{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:LXUAXOSV42QN6JV5RLARCC6J5G","short_pith_number":"pith:LXUAXOSV","canonical_record":{"source":{"id":"1602.04583","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-02-15T07:39:15Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"4ee6980bdd9e924a2e8614612a3054c7b6aa274b0d3ebc3819448b67428c1d0e","abstract_canon_sha256":"e65ef8bdcae9970441f3d54ffceb210df00d195fc615c69acfb0c7a926ddc306"},"schema_version":"1.0"},"canonical_sha256":"5de80bba55e6a0df26bd8ac1110bc9e9b70817ae26d27f9ec459a487809ca9c7","source":{"kind":"arxiv","id":"1602.04583","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.04583","created_at":"2026-05-18T01:03:59Z"},{"alias_kind":"arxiv_version","alias_value":"1602.04583v5","created_at":"2026-05-18T01:03:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.04583","created_at":"2026-05-18T01:03:59Z"},{"alias_kind":"pith_short_12","alias_value":"LXUAXOSV42QN","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LXUAXOSV42QN6JV5","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LXUAXOSV","created_at":"2026-05-18T12:30:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:LXUAXOSV42QN6JV5RLARCC6J5G","target":"record","payload":{"canonical_record":{"source":{"id":"1602.04583","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-02-15T07:39:15Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"4ee6980bdd9e924a2e8614612a3054c7b6aa274b0d3ebc3819448b67428c1d0e","abstract_canon_sha256":"e65ef8bdcae9970441f3d54ffceb210df00d195fc615c69acfb0c7a926ddc306"},"schema_version":"1.0"},"canonical_sha256":"5de80bba55e6a0df26bd8ac1110bc9e9b70817ae26d27f9ec459a487809ca9c7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:59.489914Z","signature_b64":"Ix+Zkuv7lZspQI6utBKdECbFb2QmfZIM7+88XFR853VI8hVBAg/tA2KYOSigMzOTs0lEn38XpdRCqv/78+ZfCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5de80bba55e6a0df26bd8ac1110bc9e9b70817ae26d27f9ec459a487809ca9c7","last_reissued_at":"2026-05-18T01:03:59.489262Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:59.489262Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.04583","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:03:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pDo5PAB1MRHz1UgKLe4RrOkzN8XyOPGdzHwjmOUkc0edEWzJWybpV2R9s1mg9btMaYf28evP8GC5FbXYOpZzBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T13:47:58.095718Z"},"content_sha256":"ffbbb490dacd73b63484e9f572dce12edceaa515c7bdb0f87f3147ceee9ab372","schema_version":"1.0","event_id":"sha256:ffbbb490dacd73b63484e9f572dce12edceaa515c7bdb0f87f3147ceee9ab372"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:LXUAXOSV42QN6JV5RLARCC6J5G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the construction of semisimple Lie algebras and Chevalley groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RT","authors_text":"Meinolf Geck","submitted_at":"2016-02-15T07:39:15Z","abstract_excerpt":"Let $\\mathfrak{g}$ be a semisimple complex Lie algebra. Recently, Lusztig simplified the traditional construction of the corresponding Chevalley groups (of adjoint type) using the \"canonical basis\" of the adjoint representation of~$\\mathfrak{g}$. Here, we present a variation of this idea which leads to a new, and quite elementary construction of~$\\mathfrak{g}$ itself from its root system. An additional feature of this set-up is that it also gives rise to explicit Chevalley bases of $\\mathfrak{g}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.04583","kind":"arxiv","version":5},"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":"2026-05-18T01:03:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jC5RnVzgBWOBdSOeZirM3zF1EmS8lLKxAd4AQYopFabwYgMhl+zbFaHrrhEb3NzUw7+jN62/VhWZWKiOT1cRDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T13:47:58.096072Z"},"content_sha256":"0e75d31cda7d1aa85b529f4255c6da4b89d50059bdbabbde1634c6058cb15633","schema_version":"1.0","event_id":"sha256:0e75d31cda7d1aa85b529f4255c6da4b89d50059bdbabbde1634c6058cb15633"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LXUAXOSV42QN6JV5RLARCC6J5G/bundle.json","state