{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:3KSVMG3YTQRSYKBUWQPAWUP54C","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"74f4111e2824970c7af937893a068448e90c08649c94d3eb3d1aaf084a8667c8","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"","primary_cat":"math.OA","submitted_at":"2001-02-26T14:43:48Z","title_canon_sha256":"fb9272e85a92b584332dcd5d9a1bd034bb6d44b6671680bdde2355fde91ce493"},"schema_version":"1.0","source":{"id":"math/0102196","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0102196","created_at":"2026-05-18T04:25:02Z"},{"alias_kind":"arxiv_version","alias_value":"math/0102196v2","created_at":"2026-05-18T04:25:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0102196","created_at":"2026-05-18T04:25:02Z"},{"alias_kind":"pith_short_12","alias_value":"3KSVMG3YTQRS","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"3KSVMG3YTQRSYKBU","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"3KSVMG3Y","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:9cb24a4664a5e52deab6abd0363c4e3a215429da389762ee693ff37becc176d4","target":"graph","created_at":"2026-05-18T04:25:02Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Roberto Longo","cross_cats":["hep-th","math-ph","math.MP"],"headline":"","license":"","primary_cat":"math.OA","submitted_at":"2001-02-26T14:43:48Z","title":"Conformal Subnets and Intermediate Subfactors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0102196","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:7c60adc286b024d1cb782dcf6da3dca25a10def8f83addbf4eb2fc0cc9cdfad2","target":"record","created_at":"2026-05-18T04:25:02Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"74f4111e2824970c7af937893a068448e90c08649c94d3eb3d1aaf084a8667c8","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"","primary_cat":"math.OA","submitted_at":"2001-02-26T14:43:48Z","title_canon_sha256":"fb9272e85a92b584332dcd5d9a1bd034bb6d44b6671680bdde2355fde91ce493"},"schema_version":"1.0","source":{"id":"math/0102196","kind":"arxiv","version":2}},"canonical_sha256":"daa5561b789c232c2834b41e0b51fde087457c38d05368fdd128c0acbcb3ece7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"daa5561b789c232c2834b41e0b51fde087457c38d05368fdd128c0acbcb3ece7","first_computed_at":"2026-05-18T04:25:02.233349Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:25:02.233349Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iQJ+xx4Egpj0nD53N+rosZsp0v8mP9vGMNDUK04YVxOQI29VfQ2W73GqlMKnHmvci/bp0wr2gN06qJVGsj2KAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:25:02.233755Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0102196","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7c60adc286b024d1cb782dcf6da3dca25a10def8f83addbf4eb2fc0cc9cdfad2","sha256:9cb24a4664a5e52deab6abd0363c4e3a215429da389762ee693ff37becc176d4"],"state_sha256":"3e5103ce2e60bb94e965ccd16d4ccf9f18c1a5afca5e9afc1ceaa092a687fb90"}