{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1998:K5YPQIZDRNJ6VM5IIGGMADOZSM","short_pith_number":"pith:K5YPQIZD","schema_version":"1.0","canonical_sha256":"5770f823238b53eab3a8418cc00dd9931047230ccb99a78b732a52abc5ce166c","source":{"kind":"arxiv","id":"hep-th/9801171","version":2},"attestation_state":"computed","paper":{"title":"Modular Invariants, Graphs and $\\alpha$-Induction for Nets of Subfactors I","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"D. E. Evans, J. B\\\"ockenhauer","submitted_at":"1998-01-26T15:43:14Z","abstract_excerpt":"We analyze the induction and restriction of sectors for nets of subfactors defined by Longo and Rehren. Picking a local subfactor we derive a formula which specifies the structure of the induced sectors in terms of the original DHR sectors of the smaller net and canonical endomorphisms. We also obtain a reciprocity formula for induction and restriction of sectors, and we prove a certain homomorphism property of the induction mapping.\n  Developing further some ideas of F. Xu we will apply this theory in a forthcoming paper to nets of subfactors arising from conformal field theory, in particular"},"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":"hep-th/9801171","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1998-01-26T15:43:14Z","cross_cats_sorted":[],"title_canon_sha256":"049c622a1edff2d93cb9e78a9976839e9116b8adefb0230620fd7ed2dbb7248a","abstract_canon_sha256":"1de0180763277cc3651d65327173aee5ce6bc64746932fa891c517a284d22e86"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:09:40.452427Z","signature_b64":"LXRsG5plPtMoodY0otmUGlBDJ4aINFtD0xyTUIXcvmBfusnlDNBZfBjs4LVVcJ0SWXdjIpPPQoDobLseBJdCBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5770f823238b53eab3a8418cc00dd9931047230ccb99a78b732a52abc5ce166c","last_reissued_at":"2026-07-04T16:09:40.452083Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:09:40.452083Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Modular Invariants, Graphs and $\\alpha$-Induction for Nets of Subfactors I","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"D. E. Evans, J. B\\\"ockenhauer","submitted_at":"1998-01-26T15:43:14Z","abstract_excerpt":"We analyze the induction and restriction of sectors for nets of subfactors defined by Longo and Rehren. Picking a local subfactor we derive a formula which specifies the structure of the induced sectors in terms of the original DHR sectors of the smaller net and canonical endomorphisms. We also obtain a reciprocity formula for induction and restriction of sectors, and we prove a certain homomorphism property of the induction mapping.\n  Developing further some ideas of F. Xu we will apply this theory in a forthcoming paper to nets of subfactors arising from conformal field theory, in particular"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9801171","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/hep-th/9801171/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":"hep-th/9801171","created_at":"2026-07-04T16:09:40.452141+00:00"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9801171v2","created_at":"2026-07-04T16:09:40.452141+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9801171","created_at":"2026-07-04T16:09:40.452141+00:00"},{"alias_kind":"pith_short_12","alias_value":"K5YPQIZDRNJ6","created_at":"2026-07-04T16:09:40.452141+00:00"},{"alias_kind":"pith_short_16","alias_value":"K5YPQIZDRNJ6VM5I","created_at":"2026-07-04T16:09:40.452141+00:00"},{"alias_kind":"pith_short_8","alias_value":"K5YPQIZD","created_at":"2026-07-04T16:09:40.452141+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2204.02407","citing_title":"Higher Gauging and Non-invertible Condensation Defects","ref_index":101,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/K5YPQIZDRNJ6VM5IIGGMADOZSM","json":"https://pith.science/pith/K5YPQIZDRNJ6VM5IIGGMADOZSM.json","graph_json":"https://pith.science/api/pith-number/K5YPQIZDRNJ6VM5IIGGMADOZSM/graph.json","events_json":"https://pith.science/api/pith-number/K5YPQIZDRNJ6VM5IIGGMADOZSM/events.json","paper":"https://pith.science/paper/K5YPQIZD"},"agent_actions":{"view_html":"https://pith.science/pith/K5YPQIZDRNJ6VM5IIGGMADOZSM","download_json":"https://pith.science/pith/K5YPQIZDRNJ6VM5IIGGMADOZSM.json","view_paper":"https://pith.science/paper/K5YPQIZD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=hep-th/9801171&json=true","fetch_graph":"https://pith.science/api/pith-number/K5YPQIZDRNJ6VM5IIGGMADOZSM/graph.json","fetch_events":"https://pith.science/api/pith-number/K5YPQIZDRNJ6VM5IIGGMADOZSM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/K5YPQIZDRNJ6VM5IIGGMADOZSM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/K5YPQIZDRNJ6VM5IIGGMADOZSM/action/storage_attestation","attest_author":"https://pith.science/pith/K5YPQIZDRNJ6VM5IIGGMADOZSM/action/author_attestation","sign_citation":"https://pith.science/pith/K5YPQIZDRNJ6VM5IIGGMADOZSM/action/citation_signature","submit_replication":"https://pith.science/pith/K5YPQIZDRNJ6VM5IIGGMADOZSM/action/replication_record"}},"created_at":"2026-07-04T16:09:40.452141+00:00","updated_at":"2026-07-04T16:09:40.452141+00:00"}