{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:7GLRTWFMHI5O4VTUZAXVEGCTLO","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":"ca021627f544d8c1e15ef1a44314cffb76df9cea6f88e320f5fe5bf5be61329d","cross_cats_sorted":["math.AG","math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-08-08T09:53:03Z","title_canon_sha256":"2c70ad44e4431229775285ac9bca29c8dc228b9c361ac513e1c988c163dea48d"},"schema_version":"1.0","source":{"id":"1008.1397","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.1397","created_at":"2026-05-18T03:42:44Z"},{"alias_kind":"arxiv_version","alias_value":"1008.1397v2","created_at":"2026-05-18T03:42:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.1397","created_at":"2026-05-18T03:42:44Z"},{"alias_kind":"pith_short_12","alias_value":"7GLRTWFMHI5O","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"7GLRTWFMHI5O4VTU","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"7GLRTWFM","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:5de2b3ed455d43e5e9dc0671553479943a9626b374d3e7d89698f5177359c022","target":"graph","created_at":"2026-05-18T03:42:44Z","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 investigate the surjectivity of the word map defined by the n-th Engel word on the groups PSL(2,q) and SL(2,q). For SL(2,q), we show that this map is surjective onto the subset SL(2,q)\\{-id} provided that q>Q(n) is sufficiently large. Moreover, we give an estimate for Q(n). We also present examples demonstrating that this does not hold for all q.\n  We conclude that the n-th Engel word map is surjective for the groups PSL(2,q) when q>Q(n). By using the computer, we sharpen this result and show that for any n<5, the corresponding map is surjective for all the groups PSL(2,q). This provides ev","authors_text":"Fritz Grunewald, Shelly Garion, Tatiana Bandman","cross_cats":["math.AG","math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-08-08T09:53:03Z","title":"On the Surjectivity of Engel Words on PSL(2,q)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.1397","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":"sha256:11c0bffb038842da889cae10a31972e0d9bbf97686ec5d2e6604d1d5258d9e1b","target":"record","created_at":"2026-05-18T03:42:44Z","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":"ca021627f544d8c1e15ef1a44314cffb76df9cea6f88e320f5fe5bf5be61329d","cross_cats_sorted":["math.AG","math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-08-08T09:53:03Z","title_canon_sha256":"2c70ad44e4431229775285ac9bca29c8dc228b9c361ac513e1c988c163dea48d"},"schema_version":"1.0","source":{"id":"1008.1397","kind":"arxiv","version":2}},"canonical_sha256":"f99719d8ac3a3aee5674c82f5218535b8f9c3bdd204b2eaccd589b51269082e3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f99719d8ac3a3aee5674c82f5218535b8f9c3bdd204b2eaccd589b51269082e3","first_computed_at":"2026-05-18T03:42:44.953100Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:42:44.953100Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lYxLEFkm5tKvpvknc4HbtxmjrfQ3+9dycnaqfwiiQr7nQGlfH39zQF8wTjY79HKkxR0G4yMZV+uWLpjBGp/UDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:42:44.953680Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.1397","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:11c0bffb038842da889cae10a31972e0d9bbf97686ec5d2e6604d1d5258d9e1b","sha256:5de2b3ed455d43e5e9dc0671553479943a9626b374d3e7d89698f5177359c022"],"state_sha256":"0a9a964796b9c376e75cc0f49e33bf0a7e5c754050c5be24e2f134c5137173ce"}