_url":"https://pith.science/pith/LXUAXOSV42QN6JV5RLARCC6J5G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LXUAXOSV42QN6JV5RLARCC6J5G/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":"2026-05-28T13:47:58Z","links":{"resolver":"https://pith.science/pith/LXUAXOSV42QN6JV5RLARCC6J5G","bundle":"https://pith.science/pith/LXUAXOSV42QN6JV5RLARCC6J5G/bundle.json","state":"https://pith.science/pith/LXUAXOSV42QN6JV5RLARCC6J5G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LXUAXOSV42QN6JV5RLARCC6J5G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:LXUAXOSV42QN6JV5RLARCC6J5G","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":"e65ef8bdcae9970441f3d54ffceb210df00d195fc615c69acfb0c7a926ddc306","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-02-15T07:39:15Z","title_canon_sha256":"4ee6980bdd9e924a2e8614612a3054c7b6aa274b0d3ebc3819448b67428c1d0e"},"schema_version":"1.0","source":{"id":"1602.04583","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.04583","created_at":"2026-05-18T01:03:59Z"},{"alias_kind":"arxiv_version","alias_value":"1602.04583v5","created_at":"2026-05-18T01:03:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.04583","created_at":"2026-05-18T01:03:59Z"},{"alias_kind":"pith_short_12","alias_value":"LXUAXOSV42QN","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LXUAXOSV42QN6JV5","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LXUAXOSV","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:0e75d31cda7d1aa85b529f4255c6da4b89d50059bdbabbde1634c6058cb15633","target":"graph","created_at":"2026-05-18T01:03:59Z","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 $\\mathfrak{g}$ be a semisimple complex Lie algebra. Recently, Lusztig simplified the traditional construction of the corresponding Chevalley groups (of adjoint type) using the \"canonical basis\" of the adjoint representation of~$\\mathfrak{g}$. Here, we present a variation of this idea which leads to a new, and quite elementary construction of~$\\mathfrak{g}$ itself from its root system. An additional feature of this set-up is that it also gives rise to explicit Chevalley bases of $\\mathfrak{g}$.","authors_text":"Meinolf Geck","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-02-15T07:39:15Z","title":"On the construction of semisimple Lie algebras and Chevalley groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.04583","kind":"arxiv","version":5},"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:ffbbb490dacd73b63484e9f572dce12edceaa515c7bdb0f87f3147ceee9ab372","target":"record","created_at":"2026-05-18T01:03:59Z","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":"e65ef8bdcae9970441f3d54ffceb210df00d195fc615c69acfb0c7a926ddc306","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-02-15T07:39:15Z","title_canon_sha256":"4ee6980bdd9e924a2e8614612a3054c7b6aa274b0d3ebc3819448b67428c1d0e"},"schema_version":"1.0","source":{"id":"1602.04583","kind":"arxiv","version":5}},"canonical_sha256":"5de80bba55e6a0df26bd8ac1110bc9e9b70817ae26d27f9ec459a487809ca9c7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5de80bba55e6a0df26bd8ac1110bc9e9b70817ae26d27f9ec459a487809ca9c7","first_computed_at":"2026-05-18T01:03:59.489262Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:59.489262Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ix+Zkuv7lZspQI6utBKdECbFb2QmfZIM7+88XFR853VI8hVBAg/tA2KYOSigMzOTs0lEn38XpdRCqv/78+ZfCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:59.489914Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.04583","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ffbbb490dacd73b63484e9f572dce12edceaa515c7bdb0f87f3147ceee9ab372","sha256:0e75d31cda7d1aa85b529f4255c6da4b89d50059bdbabbde1634c6058cb15633"],"state_sha256":"70e0c6a00ce580c527cce9e50a1f129e7cb2f43f6914e13c28748f21ad877b40"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+YckWdnzkiA6VwTboVQuOZrWGPCe31rYeaEKIwpaeZTY0fN9CY0B4IQMOj/ExIAkBHQ1uqhF7NfnUxumxCh+Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T13:47:58.098189Z","bundle_sha256":"ae0414810d6e45026406dfffed1268193e25b3840deffef22ce5211896ca1335"}}