{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:XKBSHTDM6FAHE4HSLY4447CR2A","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":"88c84c647582684d79c75d2a12d24b5dab03442b32d3f2c94b2721b8ccc59930","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-10-19T12:15:06Z","title_canon_sha256":"cd6d1aa03dafa08912c0eb029bccd888e70bc78edfead33b68354b780832d9d5"},"schema_version":"1.0","source":{"id":"1710.07113","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.07113","created_at":"2026-05-18T00:18:53Z"},{"alias_kind":"arxiv_version","alias_value":"1710.07113v2","created_at":"2026-05-18T00:18:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.07113","created_at":"2026-05-18T00:18:53Z"},{"alias_kind":"pith_short_12","alias_value":"XKBSHTDM6FAH","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"XKBSHTDM6FAHE4HS","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"XKBSHTDM","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:d2ab25907b623290afd44e8bfe323e0a5bbc71aaa98f14f3b74f01dd9d02782b","target":"graph","created_at":"2026-05-18T00:18:53Z","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":"Let $G$ be a finite simple group. By a theorem of Guralnick and Kantor, $G$ contains a conjugacy class $C$ such that for each non-identity element $x \\in G$, there exists $y \\in C$ with $G = \\langle x,y\\rangle$. Building on this deep result, we introduce a new invariant $\\gamma_u(G)$, which we call the uniform domination number of $G$. This is the minimal size of a subset $S$ of conjugate elements such that for each $1 \\ne x \\in G$, there exists $s \\in S$ with $G = \\langle x, s \\rangle$. (This invariant is closely related to the total domination number of the generating graph of $G$, which exp","authors_text":"Scott Harper, Timothy C. Burness","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-10-19T12:15:06Z","title":"On the uniform domination number of a finite simple group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.07113","kind":"arxiv","version":2},"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":"sha256:47e2c430bbcb4d4339e32981cf64142503deafaf6be12d63a25520d99e72de9b","target":"record","created_at":"2026-05-18T00:18:53Z","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":"88c84c647582684d79c75d2a12d24b5dab03442b32d3f2c94b2721b8ccc59930","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-10-19T12:15:06Z","title_canon_sha256":"cd6d1aa03dafa08912c0eb029bccd888e70bc78edfead33b68354b780832d9d5"},"schema_version":"1.0","source":{"id":"1710.07113","kind":"arxiv","version":2}},"canonical_sha256":"ba8323cc6cf1407270f25e39ce7c51d016b1666e524d5f8f43aae387598143d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ba8323cc6cf1407270f25e39ce7c51d016b1666e524d5f8f43aae387598143d7","first_computed_at":"2026-05-18T00:18:53.167389Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:53.167389Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6XAckUTiXS2ADNgg3N28lmgIZCFz9Xk+Fi0YuG9CoCZwD0aEXSOxonOPm7/a1amDFHv1iHSoVBYASkzOwvqQBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:53.168008Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.07113","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:47e2c430bbcb4d4339e32981cf64142503deafaf6be12d63a25520d99e72de9b","sha256:d2ab25907b623290afd44e8bfe323e0a5bbc71aaa98f14f3b74f01dd9d02782b"],"state_sha256":"518c208e2cacad08977e3e6b13242e913b2c4445d30b0769b7f68bfcc9f753d3"}