{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:6IIK5P6L2CAG5U7TUU7GKWEAJ7","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":"438c81ae5048ed12e3d9ae485fdb4c6799c870a09d7b5c0fae52873aa4c66484","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-03-11T18:31:15Z","title_canon_sha256":"38880ad5f3edb5db83ff7e669c1ab9ff87b2fbd40a137940843026c0e8be3a64"},"schema_version":"1.0","source":{"id":"1403.2679","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.2679","created_at":"2026-05-18T02:56:42Z"},{"alias_kind":"arxiv_version","alias_value":"1403.2679v1","created_at":"2026-05-18T02:56:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.2679","created_at":"2026-05-18T02:56:42Z"},{"alias_kind":"pith_short_12","alias_value":"6IIK5P6L2CAG","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6IIK5P6L2CAG5U7T","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6IIK5P6L","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:c668549c36d6a4d3c1c8bcff206953b3ddfce8f3bfa2fb9070a6d7cc016394b2","target":"graph","created_at":"2026-05-18T02:56:42Z","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 classify closed abelian subgroups of the simple groups $G_2$, $F_4$, $Aut(so(8))$ having centralizer the same dimension as the dimension of the subgroup, as well as finite abelian subgroups of certain spin and half-spin groups having finite centralizer.","authors_text":"Jun Yu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-03-11T18:31:15Z","title":"Maximal abelian subgroups of Spin groups and some exceptional simple Lie groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.2679","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":"sha256:895df17f3cfad0d06d02968d41dfcad8fb3b4aa6f121e896c689458777db0d8b","target":"record","created_at":"2026-05-18T02:56:42Z","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":"438c81ae5048ed12e3d9ae485fdb4c6799c870a09d7b5c0fae52873aa4c66484","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-03-11T18:31:15Z","title_canon_sha256":"38880ad5f3edb5db83ff7e669c1ab9ff87b2fbd40a137940843026c0e8be3a64"},"schema_version":"1.0","source":{"id":"1403.2679","kind":"arxiv","version":1}},"canonical_sha256":"f210aebfcbd0806ed3f3a53e6558804fcfa66f6f107078339e0a32febcdb0e96","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f210aebfcbd0806ed3f3a53e6558804fcfa66f6f107078339e0a32febcdb0e96","first_computed_at":"2026-05-18T02:56:42.804489Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:56:42.804489Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q/2HV6pfvQ54GWLDQBoZhKf4LdU7gblAGaBXnjBykkMy6Mpey3QaiGpTry9gvhT7YPtSBQAK8fLprcXX6nSTBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:56:42.804917Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.2679","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:895df17f3cfad0d06d02968d41dfcad8fb3b4aa6f121e896c689458777db0d8b","sha256:c668549c36d6a4d3c1c8bcff206953b3ddfce8f3bfa2fb9070a6d7cc016394b2"],"state_sha256":"8e6a2454226e43935ccfca65289a5edab8c3389c79a4b6ee9bd7d67db8fcd73f"}