{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:DS4IRAO4LMVJYWSUC6VGFB6BSJ","short_pith_number":"pith:DS4IRAO4","schema_version":"1.0","canonical_sha256":"1cb88881dc5b2a9c5a5417aa6287c19262e23174c4de24d12bcc16480280b008","source":{"kind":"arxiv","id":"1512.02012","version":2},"attestation_state":"computed","paper":{"title":"Integral almost square-free modular categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.CT","authors_text":"Jingcheng Dong, Libin Li, Li Dai","submitted_at":"2015-12-07T12:31:19Z","abstract_excerpt":"We study integral almost square-free modular categories; i.e., integral modular categories of Frobenius-Perron dimension $p^nm$, where $p$ is a prime number, $m$ is a square-free natural number and ${\\rm gcd}(p,m)=1$. We prove that if $n\\leq 5$ or $m$ is prime with $m<p$ then they are group-theoretical. This generalizes several results in the literature and gives a partial answer to the question posed by the first author and H. Tucker. As an application, we prove that an integral modular category whose Frobenius-Perron dimensions is odd and less than $1125$ is group-theoretical."},"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":"1512.02012","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2015-12-07T12:31:19Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"54432630166aced16098556d8bd2b89b61e595f799734da2db6a7b446cee06d4","abstract_canon_sha256":"9fe65e15f2bf8ffca1dcbde476dc3b0628c5a7897a61f72821d1d96f1d8b8dc1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:14:17.570816Z","signature_b64":"P+YSvX+wjN3DyPKJsZQ683OTn/PN69lZjlsQnXCMwDSldM/g8RlW0q6e4DEdmfWkH5suTXpKLIS7bMlc41t2CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1cb88881dc5b2a9c5a5417aa6287c19262e23174c4de24d12bcc16480280b008","last_reissued_at":"2026-05-18T01:14:17.570280Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:14:17.570280Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Integral almost square-free modular categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.CT","authors_text":"Jingcheng Dong, Libin Li, Li Dai","submitted_at":"2015-12-07T12:31:19Z","abstract_excerpt":"We study integral almost square-free modular categories; i.e., integral modular categories of Frobenius-Perron dimension $p^nm$, where $p$ is a prime number, $m$ is a square-free natural number and ${\\rm gcd}(p,m)=1$. We prove that if $n\\leq 5$ or $m$ is prime with $m<p$ then they are group-theoretical. This generalizes several results in the literature and gives a partial answer to the question posed by the first author and H. Tucker. As an application, we prove that an integral modular category whose Frobenius-Perron dimensions is odd and less than $1125$ is group-theoretical."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.02012","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":"1512.02012","created_at":"2026-05-18T01:14:17.570380+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.02012v2","created_at":"2026-05-18T01:14:17.570380+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.02012","created_at":"2026-05-18T01:14:17.570380+00:00"},{"alias_kind":"pith_short_12","alias_value":"DS4IRAO4LMVJ","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_16","alias_value":"DS4IRAO4LMVJYWSU","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_8","alias_value":"DS4IRAO4","created_at":"2026-05-18T12:29:17.054201+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/DS4IRAO4LMVJYWSUC6VGFB6BSJ","json":"https://pith.science/pith/DS4IRAO4LMVJYWSUC6VGFB6BSJ.json","graph_json":"https://pith.science/api/pith-number/DS4IRAO4LMVJYWSUC6VGFB6BSJ/graph.json","events_json":"https://pith.science/api/pith-number/DS4IRAO4LMVJYWSUC6VGFB6BSJ/events.json","paper":"https://pith.science/paper/DS4IRAO4"},"agent_actions":{"view_html":"https://pith.science/pith/DS4IRAO4LMVJYWSUC6VGFB6BSJ","download_json":"https://pith.science/pith/DS4IRAO4LMVJYWSUC6VGFB6BSJ.json","view_paper":"https://pith.science/paper/DS4IRAO4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.02012&json=true","fetch_graph":"https://pith.science/api/pith-number/DS4IRAO4LMVJYWSUC6VGFB6BSJ/graph.json","fetch_events":"https://pith.science/api/pith-number/DS4IRAO4LMVJYWSUC6VGFB6BSJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DS4IRAO4LMVJYWSUC6VGFB6BSJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DS4IRAO4LMVJYWSUC6VGFB6BSJ/action/storage_attestation","attest_author":"https://pith.science/pith/DS4IRAO4LMVJYWSUC6VGFB6BSJ/action/author_attestation","sign_citation":"https://pith.science/pith/DS4IRAO4LMVJYWSUC6VGFB6BSJ/action/citation_signature","submit_replication":"https://pith.science/pith/DS4IRAO4LMVJYWSUC6VGFB6BSJ/action/replication_record"}},"created_at":"2026-05-18T01:14:17.570380+00:00","updated_at":"2026-05-18T01:14:17.570380+00:00"}