{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:FNOXOSEDF326WZ4V66XCH5TRPX","short_pith_number":"pith:FNOXOSED","schema_version":"1.0","canonical_sha256":"2b5d7748832ef5eb6795f7ae23f6717df8e476bd63f3b7182c26dfb9759174ae","source":{"kind":"arxiv","id":"1303.4748","version":1},"attestation_state":"computed","paper":{"title":"Classification of integral modular categories of Frobenius-Perron dimension pq^4 and p^2q^2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"C\\'esar Galindo, Deepak Naidu, Eric. C. Rowell, Julia Yael Plavnik, Paul Bruillard, Seung-Moon Hong, Sonia Natale, Yevgenia Kashina","submitted_at":"2013-03-19T20:05:55Z","abstract_excerpt":"We classify integral modular categories of dimension pq^4 and p^2q^2 where p and q are distinct primes. We show that such categories are always group-theoretical except for categories of dimension 4q^2. In these cases there are well-known examples of non-group-theoretical categories, coming from centers of Tambara-Yamagami categories and quantum groups. We show that a non-group-theoretical integral modular category of dimension 4q^2 is equivalent to either one of these well-known examples or is of dimension 36 and is twist-equivalent to fusion categories arising from a certain quantum group."},"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":"1303.4748","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-03-19T20:05:55Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"5e88ebceae5a2eb47459e40b04c1ce5bc30d2671a3c9132989540ece728eec1b","abstract_canon_sha256":"c11238dd27e1317c84f97f995488f00971a84639b3f0f50bf5554f0570ec4aa0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:30:25.000011Z","signature_b64":"MyZ2iPwKnCgs720bmeRoqHUyK3VdIEJoHw2jMOAcZ3X3x/CXDayddABVAjd1ZAVWR6xTqiMbZ4yLBfyoO1o4DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b5d7748832ef5eb6795f7ae23f6717df8e476bd63f3b7182c26dfb9759174ae","last_reissued_at":"2026-05-18T03:30:24.999527Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:30:24.999527Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Classification of integral modular categories of Frobenius-Perron dimension pq^4 and p^2q^2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"C\\'esar Galindo, Deepak Naidu, Eric. C. Rowell, Julia Yael Plavnik, Paul Bruillard, Seung-Moon Hong, Sonia Natale, Yevgenia Kashina","submitted_at":"2013-03-19T20:05:55Z","abstract_excerpt":"We classify integral modular categories of dimension pq^4 and p^2q^2 where p and q are distinct primes. We show that such categories are always group-theoretical except for categories of dimension 4q^2. In these cases there are well-known examples of non-group-theoretical categories, coming from centers of Tambara-Yamagami categories and quantum groups. We show that a non-group-theoretical integral modular category of dimension 4q^2 is equivalent to either one of these well-known examples or is of dimension 36 and is twist-equivalent to fusion categories arising from a certain quantum group."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.4748","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":"1303.4748","created_at":"2026-05-18T03:30:24.999593+00:00"},{"alias_kind":"arxiv_version","alias_value":"1303.4748v1","created_at":"2026-05-18T03:30:24.999593+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.4748","created_at":"2026-05-18T03:30:24.999593+00:00"},{"alias_kind":"pith_short_12","alias_value":"FNOXOSEDF326","created_at":"2026-05-18T12:27:45.050594+00:00"},{"alias_kind":"pith_short_16","alias_value":"FNOXOSEDF326WZ4V","created_at":"2026-05-18T12:27:45.050594+00:00"},{"alias_kind":"pith_short_8","alias_value":"FNOXOSED","created_at":"2026-05-18T12:27:45.050594+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/FNOXOSEDF326WZ4V66XCH5TRPX","json":"https://pith.science/pith/FNOXOSEDF326WZ4V66XCH5TRPX.json","graph_json":"https://pith.science/api/pith-number/FNOXOSEDF326WZ4V66XCH5TRPX/graph.json","events_json":"https://pith.science/api/pith-number/FNOXOSEDF326WZ4V66XCH5TRPX/events.json","paper":"https://pith.science/paper/FNOXOSED"},"agent_actions":{"view_html":"https://pith.science/pith/FNOXOSEDF326WZ4V66XCH5TRPX","download_json":"https://pith.science/pith/FNOXOSEDF326WZ4V66XCH5TRPX.json","view_paper":"https://pith.science/paper/FNOXOSED","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1303.4748&json=true","fetch_graph":"https://pith.science/api/pith-number/FNOXOSEDF326WZ4V66XCH5TRPX/graph.json","fetch_events":"https://pith.science/api/pith-number/FNOXOSEDF326WZ4V66XCH5TRPX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FNOXOSEDF326WZ4V66XCH5TRPX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FNOXOSEDF326WZ4V66XCH5TRPX/action/storage_attestation","attest_author":"https://pith.science/pith/FNOXOSEDF326WZ4V66XCH5TRPX/action/author_attestation","sign_citation":"https://pith.science/pith/FNOXOSEDF326WZ4V66XCH5TRPX/action/citation_signature","submit_replication":"https://pith.science/pith/FNOXOSEDF326WZ4V66XCH5TRPX/action/replication_record"}},"created_at":"2026-05-18T03:30:24.999593+00:00","updated_at":"2026-05-18T03:30:24.999593+00:00"}