{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:G7BHNJ77UYU6ONOYZQMACWASXB","short_pith_number":"pith:G7BHNJ77","canonical_record":{"source":{"id":"1601.05373","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-01-20T19:05:26Z","cross_cats_sorted":[],"title_canon_sha256":"285f36c7c1e13f0217f3272cd6415aed434b8bfb227519935871fd47b52a16c4","abstract_canon_sha256":"0ee2ab6e775da257777f5ce1dcb1bf07051d327d3b882b7e49fe4889492f70e7"},"schema_version":"1.0"},"canonical_sha256":"37c276a7ffa629e735d8cc18015812b864ca92d2e56b761d650049c36eb5acb1","source":{"kind":"arxiv","id":"1601.05373","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.05373","created_at":"2026-05-18T01:11:41Z"},{"alias_kind":"arxiv_version","alias_value":"1601.05373v3","created_at":"2026-05-18T01:11:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.05373","created_at":"2026-05-18T01:11:41Z"},{"alias_kind":"pith_short_12","alias_value":"G7BHNJ77UYU6","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"G7BHNJ77UYU6ONOY","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"G7BHNJ77","created_at":"2026-05-18T12:30:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:G7BHNJ77UYU6ONOYZQMACWASXB","target":"record","payload":{"canonical_record":{"source":{"id":"1601.05373","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-01-20T19:05:26Z","cross_cats_sorted":[],"title_canon_sha256":"285f36c7c1e13f0217f3272cd6415aed434b8bfb227519935871fd47b52a16c4","abstract_canon_sha256":"0ee2ab6e775da257777f5ce1dcb1bf07051d327d3b882b7e49fe4889492f70e7"},"schema_version":"1.0"},"canonical_sha256":"37c276a7ffa629e735d8cc18015812b864ca92d2e56b761d650049c36eb5acb1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:41.177414Z","signature_b64":"GhsY/IjqnRXMSIT5fJcmnAsMWuzFM+EpfAXNNY5dMwE0+DfqSyCKhueuug+JYBJXgCxDm2ewPRJT9oGl7ElDAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"37c276a7ffa629e735d8cc18015812b864ca92d2e56b761d650049c36eb5acb1","last_reissued_at":"2026-05-18T01:11:41.177032Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:41.177032Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.05373","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:11:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nqGQwh+tEJ7BqdyaQ8X1cVNMM82Nq6BLFdbNhy/xaNlfA7BSwjKU2QY0Cy8lBXEmSNpg0xC+usOuN2DhEcxUAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T06:29:46.556295Z"},"content_sha256":"835bd548066c14e755fae62e09d77e71c941bf1c2fe506c17a230a94096e2bfa","schema_version":"1.0","event_id":"sha256:835bd548066c14e755fae62e09d77e71c941bf1c2fe506c17a230a94096e2bfa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:G7BHNJ77UYU6ONOYZQMACWASXB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Brauer characters of $q^\\prime$- degree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Hung P. Tong-Viet, Mark L. Lewis","submitted_at":"2016-01-20T19:05:26Z","abstract_excerpt":"We show that if $p$ is a prime and $G$ is a finite $p$-solvable group satisfying the condition that a prime $q$ divides the degree of no irreducible $p$-Brauer character of $G$, then the normalizer of some Sylow $q$-subgroup of $G$ meets all the conjugacy classes of $p$-regular elements of $G$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.05373","kind":"arxiv","version":3},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:11:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0FF00Z/0RjRlzNLp5uI16jlu7oX8HARBOp4B4dY+LaeBzzjBf1w/S5mTvhMRgPZymvrh6JxxjE3R4Mnw5CoJCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T06:29:46.556673Z"},"content_sha256":"6c9c0717af818126b595b3a1fa8723209bb05dd885f3dca91ba361639fa60496","schema_version":"1.0","event_id":"sha256:6c9c0717af818126b595b3a1fa8723209bb05dd885f3dca91ba361639fa60496"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G7BHNJ77UYU6ONOYZQMACWASXB/bundle.json","state