{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:HQZBDHNY4LGK26RXK6TPXBY7CC","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":"1aca8daf9d6dc1e8c87b2dca024857c56c4b827c94eb4b1ded62a7019f866d2d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-02-04T12:51:42Z","title_canon_sha256":"f5f3e777db48a1a3e6909bc8c9a62987fb3e60815518cd71502111c2566ddb5d"},"schema_version":"1.0","source":{"id":"1602.01661","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.01661","created_at":"2026-05-18T01:21:18Z"},{"alias_kind":"arxiv_version","alias_value":"1602.01661v1","created_at":"2026-05-18T01:21:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.01661","created_at":"2026-05-18T01:21:18Z"},{"alias_kind":"pith_short_12","alias_value":"HQZBDHNY4LGK","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"HQZBDHNY4LGK26RX","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"HQZBDHNY","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:81f5e59e8284b504c2e65f402288a95ad615e73f53ebc0f6cda9f3e93f64a05e","target":"graph","created_at":"2026-05-18T01:21:18Z","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 main result of the paper is the following theorem. Let $q$ be a prime, $n$ a positive integer and $A$ an elementary abelian group of order $q^2$. Suppose that $A$ acts coprimely on a finite group $G$ and assume that for each $a\\in A^{\\#}$ every element of $C_{G}(a)$ is $n$-Engel in $G$. Then the group $G$ is $k$-Engel for some $\\{n,q\\}$-bounded number $k$.","authors_text":"Danilo San\\c{c}\\~ao da Silveira, Pavel Shumyatsky","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-02-04T12:51:42Z","title":"On finite groups with automorphisms whose fixed points are Engel"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.01661","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:de9a714d86561cf728cf19168cc81a915a886d60876426ddbc7040c9bc25592c","target":"record","created_at":"2026-05-18T01:21:18Z","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":"1aca8daf9d6dc1e8c87b2dca024857c56c4b827c94eb4b1ded62a7019f866d2d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-02-04T12:51:42Z","title_canon_sha256":"f5f3e777db48a1a3e6909bc8c9a62987fb3e60815518cd71502111c2566ddb5d"},"schema_version":"1.0","source":{"id":"1602.01661","kind":"arxiv","version":1}},"canonical_sha256":"3c32119db8e2ccad7a3757a6fb871f1093f0cdf544dc0bb5533b43bd2cddb80d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3c32119db8e2ccad7a3757a6fb871f1093f0cdf544dc0bb5533b43bd2cddb80d","first_computed_at":"2026-05-18T01:21:18.427623Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:18.427623Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6nvHKIn+A9s3HVr44smgXre/soxgcGSmyou1ZZ0IYt1Rsqj+G+WGDHudWaLMzEIVgl61VgtmlPbrU9oNHpKuBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:18.428296Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.01661","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:de9a714d86561cf728cf19168cc81a915a886d60876426ddbc7040c9bc25592c","sha256:81f5e59e8284b504c2e65f402288a95ad615e73f53ebc0f6cda9f3e93f64a05e"],"state_sha256":"6534a36b9c5059ae80e6d57ef9fd0a65c9709595d9367e70f5e04cb3f3c3d040"}