{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:DKLAQDGOPEUARCLMRMFGACGE4X","short_pith_number":"pith:DKLAQDGO","schema_version":"1.0","canonical_sha256":"1a96080cce792808896c8b0a6008c4e5db2e771a1b975e6fb1d041da0a7b1c98","source":{"kind":"arxiv","id":"1310.8566","version":1},"attestation_state":"computed","paper":{"title":"1-supertransitive subfactors with index at most 6+1/5","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.OA","authors_text":"David Penneys, Scott Morrison, Zhengwei Liu","submitted_at":"2013-10-31T16:04:58Z","abstract_excerpt":"We classify irreducible II_1 subfactors A \\subset B such that B \\ominus A is reducible as an A-A bimodule, with index at most 6+1/5, leaving aside the composite subfactors at index exactly 6. Previous work has already achieved this up to index 3+\\sqrt{5} \\approx 5.23. We find there are exactly three such subfactors with index in (3+\\sqrt{5}, 6+1/5], all with index 3+2\\sqrt{2}. One of these comes from SO(3)_q at a root of unity, while the other two appear to be closely related, and are `braided up to a sign'."},"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":"1310.8566","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-10-31T16:04:58Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"cd2f768d1d97e6cc9a48dbc0a2718e6a1b940411bcde5b1b59244c8707488324","abstract_canon_sha256":"ca83fcc16e8465b821f260986546b18c069076c8afc9c6ef368aff4288fe4676"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:13.672470Z","signature_b64":"+GSFHZtKGAsO2Q6WdB5RyaVP5vqRIF8WPdkbQasxcaT5O1KPOmBjQxRL9cy0poNP4urtl2NnoYKRbs95QhO7AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1a96080cce792808896c8b0a6008c4e5db2e771a1b975e6fb1d041da0a7b1c98","last_reissued_at":"2026-05-18T01:34:13.671900Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:13.671900Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"1-supertransitive subfactors with index at most 6+1/5","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.OA","authors_text":"David Penneys, Scott Morrison, Zhengwei Liu","submitted_at":"2013-10-31T16:04:58Z","abstract_excerpt":"We classify irreducible II_1 subfactors A \\subset B such that B \\ominus A is reducible as an A-A bimodule, with index at most 6+1/5, leaving aside the composite subfactors at index exactly 6. Previous work has already achieved this up to index 3+\\sqrt{5} \\approx 5.23. We find there are exactly three such subfactors with index in (3+\\sqrt{5}, 6+1/5], all with index 3+2\\sqrt{2}. One of these comes from SO(3)_q at a root of unity, while the other two appear to be closely related, and are `braided up to a sign'."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.8566","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":"1310.8566","created_at":"2026-05-18T01:34:13.671990+00:00"},{"alias_kind":"arxiv_version","alias_value":"1310.8566v1","created_at":"2026-05-18T01:34:13.671990+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.8566","created_at":"2026-05-18T01:34:13.671990+00:00"},{"alias_kind":"pith_short_12","alias_value":"DKLAQDGOPEUA","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_16","alias_value":"DKLAQDGOPEUARCLM","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_8","alias_value":"DKLAQDGO","created_at":"2026-05-18T12:27:43.054852+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DKLAQDGOPEUARCLMRMFGACGE4X","json":"https://pith.science/pith/DKLAQDGOPEUARCLMRMFGACGE4X.json","graph_json":"https://pith.science/api/pith-number/DKLAQDGOPEUARCLMRMFGACGE4X/graph.json","events_json":"https://pith.science/api/pith-number/DKLAQDGOPEUARCLMRMFGACGE4X/events.json","paper":"https://pith.science/paper/DKLAQDGO"},"agent_actions":{"view_html":"https://pith.science/pith/DKLAQDGOPEUARCLMRMFGACGE4X","download_json":"https://pith.science/pith/DKLAQDGOPEUARCLMRMFGACGE4X.json","view_paper":"https://pith.science/paper/DKLAQDGO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1310.8566&json=true","fetch_graph":"https://pith.science/api/pith-number/DKLAQDGOPEUARCLMRMFGACGE4X/graph.json","fetch_events":"https://pith.science/api/pith-number/DKLAQDGOPEUARCLMRMFGACGE4X/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DKLAQDGOPEUARCLMRMFGACGE4X/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DKLAQDGOPEUARCLMRMFGACGE4X/action/storage_attestation","attest_author":"https://pith.science/pith/DKLAQDGOPEUARCLMRMFGACGE4X/action/author_attestation","sign_citation":"https://pith.science/pith/DKLAQDGOPEUARCLMRMFGACGE4X/action/citation_signature","submit_replication":"https://pith.science/pith/DKLAQDGOPEUARCLMRMFGACGE4X/action/replication_record"}},"created_at":"2026-05-18T01:34:13.671990+00:00","updated_at":"2026-05-18T01:34:13.671990+00:00"}