{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:LMOCXFX6OWXCGOOA7MOC2Z5TTF","short_pith_number":"pith:LMOCXFX6","canonical_record":{"source":{"id":"1109.5487","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-09-26T08:46:14Z","cross_cats_sorted":[],"title_canon_sha256":"7f5f02d49646204a27e811a648b48f3c54ee0494a705a77e82e3bcdb793a4b0a","abstract_canon_sha256":"259135de69d2561c2bf41bc22f4c24edba8f68ec62a66e720d22caac6f403cf6"},"schema_version":"1.0"},"canonical_sha256":"5b1c2b96fe75ae2339c0fb1c2d67b3994380903ef20e254c630843bfb693b441","source":{"kind":"arxiv","id":"1109.5487","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.5487","created_at":"2026-05-18T04:12:19Z"},{"alias_kind":"arxiv_version","alias_value":"1109.5487v1","created_at":"2026-05-18T04:12:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.5487","created_at":"2026-05-18T04:12:19Z"},{"alias_kind":"pith_short_12","alias_value":"LMOCXFX6OWXC","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"LMOCXFX6OWXCGOOA","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"LMOCXFX6","created_at":"2026-05-18T12:26:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:LMOCXFX6OWXCGOOA7MOC2Z5TTF","target":"record","payload":{"canonical_record":{"source":{"id":"1109.5487","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-09-26T08:46:14Z","cross_cats_sorted":[],"title_canon_sha256":"7f5f02d49646204a27e811a648b48f3c54ee0494a705a77e82e3bcdb793a4b0a","abstract_canon_sha256":"259135de69d2561c2bf41bc22f4c24edba8f68ec62a66e720d22caac6f403cf6"},"schema_version":"1.0"},"canonical_sha256":"5b1c2b96fe75ae2339c0fb1c2d67b3994380903ef20e254c630843bfb693b441","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:12:19.667138Z","signature_b64":"c2MYb+YlqFgIYjOJPirJempmlHdZOF1kdWsWmKWguHzJf5jX+YhIEtOxT3K9yhhyLzBxDnqqWB+gmlnYMpNiBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5b1c2b96fe75ae2339c0fb1c2d67b3994380903ef20e254c630843bfb693b441","last_reissued_at":"2026-05-18T04:12:19.666442Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:12:19.666442Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.5487","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:12:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kjc82t+VqKnWV0qU+RdNoVAd0XGPH6/W8L7yKWL5LYhl0wjKzSAT9Lw7r+g3fbKBrae8Kqd1N52hgOykz9Y4Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T14:13:41.521671Z"},"content_sha256":"f16ed64ba6189989ea463cd7f491406c1bb0322a6c4cceed3531c5c32dd477f6","schema_version":"1.0","event_id":"sha256:f16ed64ba6189989ea463cd7f491406c1bb0322a6c4cceed3531c5c32dd477f6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:LMOCXFX6OWXCGOOA7MOC2Z5TTF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Representatives of elliptic Weyl group elements in algebraic groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Matthew C. B. Zaremsky","submitted_at":"2011-09-26T08:46:14Z","abstract_excerpt":"An element w of a Weyl group W is called elliptic if it has no eigenvalue 1 in the standard reflection representation. We determine the order of any representative g in a semisimple algebraic group G of an elliptic element w in the corresponding Weyl group W. In particular if w has order d and G is simple of type different from C_n or F_4, then g has order d in G."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5487","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:12:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"czI/2hbHUITSd9Q2f9XXR0YDiBAqArbppFCC2rzHhOrQQYu1fPP+pL2e8pxOZQo33tom5U4/xM3Z0yuale2qAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T14:13:41.522367Z"},"content_sha256":"e7dce4e7506eb302cbdcd521f17220c6b9891f932c43f212001cbeca49ede5eb","schema_version":"1.0","event_id":"sha256:e7dce4e7506eb302cbdcd521f17220c6b9891f932c43f212001cbeca49ede5eb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LMOCXFX6OWXCGOOA7MOC2Z5TTF/bundle.json","state_url":"https://pith