{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:JUU3CJWJLFTD6RYOK2CGHXHX32","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":"0cf68f34a0daef770d1a7c2e67893eee8b90e6e363b19a835e4c9a91131e47dd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-07-07T09:19:53Z","title_canon_sha256":"17e94ccc413d80b8da454778b51824e9c4f2d0bf2120632123d605311bf30583"},"schema_version":"1.0","source":{"id":"1707.02095","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.02095","created_at":"2026-05-18T00:40:42Z"},{"alias_kind":"arxiv_version","alias_value":"1707.02095v1","created_at":"2026-05-18T00:40:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.02095","created_at":"2026-05-18T00:40:42Z"},{"alias_kind":"pith_short_12","alias_value":"JUU3CJWJLFTD","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"JUU3CJWJLFTD6RYO","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"JUU3CJWJ","created_at":"2026-05-18T12:31:24Z"}],"graph_snapshots":[{"event_id":"sha256:ba73ef46637f2fc759b6dd75c4cedab7c0f1f2061b88bb7a5a21ba51ae8e4303","target":"graph","created_at":"2026-05-18T00:40:42Z","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":"A nonzero element $x$ in a Lie algebra $\\mathfrak{g}$ with Lie product $[ , ]$ is called extremal if $[x,[x,y]]$ is a multiple of $x$ for all $y$. In this paper we characterize the (finitary) symplectic Lie algebras as simple Lie algebras generated by their extremal elements satisying the condition that any two noncommuting extremal elements $x,y$ generate an $\\mathfrak{sl}_2$ and any third extremal element $z$ commutes with at least one extremal element in this $\\mathfrak{sl}_2$.","authors_text":"Hans Cuypers, Yael Fleischmann","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-07-07T09:19:53Z","title":"A geometric characterization of the symplectic Lie algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.02095","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":"sha256:144d7fb7c3037792b45d8842d041aae409743dc71fbc309bb4c2e928d81ed707","target":"record","created_at":"2026-05-18T00:40:42Z","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":"0cf68f34a0daef770d1a7c2e67893eee8b90e6e363b19a835e4c9a91131e47dd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-07-07T09:19:53Z","title_canon_sha256":"17e94ccc413d80b8da454778b51824e9c4f2d0bf2120632123d605311bf30583"},"schema_version":"1.0","source":{"id":"1707.02095","kind":"arxiv","version":1}},"canonical_sha256":"4d29b126c959663f470e568463dcf7deb54dccb8c9e0bec41b98c8062afd260d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4d29b126c959663f470e568463dcf7deb54dccb8c9e0bec41b98c8062afd260d","first_computed_at":"2026-05-18T00:40:42.962927Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:42.962927Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PMvHrqQw3kzxm898tzfr5GBny1hoWAMmoOOhzOn5g8wcH312g85gb6MtaKwalG5Qw/II0K9WyKqayWVFYUZLBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:42.963668Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.02095","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:144d7fb7c3037792b45d8842d041aae409743dc71fbc309bb4c2e928d81ed707","sha256:ba73ef46637f2fc759b6dd75c4cedab7c0f1f2061b88bb7a5a21ba51ae8e4303"],"state_sha256":"007ef408e14799510f6c96291dde7786a78aca243e2d38a741246601caf9dbab"}