{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:JKZM4UA52U7TXFDT3N2S3AL3BS","short_pith_number":"pith:JKZM4UA5","schema_version":"1.0","canonical_sha256":"4ab2ce501dd53f3b9473db752d817b0c8380b92e1dd64ce141843ffc9e34b678","source":{"kind":"arxiv","id":"1706.05611","version":1},"attestation_state":"computed","paper":{"title":"On vanishing class sizes in finite groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Emanuele Pacifici, Julian M.A. Brough, Mariagrazia Bianchi, Rachel D. Camina","submitted_at":"2017-06-18T06:31:57Z","abstract_excerpt":"Let $G$ be a finite group. An element $g$ of $G$ is called a vanishing element if there exists an irreducible character $\\chi$ of $G$ such that $\\chi(g) = 0$; in this case, we say that the conjugacy class of $g$ is a vanishing conjugacy class. In this paper, we discuss some arithmetical properties concerning the sizes of the vanishing conjugacy classes in a finite 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":"1706.05611","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-06-18T06:31:57Z","cross_cats_sorted":[],"title_canon_sha256":"01fdfd265cc18f450e5d22d8e03bf19ef88c2e54174b38312a9bef02a0c5b5e5","abstract_canon_sha256":"b9b2a67458ceb12d71ed7d30987857d932203891ca8d621a92344cf73d4dd620"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:09.410082Z","signature_b64":"Pa4lGsUOMxTT4bjrd73TyqkLZXrrS5novZFVODAJkkLXgwyJggFI6zVrwqof3nFH5pqjGJhrWU1hvIrruNkhCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4ab2ce501dd53f3b9473db752d817b0c8380b92e1dd64ce141843ffc9e34b678","last_reissued_at":"2026-05-18T00:42:09.409678Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:09.409678Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On vanishing class sizes in finite groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Emanuele Pacifici, Julian M.A. Brough, Mariagrazia Bianchi, Rachel D. Camina","submitted_at":"2017-06-18T06:31:57Z","abstract_excerpt":"Let $G$ be a finite group. An element $g$ of $G$ is called a vanishing element if there exists an irreducible character $\\chi$ of $G$ such that $\\chi(g) = 0$; in this case, we say that the conjugacy class of $g$ is a vanishing conjugacy class. In this paper, we discuss some arithmetical properties concerning the sizes of the vanishing conjugacy classes in a finite group."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.05611","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":"1706.05611","created_at":"2026-05-18T00:42:09.409743+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.05611v1","created_at":"2026-05-18T00:42:09.409743+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.05611","created_at":"2026-05-18T00:42:09.409743+00:00"},{"alias_kind":"pith_short_12","alias_value":"JKZM4UA52U7T","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_16","alias_value":"JKZM4UA52U7TXFDT","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_8","alias_value":"JKZM4UA5","created_at":"2026-05-18T12:31:24.725408+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/JKZM4UA52U7TXFDT3N2S3AL3BS","json":"https://pith.science/pith/JKZM4UA52U7TXFDT3N2S3AL3BS.json","graph_json":"https://pith.science/api/pith-number/JKZM4UA52U7TXFDT3N2S3AL3BS/graph.json","events_json":"https://pith.science/api/pith-number/JKZM4UA52U7TXFDT3N2S3AL3BS/events.json","paper":"https://pith.science/paper/JKZM4UA5"},"agent_actions":{"view_html":"https://pith.science/pith/JKZM4UA52U7TXFDT3N2S3AL3BS","download_json":"https://pith.science/pith/JKZM4UA52U7TXFDT3N2S3AL3BS.json","view_paper":"https://pith.science/paper/JKZM4UA5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.05611&json=true","fetch_graph":"https://pith.science/api/pith-number/JKZM4UA52U7TXFDT3N2S3AL3BS/graph.json","fetch_events":"https://pith.science/api/pith-number/JKZM4UA52U7TXFDT3N2S3AL3BS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JKZM4UA52U7TXFDT3N2S3AL3BS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JKZM4UA52U7TXFDT3N2S3AL3BS/action/storage_attestation","attest_author":"https://pith.science/pith/JKZM4UA52U7TXFDT3N2S3AL3BS/action/author_attestation","sign_citation":"https://pith.science/pith/JKZM4UA52U7TXFDT3N2S3AL3BS/action/citation_signature","submit_replication":"https://pith.science/pith/JKZM4UA52U7TXFDT3N2S3AL3BS/action/replication_record"}},"created_at":"2026-05-18T00:42:09.409743+00:00","updated_at":"2026-05-18T00:42:09.409743+00:00"}