{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:YA2SJF5UCMJHMA3RVJM5OK3F43","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":"aaae9446602cb36574c1025d1d36dbf7ba7ec003f4d094a4780aec3c7bacd537","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-01-01T01:38:30Z","title_canon_sha256":"62515982c1dbe11cdc943c240ff94acbacaeaaceb4e1bc84bea37083f9c0bd6e"},"schema_version":"1.0","source":{"id":"1801.00381","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.00381","created_at":"2026-05-18T00:17:32Z"},{"alias_kind":"arxiv_version","alias_value":"1801.00381v2","created_at":"2026-05-18T00:17:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.00381","created_at":"2026-05-18T00:17:32Z"},{"alias_kind":"pith_short_12","alias_value":"YA2SJF5UCMJH","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"YA2SJF5UCMJHMA3R","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"YA2SJF5U","created_at":"2026-05-18T12:33:04Z"}],"graph_snapshots":[{"event_id":"sha256:209a5c5b8f993b4241f4394e1a903a7cd983a6779d26ec15c54a75060576a83c","target":"graph","created_at":"2026-05-18T00:17:32Z","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 extend Borel's theorem on the dominance of word maps from semisimple algebraic groups to some perfect groups. In another direction, we generalize Borel's theorem to some words with constants. We also consider the surjectivity problem for particular words and groups, give a brief survey of recent results, present some generalizations and variations and discuss various approaches, with emphasis on new ideas, constructions and connections.","authors_text":"Boris Kunyavskii, Eugene Plotkin, Nikolai Gordeev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-01-01T01:38:30Z","title":"Word maps on perfect algebraic groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.00381","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":"sha256:560df4952fe18fdeb53c9c0f9b53daf352df8740a307c3ef1ee7174d1e242e5f","target":"record","created_at":"2026-05-18T00:17:32Z","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":"aaae9446602cb36574c1025d1d36dbf7ba7ec003f4d094a4780aec3c7bacd537","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-01-01T01:38:30Z","title_canon_sha256":"62515982c1dbe11cdc943c240ff94acbacaeaaceb4e1bc84bea37083f9c0bd6e"},"schema_version":"1.0","source":{"id":"1801.00381","kind":"arxiv","version":2}},"canonical_sha256":"c0352497b41312760371aa59d72b65e6c4585b66ed636ad15afb1bd1e7d11184","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c0352497b41312760371aa59d72b65e6c4585b66ed636ad15afb1bd1e7d11184","first_computed_at":"2026-05-18T00:17:32.952469Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:32.952469Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rqvB9chNNvm2za9lB3nx0kWwc0qrwSW+KQhZMCH3Zi3AqRWkBslJ8Ib5Yos6xzG1WKMM0eJ1UxGndwA7uxgjAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:32.952954Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.00381","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:560df4952fe18fdeb53c9c0f9b53daf352df8740a307c3ef1ee7174d1e242e5f","sha256:209a5c5b8f993b4241f4394e1a903a7cd983a6779d26ec15c54a75060576a83c"],"state_sha256":"6d3ba53b1b407ad684303314d729bd45fced4a776827c030631dea53abfe9621"}