{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2001:3KSVMG3YTQRSYKBUWQPAWUP54C","short_pith_number":"pith:3KSVMG3Y","schema_version":"1.0","canonical_sha256":"daa5561b789c232c2834b41e0b51fde087457c38d05368fdd128c0acbcb3ece7","source":{"kind":"arxiv","id":"math/0102196","version":2},"attestation_state":"computed","paper":{"title":"Conformal Subnets and Intermediate Subfactors","license":"","headline":"","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"math.OA","authors_text":"Roberto Longo","submitted_at":"2001-02-26T14:43:48Z","abstract_excerpt":"Given an irreducible local conformal net A of von Neumann algebras on the circle and a finite-index conformal subnet B of A, we show that A is completely rational iff B is completely rational. In particular this extends a result of F. Xu for the orbifold construction. By applying previous results of Xu, many coset models turn out to be completely rational and the structure results in [KLM] hold. Our proofs are based on an analysis of the net inclusion B in A; among other things we show that, for a fixed interval I, every von Neumann algebra R intermediate between B(I) and A(I) comes from an in"},"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":"math/0102196","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.OA","submitted_at":"2001-02-26T14:43:48Z","cross_cats_sorted":["hep-th","math-ph","math.MP"],"title_canon_sha256":"fb9272e85a92b584332dcd5d9a1bd034bb6d44b6671680bdde2355fde91ce493","abstract_canon_sha256":"74f4111e2824970c7af937893a068448e90c08649c94d3eb3d1aaf084a8667c8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:25:02.233755Z","signature_b64":"iQJ+xx4Egpj0nD53N+rosZsp0v8mP9vGMNDUK04YVxOQI29VfQ2W73GqlMKnHmvci/bp0wr2gN06qJVGsj2KAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"daa5561b789c232c2834b41e0b51fde087457c38d05368fdd128c0acbcb3ece7","last_reissued_at":"2026-05-18T04:25:02.233349Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:25:02.233349Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Conformal Subnets and Intermediate Subfactors","license":"","headline":"","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"math.OA","authors_text":"Roberto Longo","submitted_at":"2001-02-26T14:43:48Z","abstract_excerpt":"Given an irreducible local conformal net A of von Neumann algebras on the circle and a finite-index conformal subnet B of A, we show that A is completely rational iff B is completely rational. In particular this extends a result of F. Xu for the orbifold construction. By applying previous results of Xu, many coset models turn out to be completely rational and the structure results in [KLM] hold. Our proofs are based on an analysis of the net inclusion B in A; among other things we show that, for a fixed interval I, every von Neumann algebra R intermediate between B(I) and A(I) comes from an in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0102196","kind":"arxiv","version":2},"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":"math/0102196","created_at":"2026-05-18T04:25:02.233405+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0102196v2","created_at":"2026-05-18T04:25:02.233405+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0102196","created_at":"2026-05-18T04:25:02.233405+00:00"},{"alias_kind":"pith_short_12","alias_value":"3KSVMG3YTQRS","created_at":"2026-05-18T12:25:50.254431+00:00"},{"alias_kind":"pith_short_16","alias_value":"3KSVMG3YTQRSYKBU","created_at":"2026-05-18T12:25:50.254431+00:00"},{"alias_kind":"pith_short_8","alias_value":"3KSVMG3Y","created_at":"2026-05-18T12:25:50.254431+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.01008","citing_title":"Rational and non-rational two-dimensional conformal field theories arising from lattices","ref_index":40,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3KSVMG3YTQRSYKBUWQPAWUP54C","json":"https://pith.science/pith/3KSVMG3YTQRSYKBUWQPAWUP54C.json","graph_json":"https://pith.science/api/pith-number/3KSVMG3YTQRSYKBUWQPAWUP54C/graph.json","events_json":"https://pith.science/api/pith-number/3KSVMG3YTQRSYKBUWQPAWUP54C/events.json","paper":"https://pith.science/paper/3KSVMG3Y"},"agent_actions":{"view_html":"https://pith.science/pith/3KSVMG3YTQRSYKBUWQPAWUP54C","download_json":"https://pith.science/pith/3KSVMG3YTQRSYKBUWQPAWUP54C.json","view_paper":"https://pith.science/paper/3KSVMG3Y","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0102196&json=true","fetch_graph":"https://pith.science/api/pith-number/3KSVMG3YTQRSYKBUWQPAWUP54C/graph.json","fetch_events":"https://pith.science/api/pith-number/3KSVMG3YTQRSYKBUWQPAWUP54C/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3KSVMG3YTQRSYKBUWQPAWUP54C/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3KSVMG3YTQRSYKBUWQPAWUP54C/action/storage_attestation","attest_author":"https://pith.science/pith/3KSVMG3YTQRSYKBUWQPAWUP54C/action/author_attestation","sign_citation":"https://pith.science/pith/3KSVMG3YTQRSYKBUWQPAWUP54C/action/citation_signature","submit_replication":"https://pith.science/pith/3KSVMG3YTQRSYKBUWQPAWUP54C/action/replication_record"}},"created_at":"2026-05-18T04:25:02.233405+00:00","updated_at":"2026-05-18T04:25:02.233405+00:00"}