{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:GKQVUTQLQ2ULGBQZY6OM3M5QWJ","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":"235df611c6114e55396adb3818f555a0b81224a3e99c6aff5b26133ab778da80","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-01-02T15:11:50Z","title_canon_sha256":"d824cce9ecf0b948d06e5c11b1585c042364c8d770fe0de6579b3a0f790f1ee8"},"schema_version":"1.0","source":{"id":"0901.0244","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0901.0244","created_at":"2026-05-18T04:18:35Z"},{"alias_kind":"arxiv_version","alias_value":"0901.0244v3","created_at":"2026-05-18T04:18:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.0244","created_at":"2026-05-18T04:18:35Z"},{"alias_kind":"pith_short_12","alias_value":"GKQVUTQLQ2UL","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"GKQVUTQLQ2ULGBQZ","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"GKQVUTQL","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:3c92bd550956dc1d84bb2394ecaee6a5e8411d5aa16e0ee8a571856d0306911f","target":"graph","created_at":"2026-05-18T04:18:35Z","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 whether a finitely generated profinite group G could have a finitely generated infinite image. A result of Dan Segal shows that this is impossible if G is prosoluble. We prove that such an image does not exist if G is semisimple or nonuniversal. We also investigate the existense of dense normal subgroups in $G$.","authors_text":"Nikolay Nikolov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-01-02T15:11:50Z","title":"Strange images of profinite groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.0244","kind":"arxiv","version":3},"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":"sha256:373aaa2153df6b30c50b15187e2000a24867208b29ff4f6aab48388a9361398e","target":"record","created_at":"2026-05-18T04:18:35Z","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":"235df611c6114e55396adb3818f555a0b81224a3e99c6aff5b26133ab778da80","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-01-02T15:11:50Z","title_canon_sha256":"d824cce9ecf0b948d06e5c11b1585c042364c8d770fe0de6579b3a0f790f1ee8"},"schema_version":"1.0","source":{"id":"0901.0244","kind":"arxiv","version":3}},"canonical_sha256":"32a15a4e0b86a8b30619c79ccdb3b0b27dbeb0be61f604a8cb06e62b70daf72f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"32a15a4e0b86a8b30619c79ccdb3b0b27dbeb0be61f604a8cb06e62b70daf72f","first_computed_at":"2026-05-18T04:18:35.022185Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:18:35.022185Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+GdM0Km1nOv8a6H8kfkSOqHthT3RGOaNrPkW9J1w72nd4/HR0jVGoH/Ngoh6IgePpCdcyfwzh+mOtgCpwTQNAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:18:35.022885Z","signed_message":"canonical_sha256_bytes"},"source_id":"0901.0244","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:373aaa2153df6b30c50b15187e2000a24867208b29ff4f6aab48388a9361398e","sha256:3c92bd550956dc1d84bb2394ecaee6a5e8411d5aa16e0ee8a571856d0306911f"],"state_sha256":"ad2958bf8d68bedcadf2ef54b044f6c7207230c91f32d45a6276baf1b40e882d"}