{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:I4OMWMUYPQHCHX33IEULOS4GPT","short_pith_number":"pith:I4OMWMUY","schema_version":"1.0","canonical_sha256":"471ccb32987c0e23df7b4128b74b867cddfc32d5b1dd1dd34c7d124d52954285","source":{"kind":"arxiv","id":"2102.10953","version":1},"attestation_state":"computed","paper":{"title":"Two-dimensional topological order and operator algebras","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.str-el","math.MP","math.OA","math.QA"],"primary_cat":"math-ph","authors_text":"Yasuyuki Kawahigashi","submitted_at":"2021-02-22T12:43:38Z","abstract_excerpt":"We review recent interactions between mathematical theory of two-dimensional topological order and operator algebras, particularly the Jones theory of subfactors. The role of representation theory in terms of tensor categories is emphasized. Connections to 2-dimensional conformal field theory are also presented. In particular, we discuss anyon condensation, gapped domain walls and matrix product operators in terms of operator algebras."},"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":"2102.10953","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2021-02-22T12:43:38Z","cross_cats_sorted":["cond-mat.str-el","math.MP","math.OA","math.QA"],"title_canon_sha256":"decf1af7c326e2b84614380f649d557afa0c05ea109454e8aed3bdf424ddbca4","abstract_canon_sha256":"3cf345c4e62220d39da8441752609024674757b7d7ee49a322ded9c1c126752f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:01:55.040301Z","signature_b64":"M6KuH6MwNauiSBZeBdIYstlzQRovILVqz14Ksaxcq4+UU3w7ZdVei7LY1m9CwYrtqgevadTVB33S7S+PmF77Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"471ccb32987c0e23df7b4128b74b867cddfc32d5b1dd1dd34c7d124d52954285","last_reissued_at":"2026-07-05T03:01:55.039748Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:01:55.039748Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Two-dimensional topological order and operator algebras","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.str-el","math.MP","math.OA","math.QA"],"primary_cat":"math-ph","authors_text":"Yasuyuki Kawahigashi","submitted_at":"2021-02-22T12:43:38Z","abstract_excerpt":"We review recent interactions between mathematical theory of two-dimensional topological order and operator algebras, particularly the Jones theory of subfactors. The role of representation theory in terms of tensor categories is emphasized. Connections to 2-dimensional conformal field theory are also presented. In particular, we discuss anyon condensation, gapped domain walls and matrix product operators in terms of operator algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.10953","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/2102.10953/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":"2102.10953","created_at":"2026-07-05T03:01:55.039910+00:00"},{"alias_kind":"arxiv_version","alias_value":"2102.10953v1","created_at":"2026-07-05T03:01:55.039910+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.10953","created_at":"2026-07-05T03:01:55.039910+00:00"},{"alias_kind":"pith_short_12","alias_value":"I4OMWMUYPQHC","created_at":"2026-07-05T03:01:55.039910+00:00"},{"alias_kind":"pith_short_16","alias_value":"I4OMWMUYPQHCHX33","created_at":"2026-07-05T03:01:55.039910+00:00"},{"alias_kind":"pith_short_8","alias_value":"I4OMWMUY","created_at":"2026-07-05T03:01:55.039910+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2508.08639","citing_title":"Extending fusion rules with finite subgroups: A general construction of $Z_{N}$ extended conformal field theories and their orbifoldings","ref_index":14,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/I4OMWMUYPQHCHX33IEULOS4GPT","json":"https://pith.science/pith/I4OMWMUYPQHCHX33IEULOS4GPT.json","graph_json":"https://pith.science/api/pith-number/I4OMWMUYPQHCHX33IEULOS4GPT/graph.json","events_json":"https://pith.science/api/pith-number/I4OMWMUYPQHCHX33IEULOS4GPT/events.json","paper":"https://pith.science/paper/I4OMWMUY"},"agent_actions":{"view_html":"https://pith.science/pith/I4OMWMUYPQHCHX33IEULOS4GPT","download_json":"https://pith.science/pith/I4OMWMUYPQHCHX33IEULOS4GPT.json","view_paper":"https://pith.science/paper/I4OMWMUY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2102.10953&json=true","fetch_graph":"https://pith.science/api/pith-number/I4OMWMUYPQHCHX33IEULOS4GPT/graph.json","fetch_events":"https://pith.science/api/pith-number/I4OMWMUYPQHCHX33IEULOS4GPT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/I4OMWMUYPQHCHX33IEULOS4GPT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/I4OMWMUYPQHCHX33IEULOS4GPT/action/storage_attestation","attest_author":"https://pith.science/pith/I4OMWMUYPQHCHX33IEULOS4GPT/action/author_attestation","sign_citation":"https://pith.science/pith/I4OMWMUYPQHCHX33IEULOS4GPT/action/citation_signature","submit_replication":"https://pith.science/pith/I4OMWMUYPQHCHX33IEULOS4GPT/action/replication_record"}},"created_at":"2026-07-05T03:01:55.039910+00:00","updated_at":"2026-07-05T03:01:55.039910+00:00"}