{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:FJAAXMI2PVHEJAVIN5XORAULNK","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":"789931dede3f6841027f6acc666d8073911b797930e54b6b69ca85f8e3ad4fd9","cross_cats_sorted":["math.AT","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-10-21T15:29:05Z","title_canon_sha256":"26780e59639bc3bca8c5747f8d53fd268406ccfcb32e7bbbff669711116e7f71"},"schema_version":"1.0","source":{"id":"1410.5705","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.5705","created_at":"2026-05-18T02:39:39Z"},{"alias_kind":"arxiv_version","alias_value":"1410.5705v1","created_at":"2026-05-18T02:39:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.5705","created_at":"2026-05-18T02:39:39Z"},{"alias_kind":"pith_short_12","alias_value":"FJAAXMI2PVHE","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"FJAAXMI2PVHEJAVI","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"FJAAXMI2","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:e76b5d1ce4d0eba292ef900ae7a446660caf0db13c4fd8bfe097244f55703d1b","target":"graph","created_at":"2026-05-18T02:39:39Z","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":"Suppose that all nontrivial subsections of a $p$-block $B$ are conjugate (where $p$ is a prime). By using the classification of the finite simple groups, we prove that the defect groups of $B$ are either extraspecial of order $p^3$ with $p \\in \\{3,5\\}$ or elementary abelian.","authors_text":"Benjamin Sambale, Burkhard K\\\"ulshammer, L\\'azl\\'o H\\'ethelyi, Radha Kessar","cross_cats":["math.AT","math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-10-21T15:29:05Z","title":"Blocks with transitive fusion systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.5705","kind":"arxiv","version":1},"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:a2a2360b8b92daad8cfd943643af527a1f4af0353e0c905c52ed02ce2de500ef","target":"record","created_at":"2026-05-18T02:39:39Z","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":"789931dede3f6841027f6acc666d8073911b797930e54b6b69ca85f8e3ad4fd9","cross_cats_sorted":["math.AT","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-10-21T15:29:05Z","title_canon_sha256":"26780e59639bc3bca8c5747f8d53fd268406ccfcb32e7bbbff669711116e7f71"},"schema_version":"1.0","source":{"id":"1410.5705","kind":"arxiv","version":1}},"canonical_sha256":"2a400bb11a7d4e4482a86f6ee8828b6ab34dc6fa51a317da7daa949f1a35c5e7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2a400bb11a7d4e4482a86f6ee8828b6ab34dc6fa51a317da7daa949f1a35c5e7","first_computed_at":"2026-05-18T02:39:39.275430Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:39:39.275430Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Hos0u2CM+Q6YbnQk0t1yo/jPRGbUEyaeBP7DiE1b4ukTeXC2z3FdUlDhELRoZuj8ZLhSliLRjEc8X9uIjQemAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:39:39.275992Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.5705","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a2a2360b8b92daad8cfd943643af527a1f4af0353e0c905c52ed02ce2de500ef","sha256:e76b5d1ce4d0eba292ef900ae7a446660caf0db13c4fd8bfe097244f55703d1b"],"state_sha256":"8aa06ff233adac848e97ffc096c7580cf83fc1a89e7e294a6d8d1e7a31b14565"}