{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:CM5RGAYAK4R52EUE25UDZIB5AW","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":"3de2b737f4b2983dbde25b273fb27c7fcc9264a8077fc18e5fd8f3b4b7ee089b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-11-05T14:37:12Z","title_canon_sha256":"bca8615eec508cae848d245db08f53c4670756229c65e5e288e9e4a051759281"},"schema_version":"1.0","source":{"id":"1811.01736","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.01736","created_at":"2026-05-18T00:01:33Z"},{"alias_kind":"arxiv_version","alias_value":"1811.01736v1","created_at":"2026-05-18T00:01:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.01736","created_at":"2026-05-18T00:01:33Z"},{"alias_kind":"pith_short_12","alias_value":"CM5RGAYAK4R5","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"CM5RGAYAK4R52EUE","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"CM5RGAYA","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:ba6cf7542d64826560ec134b4413f2a4457070abbc56a464eec0a8bce7552f5a","target":"graph","created_at":"2026-05-18T00:01:33Z","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":"The goal of this paper is to generalize several group theoretic concepts such as the center and commutator subgroup, central series, and ultimately nilpotence to a supercharacter theoretic setting, and to use these concepts to show that there can be a strong connection between the structure of a group and the structure of its supercharacter theories. We then use these concepts to show that the upper and lower annihilator series of $J$ can be described in terms of certain central series for the algebra group $G=1+J$ defined by $\\mathsf{S}$, when $\\mathsf{S}$ is the algebra group supercharacter ","authors_text":"Shawn T. Burkett","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-11-05T14:37:12Z","title":"An analog of nilpotence arising from supercharacter theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.01736","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":"sha256:2d62cfa14aee926057b223728cef5788c925daa85db7b1b53c073872a3d7285f","target":"record","created_at":"2026-05-18T00:01:33Z","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":"3de2b737f4b2983dbde25b273fb27c7fcc9264a8077fc18e5fd8f3b4b7ee089b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-11-05T14:37:12Z","title_canon_sha256":"bca8615eec508cae848d245db08f53c4670756229c65e5e288e9e4a051759281"},"schema_version":"1.0","source":{"id":"1811.01736","kind":"arxiv","version":1}},"canonical_sha256":"133b1303005723dd1284d7683ca03d059aeb0154acfc5aaa3bd4d7936e937c98","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"133b1303005723dd1284d7683ca03d059aeb0154acfc5aaa3bd4d7936e937c98","first_computed_at":"2026-05-18T00:01:33.418333Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:33.418333Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q/G2etJ7quGf1ES2QTxAKNjl1CtXjJ4EJM0QM93UP7bqtzlbGTKX8kkE//QmEBDpVfQOu1Hh8nS4W/PM/I7cCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:33.418802Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.01736","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d62cfa14aee926057b223728cef5788c925daa85db7b1b53c073872a3d7285f","sha256:ba6cf7542d64826560ec134b4413f2a4457070abbc56a464eec0a8bce7552f5a"],"state_sha256":"51a005eb203696ab1f1f8c709a44aea4d72911dfe41db63153a6db989b14d59c"}