_url":"https://pith.science/pith/G7BHNJ77UYU6ONOYZQMACWASXB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G7BHNJ77UYU6ONOYZQMACWASXB/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-20T06:29:46Z","links":{"resolver":"https://pith.science/pith/G7BHNJ77UYU6ONOYZQMACWASXB","bundle":"https://pith.science/pith/G7BHNJ77UYU6ONOYZQMACWASXB/bundle.json","state":"https://pith.science/pith/G7BHNJ77UYU6ONOYZQMACWASXB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G7BHNJ77UYU6ONOYZQMACWASXB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:G7BHNJ77UYU6ONOYZQMACWASXB","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"0ee2ab6e775da257777f5ce1dcb1bf07051d327d3b882b7e49fe4889492f70e7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-01-20T19:05:26Z","title_canon_sha256":"285f36c7c1e13f0217f3272cd6415aed434b8bfb227519935871fd47b52a16c4"},"schema_version":"1.0","source":{"id":"1601.05373","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.05373","created_at":"2026-05-18T01:11:41Z"},{"alias_kind":"arxiv_version","alias_value":"1601.05373v3","created_at":"2026-05-18T01:11:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.05373","created_at":"2026-05-18T01:11:41Z"},{"alias_kind":"pith_short_12","alias_value":"G7BHNJ77UYU6","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"G7BHNJ77UYU6ONOY","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"G7BHNJ77","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:6c9c0717af818126b595b3a1fa8723209bb05dd885f3dca91ba361639fa60496","target":"graph","created_at":"2026-05-18T01:11:41Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We show that if $p$ is a prime and $G$ is a finite $p$-solvable group satisfying the condition that a prime $q$ divides the degree of no irreducible $p$-Brauer character of $G$, then the normalizer of some Sylow $q$-subgroup of $G$ meets all the conjugacy classes of $p$-regular elements of $G$.","authors_text":"Hung P. Tong-Viet, Mark L. Lewis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-01-20T19:05:26Z","title":"Brauer characters of $q^\\prime$- degree"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.05373","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:835bd548066c14e755fae62e09d77e71c941bf1c2fe506c17a230a94096e2bfa","target":"record","created_at":"2026-05-18T01:11:41Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"0ee2ab6e775da257777f5ce1dcb1bf07051d327d3b882b7e49fe4889492f70e7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-01-20T19:05:26Z","title_canon_sha256":"285f36c7c1e13f0217f3272cd6415aed434b8bfb227519935871fd47b52a16c4"},"schema_version":"1.0","source":{"id":"1601.05373","kind":"arxiv","version":3}},"canonical_sha256":"37c276a7ffa629e735d8cc18015812b864ca92d2e56b761d650049c36eb5acb1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"37c276a7ffa629e735d8cc18015812b864ca92d2e56b761d650049c36eb5acb1","first_computed_at":"2026-05-18T01:11:41.177032Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:41.177032Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GhsY/IjqnRXMSIT5fJcmnAsMWuzFM+EpfAXNNY5dMwE0+DfqSyCKhueuug+JYBJXgCxDm2ewPRJT9oGl7ElDAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:41.177414Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.05373","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:835bd548066c14e755fae62e09d77e71c941bf1c2fe506c17a230a94096e2bfa","sha256:6c9c0717af818126b595b3a1fa8723209bb05dd885f3dca91ba361639fa60496"],"state_sha256":"c5061d139d6c34fed85031fb2c065095d5cba295d4fcb446aaf5d13428778eb8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U7GoktHVaUgOSpD4niYVlnxvm9N26NiWCrezqZECc9TpMZj8Q66AsT1JLLlZSP+wB2NAZu6aiRQn/1UIKls8Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T06:29:46.558675Z","bundle_sha256":"1569282f55e0257600ac8ad96be0cddd9a412e8acf7b5b06f4d1a7a655879bc9"}}