026-07-05T04:31:19.472557+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2003.06663","created_at":"2026-07-05T04:31:19.472557+00:00"},{"alias_kind":"pith_short_12","alias_value":"V37SHE3MNPS6","created_at":"2026-07-05T04:31:19.472557+00:00"},{"alias_kind":"pith_short_16","alias_value":"V37SHE3MNPS66E65","created_at":"2026-07-05T04:31:19.472557+00:00"},{"alias_kind":"pith_short_8","alias_value":"V37SHE3M","created_at":"2026-07-05T04:31:19.472557+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":6,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.17708","citing_title":"Monopoles, Center Vortices, Confinement in (3+1)d, and the Lens-Space Twisted Partition Function","ref_index":65,"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":273,"is_internal_anchor":false},{"citing_arxiv_id":"2305.18296","citing_title":"ICTP Lectures on (Non-)Invertible Generalized Symmetries","ref_index":112,"is_internal_anchor":false},{"citing_arxiv_id":"2603.12323","citing_title":"On the SymTFTs of Finite Non-Abelian Symmetries","ref_index":63,"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":87,"is_internal_anchor":false},{"citing_arxiv_id":"2604.24847","citing_title":"The Classification of Pauli Stabilizer Codes: A Lattice and Continuum Treatise","ref_index":32,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/V37SHE3MNPS66E65Q6K3HF7AM4","json":"https://pith.science/pith/V37SHE3MNPS66E65Q6K3HF7AM4.json","graph_json":"https://pith.science/api/pith-number/V37SHE3MNPS66E65Q6K3HF7AM4/graph.json","events_json":"https://pith.science/api/pith-number/V37SHE3MNPS66E65Q6K3HF7AM4/events.json","paper":"https://pith.science/paper/V37SHE3M"},"agent_actions":{"view_html":"https://pith.science/pith/V37SHE3MNPS66E65Q6K3HF7AM4","download_json":"https://pith.science/pith/V37SHE3MNPS66E65Q6K3HF7AM4.json","view_paper":"https://pith.science/paper/V37SHE3M","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2003.06663&json=true","fetch_graph":"https://pith.science/api/pith-number/V37SHE3MNPS66E65Q6K3HF7AM4/graph.json","fetch_events":"https://pith.science/api/pith-number/V37SHE3MNPS66E65Q6K3HF7AM4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/V37SHE3MNPS66E65Q6K3HF7AM4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/V37SHE3MNPS66E65Q6K3HF7AM4/action/storage_attestation","attest_author":"https://pith.science/pith/V37SHE3MNPS66E65Q6K3HF7AM4/action/author_attestation","sign_citation":"https://pith.science/pith/V37SHE3MNPS66E65Q6K3HF7AM4/action/citation_signature","submit_replication":"https://pith.science/pith/V37SHE3MNPS66E65Q6K3HF7AM4/action/replication_record"}},"created_at":"2026-07-05T04:31:19.472557+00:00","updated_at":"2026-07-05T04:31:19.472557+00:00"}