{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:3OTKBQFZFXCWCS3WOKZ4VUCFDW","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":"015cb6dafbef8e2278453c13ea32714ad92121f4bf5504842d017111bfbe64d3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-12-31T15:55:24Z","title_canon_sha256":"d70bdd25f1dc7bf374ea3f303441c15f87eeaa062da218b18efd3ab9095fd7a6"},"schema_version":"1.0","source":{"id":"1701.00125","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.00125","created_at":"2026-05-18T00:53:36Z"},{"alias_kind":"arxiv_version","alias_value":"1701.00125v1","created_at":"2026-05-18T00:53:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.00125","created_at":"2026-05-18T00:53:36Z"},{"alias_kind":"pith_short_12","alias_value":"3OTKBQFZFXCW","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"3OTKBQFZFXCWCS3W","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"3OTKBQFZ","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:1f574328f6485ddb793e0720587f330b5a8e129b77b2fed3f1770815da2ac500","target":"graph","created_at":"2026-05-18T00:53:36Z","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":"In this paper we prove the following result.\n  Let $G$ be a simply connected simple linear algebraic group of exceptional Lie type over an algebraically closed field $F$ of characteristic $p\\geq 0$, and let $u\\in G$ be a nonidentity unipotent element. Let $\\phi$ be a non-trivial irreducible representation of $G$.\n  Then the Jordan normal form of $\\phi(u)$ contains at most one non-trivial block if and only if $G$ is of type $G_2$, $u$ is a regular unipotent element and $\\dim \\phi\\leq 7$.\n  Note that the irreducible representations of the simple classical algebraic groups in which a non-trivial ","authors_text":"Alexandre Zalesski, Donna Testerman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-12-31T15:55:24Z","title":"Irreducible representations of simple algebraic groups in which a unipotent element is represented by a matrix with single non-trivial Jordan block"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.00125","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:eec2a0375184989a1cd544221b6fbd2523cc163bf4be28c39698fae5a61b523c","target":"record","created_at":"2026-05-18T00:53:36Z","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":"015cb6dafbef8e2278453c13ea32714ad92121f4bf5504842d017111bfbe64d3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-12-31T15:55:24Z","title_canon_sha256":"d70bdd25f1dc7bf374ea3f303441c15f87eeaa062da218b18efd3ab9095fd7a6"},"schema_version":"1.0","source":{"id":"1701.00125","kind":"arxiv","version":1}},"canonical_sha256":"dba6a0c0b92dc5614b7672b3cad0451da630b287ffbc0592fa25c7cbee083c3d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dba6a0c0b92dc5614b7672b3cad0451da630b287ffbc0592fa25c7cbee083c3d","first_computed_at":"2026-05-18T00:53:36.311177Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:36.311177Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RYxi0Y/zjqaurKO77y/RYUKHupDSwkee2fp+mrG8cyCoRY9PpDxnmzUj6WFfpCwENGachGt+zqFbYJxCxM5mCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:36.311640Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.00125","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eec2a0375184989a1cd544221b6fbd2523cc163bf4be28c39698fae5a61b523c","sha256:1f574328f6485ddb793e0720587f330b5a8e129b77b2fed3f1770815da2ac500"],"state_sha256":"90a73651f49f5ba9c525e74ddd0c54ad34bd13601685d41f1c74435e5a2a79b1"}