{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:NJQOSZDJPZD2VOJCTYHQC2BTOD","short_pith_number":"pith:NJQOSZDJ","schema_version":"1.0","canonical_sha256":"6a60e964697e47aab9229e0f01683370f7cd5b3bde40f6f3704062255eb93d22","source":{"kind":"arxiv","id":"1004.4725","version":1},"attestation_state":"computed","paper":{"title":"Invertible defects and isomorphisms of rational CFTs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.QA"],"primary_cat":"hep-th","authors_text":"Alexei Davydov, Ingo Runkel, Liang Kong","submitted_at":"2010-04-27T06:51:06Z","abstract_excerpt":"Given two two-dimensional conformal field theories, a domain wall -- or defect line -- between them is called invertible if there is another defect with which it fuses to the identity defect. A defect is called topological if it is transparent to the stress tensor. A conformal isomorphism between the two CFTs is a linear isomorphism between their state spaces which preserves the stress tensor and is compatible with the operator product expansion. We show that for rational CFTs there is a one-to-one correspondence between invertible topological defects and conformal isomorphisms if both preserv"},"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":"1004.4725","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2010-04-27T06:51:06Z","cross_cats_sorted":["math.CT","math.QA"],"title_canon_sha256":"227d5549a7eb29c67d2b543a52c6e45a82c8438f187aec8e210c0f3566c50b7a","abstract_canon_sha256":"b31aeea3deae8ddd6132e8fe016e5147cf18464847e04df041474381cc28ad57"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:06:05.188894Z","signature_b64":"+fESTRFYPQppKegKcEJ8w6AlUXP5jwdwpj781VjOviC5HbQ5GCwbU9vZwDn4z3y7Ddo33wIcp+OxpPgidLXYBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a60e964697e47aab9229e0f01683370f7cd5b3bde40f6f3704062255eb93d22","last_reissued_at":"2026-05-18T03:06:05.188111Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:06:05.188111Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Invertible defects and isomorphisms of rational CFTs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.QA"],"primary_cat":"hep-th","authors_text":"Alexei Davydov, Ingo Runkel, Liang Kong","submitted_at":"2010-04-27T06:51:06Z","abstract_excerpt":"Given two two-dimensional conformal field theories, a domain wall -- or defect line -- between them is called invertible if there is another defect with which it fuses to the identity defect. A defect is called topological if it is transparent to the stress tensor. A conformal isomorphism between the two CFTs is a linear isomorphism between their state spaces which preserves the stress tensor and is compatible with the operator product expansion. We show that for rational CFTs there is a one-to-one correspondence between invertible topological defects and conformal isomorphisms if both preserv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.4725","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":""},"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":"1004.4725","created_at":"2026-05-18T03:06:05.188243+00:00"},{"alias_kind":"arxiv_version","alias_value":"1004.4725v1","created_at":"2026-05-18T03:06:05.188243+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.4725","created_at":"2026-05-18T03:06:05.188243+00:00"},{"alias_kind":"pith_short_12","alias_value":"NJQOSZDJPZD2","created_at":"2026-05-18T12:26:10.704358+00:00"},{"alias_kind":"pith_short_16","alias_value":"NJQOSZDJPZD2VOJC","created_at":"2026-05-18T12:26:10.704358+00:00"},{"alias_kind":"pith_short_8","alias_value":"NJQOSZDJ","created_at":"2026-05-18T12:26:10.704358+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":2,"sample":[{"citing_arxiv_id":"2308.00747","citing_title":"What's Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries","ref_index":17,"is_internal_anchor":true},{"citing_arxiv_id":"2307.07547","citing_title":"Lectures on Generalized Symmetries","ref_index":38,"is_internal_anchor":true},{"citing_arxiv_id":"1412.5148","citing_title":"Generalized Global Symmetries","ref_index":24,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NJQOSZDJPZD2VOJCTYHQC2BTOD","json":"https://pith.science/pith/NJQOSZDJPZD2VOJCTYHQC2BTOD.json","graph_json":"https://pith.science/api/pith-number/NJQOSZDJPZD2VOJCTYHQC2BTOD/graph.json","events_json":"https://pith.science/api/pith-number/NJQOSZDJPZD2VOJCTYHQC2BTOD/events.json","paper":"https://pith.science/paper/NJQOSZDJ"},"agent_actions":{"view_html":"https://pith.science/pith/NJQOSZDJPZD2VOJCTYHQC2BTOD","download_json":"https://pith.science/pith/NJQOSZDJPZD2VOJCTYHQC2BTOD.json","view_paper":"https://pith.science/paper/NJQOSZDJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1004.4725&json=true","fetch_graph":"https://pith.science/api/pith-number/NJQOSZDJPZD2VOJCTYHQC2BTOD/graph.json","fetch_events":"https://pith.science/api/pith-number/NJQOSZDJPZD2VOJCTYHQC2BTOD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NJQOSZDJPZD2VOJCTYHQC2BTOD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NJQOSZDJPZD2VOJCTYHQC2BTOD/action/storage_attestation","attest_author":"https://pith.science/pith/NJQOSZDJPZD2VOJCTYHQC2BTOD/action/author_attestation","sign_citation":"https://pith.science/pith/NJQOSZDJPZD2VOJCTYHQC2BTOD/action/citation_signature","submit_replication":"https://pith.science/pith/NJQOSZDJPZD2VOJCTYHQC2BTOD/action/replication_record"}},"created_at":"2026-05-18T03:06:05.188243+00:00","updated_at":"2026-05-18T03:06:05.188243+00:00"}