.science/pith/LMOCXFX6OWXCGOOA7MOC2Z5TTF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LMOCXFX6OWXCGOOA7MOC2Z5TTF/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-07T14:13:41Z","links":{"resolver":"https://pith.science/pith/LMOCXFX6OWXCGOOA7MOC2Z5TTF","bundle":"https://pith.science/pith/LMOCXFX6OWXCGOOA7MOC2Z5TTF/bundle.json","state":"https://pith.science/pith/LMOCXFX6OWXCGOOA7MOC2Z5TTF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LMOCXFX6OWXCGOOA7MOC2Z5TTF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:LMOCXFX6OWXCGOOA7MOC2Z5TTF","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":"259135de69d2561c2bf41bc22f4c24edba8f68ec62a66e720d22caac6f403cf6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-09-26T08:46:14Z","title_canon_sha256":"7f5f02d49646204a27e811a648b48f3c54ee0494a705a77e82e3bcdb793a4b0a"},"schema_version":"1.0","source":{"id":"1109.5487","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.5487","created_at":"2026-05-18T04:12:19Z"},{"alias_kind":"arxiv_version","alias_value":"1109.5487v1","created_at":"2026-05-18T04:12:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.5487","created_at":"2026-05-18T04:12:19Z"},{"alias_kind":"pith_short_12","alias_value":"LMOCXFX6OWXC","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"LMOCXFX6OWXCGOOA","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"LMOCXFX6","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:e7dce4e7506eb302cbdcd521f17220c6b9891f932c43f212001cbeca49ede5eb","target":"graph","created_at":"2026-05-18T04:12:19Z","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":"An element w of a Weyl group W is called elliptic if it has no eigenvalue 1 in the standard reflection representation. We determine the order of any representative g in a semisimple algebraic group G of an elliptic element w in the corresponding Weyl group W. In particular if w has order d and G is simple of type different from C_n or F_4, then g has order d in G.","authors_text":"Matthew C. B. Zaremsky","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-09-26T08:46:14Z","title":"Representatives of elliptic Weyl group elements in algebraic groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5487","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:f16ed64ba6189989ea463cd7f491406c1bb0322a6c4cceed3531c5c32dd477f6","target":"record","created_at":"2026-05-18T04:12:19Z","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":"259135de69d2561c2bf41bc22f4c24edba8f68ec62a66e720d22caac6f403cf6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-09-26T08:46:14Z","title_canon_sha256":"7f5f02d49646204a27e811a648b48f3c54ee0494a705a77e82e3bcdb793a4b0a"},"schema_version":"1.0","source":{"id":"1109.5487","kind":"arxiv","version":1}},"canonical_sha256":"5b1c2b96fe75ae2339c0fb1c2d67b3994380903ef20e254c630843bfb693b441","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5b1c2b96fe75ae2339c0fb1c2d67b3994380903ef20e254c630843bfb693b441","first_computed_at":"2026-05-18T04:12:19.666442Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:12:19.666442Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c2MYb+YlqFgIYjOJPirJempmlHdZOF1kdWsWmKWguHzJf5jX+YhIEtOxT3K9yhhyLzBxDnqqWB+gmlnYMpNiBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:12:19.667138Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.5487","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f16ed64ba6189989ea463cd7f491406c1bb0322a6c4cceed3531c5c32dd477f6","sha256:e7dce4e7506eb302cbdcd521f17220c6b9891f932c43f212001cbeca49ede5eb"],"state_sha256":"79881c1303d6b805f992bb628f5a631c56a536e5407b13f818f7938bc2117133"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iTUIn3kW4ipHqmGPCbOhnAbuU1LtcF76BfcjqsBSg26fApR6sBewHiw8/yx9FG1kQD9vqpIA98H6VDZfm+CmBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T14:13:41.525893Z","bundle_sha256":"eb73a28425ce05d44fc5c761af99da620870547b86be3a234d80e230936ae662"}}