{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:H4ZMOBPNFSF6AFZQ4ZHSHXONW2","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":"3f57e5acfba3c5919984438d6bc79fba4f6694edf8ccc9f615319b1418707dad","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-09-15T06:23:27Z","title_canon_sha256":"0d6c846d62dab92f0b455bdc20988a8d750586c239502966c04cdb3bd3c298e3"},"schema_version":"1.0","source":{"id":"1709.05068","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.05068","created_at":"2026-05-18T00:19:41Z"},{"alias_kind":"arxiv_version","alias_value":"1709.05068v3","created_at":"2026-05-18T00:19:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.05068","created_at":"2026-05-18T00:19:41Z"},{"alias_kind":"pith_short_12","alias_value":"H4ZMOBPNFSF6","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"H4ZMOBPNFSF6AFZQ","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"H4ZMOBPN","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:6d6c79e59621384e6bd4816580cda314a85e1cca00aa4ce1fa367799fcd1114b","target":"graph","created_at":"2026-05-18T00:19:41Z","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 study Brauer's long-standing $k(B)$-conjecture on the number of characters in $p$-blocks for finite quasi-simple groups and show that their blocks do not occur as a minimal counterexample for $p\\ge5$ nor in the case of abelian defect. For $p=3$ we obtain that the principal 3-blocks do not provide minimal counterexamples. We also determine the precise number of irreducible characters in unipotent blocks of classical groups for odd primes.","authors_text":"Gunter Malle","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-09-15T06:23:27Z","title":"On a minimal counterexample to Brauer's $k(B)$-conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.05068","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":"sha256:6bf2910c93ffe5e6d415c0df27976fb3dde4cf7d2711cf328ef44f7635196c98","target":"record","created_at":"2026-05-18T00:19:41Z","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":"3f57e5acfba3c5919984438d6bc79fba4f6694edf8ccc9f615319b1418707dad","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-09-15T06:23:27Z","title_canon_sha256":"0d6c846d62dab92f0b455bdc20988a8d750586c239502966c04cdb3bd3c298e3"},"schema_version":"1.0","source":{"id":"1709.05068","kind":"arxiv","version":3}},"canonical_sha256":"3f32c705ed2c8be01730e64f23ddcdb6be9a38910d7bba62ccde0419594e2587","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3f32c705ed2c8be01730e64f23ddcdb6be9a38910d7bba62ccde0419594e2587","first_computed_at":"2026-05-18T00:19:41.837623Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:19:41.837623Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HvoQFGug8lKdGvl69wMW5bApJ6pxid0zhqwnl7IPloupD/bq7E8llcr7wbz1oITqLkFfJNc1AzQ5r9rEY6KtBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:19:41.838388Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.05068","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6bf2910c93ffe5e6d415c0df27976fb3dde4cf7d2711cf328ef44f7635196c98","sha256:6d6c79e59621384e6bd4816580cda314a85e1cca00aa4ce1fa367799fcd1114b"],"state_sha256":"7fe2f9ae1e80698427d7213b9bfda179705f487eb1107ff7ef46f517292df057"}