{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ZGILZUN4ZGLREQ7WIAAUY3S4AK","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":"dc79e019ccf56227cd69b8ec7c733aa9fc5595c249ba03c6c645e868983dbf77","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-05-02T22:42:04Z","title_canon_sha256":"1955e9926fa0e1e0f1c52f6c3218e3c632c5568d46e62bf062f82c306bfbf068"},"schema_version":"1.0","source":{"id":"1505.00377","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.00377","created_at":"2026-05-18T02:03:59Z"},{"alias_kind":"arxiv_version","alias_value":"1505.00377v2","created_at":"2026-05-18T02:03:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.00377","created_at":"2026-05-18T02:03:59Z"},{"alias_kind":"pith_short_12","alias_value":"ZGILZUN4ZGLR","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZGILZUN4ZGLREQ7W","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZGILZUN4","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:b639bbc182f9431d4a755c2e381164abd0e48e85195c4f242d8ac2bd8455eefa","target":"graph","created_at":"2026-05-18T02:03:59Z","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 simple algebraic group of type $G_2$ over an algebraically closed field of characteristic $2$. We give an example of a finite group $\\Gamma$ with Sylow $2$-subgroup $\\Gamma_2$ and an infinite family of pairwise non-conjugate homomorphisms $\\rho\\colon \\Gamma\\rightarrow G$ whose restrictions to $\\Gamma_2$ are all conjugate. This answers a question of Burkhard K\\\"ulshammer from 1995. We also give an action of $\\Gamma$ on a connected unipotent group $V$ such that the map of 1-cohomologies ${\\rm H}^1(\\Gamma,V)\\rightarrow {\\rm H}^1(\\Gamma_p,V)$ induced by restriction of 1-cocycles has a","authors_text":"Benjamin Martin, Gerhard R\\\"ohrle, Michael Bate","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-05-02T22:42:04Z","title":"On a question of K\\\"ulshammer for representations of finite groups in reductive groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.00377","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":"sha256:4b2cc517399295d34aaf628297384e252e52e368467d4ed26f10229646a943e9","target":"record","created_at":"2026-05-18T02:03:59Z","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":"dc79e019ccf56227cd69b8ec7c733aa9fc5595c249ba03c6c645e868983dbf77","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-05-02T22:42:04Z","title_canon_sha256":"1955e9926fa0e1e0f1c52f6c3218e3c632c5568d46e62bf062f82c306bfbf068"},"schema_version":"1.0","source":{"id":"1505.00377","kind":"arxiv","version":2}},"canonical_sha256":"c990bcd1bcc9971243f640014c6e5c02ab126a15f79b3389feada53c20a4510b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c990bcd1bcc9971243f640014c6e5c02ab126a15f79b3389feada53c20a4510b","first_computed_at":"2026-05-18T02:03:59.484024Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:03:59.484024Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UhzonWWOC/2dK1UrzwFubs1veczYL8QQB+t75qQ1PRib9jHGYCJnpJpL12tbLmYiLvgStLwEMypQWTd7gpn5Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:03:59.484792Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.00377","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4b2cc517399295d34aaf628297384e252e52e368467d4ed26f10229646a943e9","sha256:b639bbc182f9431d4a755c2e381164abd0e48e85195c4f242d8ac2bd8455eefa"],"state_sha256":"4fbaf9551fa234bbaa0d15d1ea5811cfe8c0b8483f0885ea0fd72e4deb7b95bf"}