{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:AMCPQ2PRY4PLQ4PW5MSTC7G3RT","short_pith_number":"pith:AMCPQ2PR","schema_version":"1.0","canonical_sha256":"0304f869f1c71eb871f6eb25317cdb8cea98ddb9ca7ab4d569e955336cf15c4f","source":{"kind":"arxiv","id":"1601.06380","version":2},"attestation_state":"computed","paper":{"title":"On groups with the same character degrees as almost simple groups with socle sporadic simple groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Ali Jafari, Ashraf Daneshkhah, Seyed Hassan Alavi","submitted_at":"2016-01-24T13:08:57Z","abstract_excerpt":"Let G be a finite group and cd(G) denote the set of complex irreducible character degrees of G. In this paper, we prove that if G is a finite group and H is an almost simple group whose socle is a sporadic simple group H0 such that cd(G) = cd(H), then G' = H0 and there exists an abelian subgroup A of G such that G/A is isomorphic to H. In view of Huppert's conjecture (2000), we also provide some examples to show that G is not necessarily a direct product of A and H, and hence we cannot extend this conjecture to almost simple groups."},"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":"1601.06380","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-01-24T13:08:57Z","cross_cats_sorted":[],"title_canon_sha256":"f6336fa30335cfe3256f98c1afe9ecf0048434e3fd14a0965736346dfcc40218","abstract_canon_sha256":"3be865b837a602b8ec904098411e351666be830879d5b6ee3394be9d5f313687"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:53.077926Z","signature_b64":"ILEb/xXV8GZ4cEyxJB2kwKH6QVSQ3f235UZ4wCUalxgiuHNldECLo92mFAGv1DVH9H51ZujetaDPngzTBrRkAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0304f869f1c71eb871f6eb25317cdb8cea98ddb9ca7ab4d569e955336cf15c4f","last_reissued_at":"2026-05-18T01:19:53.077342Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:53.077342Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On groups with the same character degrees as almost simple groups with socle sporadic simple groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Ali Jafari, Ashraf Daneshkhah, Seyed Hassan Alavi","submitted_at":"2016-01-24T13:08:57Z","abstract_excerpt":"Let G be a finite group and cd(G) denote the set of complex irreducible character degrees of G. In this paper, we prove that if G is a finite group and H is an almost simple group whose socle is a sporadic simple group H0 such that cd(G) = cd(H), then G' = H0 and there exists an abelian subgroup A of G such that G/A is isomorphic to H. In view of Huppert's conjecture (2000), we also provide some examples to show that G is not necessarily a direct product of A and H, and hence we cannot extend this conjecture to almost simple groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.06380","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":"1601.06380","created_at":"2026-05-18T01:19:53.077430+00:00"},{"alias_kind":"arxiv_version","alias_value":"1601.06380v2","created_at":"2026-05-18T01:19:53.077430+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.06380","created_at":"2026-05-18T01:19:53.077430+00:00"},{"alias_kind":"pith_short_12","alias_value":"AMCPQ2PRY4PL","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_16","alias_value":"AMCPQ2PRY4PLQ4PW","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_8","alias_value":"AMCPQ2PR","created_at":"2026-05-18T12:30:07.202191+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/AMCPQ2PRY4PLQ4PW5MSTC7G3RT","json":"https://pith.science/pith/AMCPQ2PRY4PLQ4PW5MSTC7G3RT.json","graph_json":"https://pith.science/api/pith-number/AMCPQ2PRY4PLQ4PW5MSTC7G3RT/graph.json","events_json":"https://pith.science/api/pith-number/AMCPQ2PRY4PLQ4PW5MSTC7G3RT/events.json","paper":"https://pith.science/paper/AMCPQ2PR"},"agent_actions":{"view_html":"https://pith.science/pith/AMCPQ2PRY4PLQ4PW5MSTC7G3RT","download_json":"https://pith.science/pith/AMCPQ2PRY4PLQ4PW5MSTC7G3RT.json","view_paper":"https://pith.science/paper/AMCPQ2PR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1601.06380&json=true","fetch_graph":"https://pith.science/api/pith-number/AMCPQ2PRY4PLQ4PW5MSTC7G3RT/graph.json","fetch_events":"https://pith.science/api/pith-number/AMCPQ2PRY4PLQ4PW5MSTC7G3RT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AMCPQ2PRY4PLQ4PW5MSTC7G3RT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AMCPQ2PRY4PLQ4PW5MSTC7G3RT/action/storage_attestation","attest_author":"https://pith.science/pith/AMCPQ2PRY4PLQ4PW5MSTC7G3RT/action/author_attestation","sign_citation":"https://pith.science/pith/AMCPQ2PRY4PLQ4PW5MSTC7G3RT/action/citation_signature","submit_replication":"https://pith.science/pith/AMCPQ2PRY4PLQ4PW5MSTC7G3RT/action/replication_record"}},"created_at":"2026-05-18T01:19:53.077430+00:00","updated_at":"2026-05-18T01:19:53.077430+00:00"}