{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:CPXDZ7R6DBK56WEZIH256HXK22","short_pith_number":"pith:CPXDZ7R6","canonical_record":{"source":{"id":"1208.3967","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-08-20T10:31:55Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"1fbc8fe45899bee7b7f570006ffcce3e5678ad5eac3aee0a4b4783dc148d3e8a","abstract_canon_sha256":"6181bed4a3e14a6ae661f49843e9cdd17001a69f34be9e2ce6f453793b021caa"},"schema_version":"1.0"},"canonical_sha256":"13ee3cfe3e1855df589941f5df1eead699f269eda5be882595fe5aaaff247b29","source":{"kind":"arxiv","id":"1208.3967","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.3967","created_at":"2026-05-18T03:48:25Z"},{"alias_kind":"arxiv_version","alias_value":"1208.3967v1","created_at":"2026-05-18T03:48:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.3967","created_at":"2026-05-18T03:48:25Z"},{"alias_kind":"pith_short_12","alias_value":"CPXDZ7R6DBK5","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CPXDZ7R6DBK56WEZ","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CPXDZ7R6","created_at":"2026-05-18T12:27:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:CPXDZ7R6DBK56WEZIH256HXK22","target":"record","payload":{"canonical_record":{"source":{"id":"1208.3967","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-08-20T10:31:55Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"1fbc8fe45899bee7b7f570006ffcce3e5678ad5eac3aee0a4b4783dc148d3e8a","abstract_canon_sha256":"6181bed4a3e14a6ae661f49843e9cdd17001a69f34be9e2ce6f453793b021caa"},"schema_version":"1.0"},"canonical_sha256":"13ee3cfe3e1855df589941f5df1eead699f269eda5be882595fe5aaaff247b29","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:48:25.626616Z","signature_b64":"8UaalFHNhHpE1uwfV60bqYRX1cyGytdj2l+E+5lRXGi9me6zDnxr+xxE6xcdjgoV2L1FP5kuCbm04upq0oPDBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"13ee3cfe3e1855df589941f5df1eead699f269eda5be882595fe5aaaff247b29","last_reissued_at":"2026-05-18T03:48:25.625736Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:48:25.625736Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.3967","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":"2026-05-18T03:48:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qxmxk/emExGZR+EIjg9DFUFfQJ3KRgudadgJ6rGIgJXFF0EijlqPwtFbh2lSEEG2BTcuRkn/P2djvmn0eJb5Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T15:01:49.468022Z"},"content_sha256":"ba14ddca6d7023a6dfa219dcf81b0a05430ef0272380e9b963fcc498859942fb","schema_version":"1.0","event_id":"sha256:ba14ddca6d7023a6dfa219dcf81b0a05430ef0272380e9b963fcc498859942fb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:CPXDZ7R6DBK56WEZIH256HXK22","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the compact real forms of the Lie algebras of type $E_6$ and $F_4$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RA","authors_text":"Robert A. Wilson","submitted_at":"2012-08-20T10:31:55Z","abstract_excerpt":"We give a construction of the compact real form of the Lie algebra of type $E_6$, using the finite irreducible subgroup of shape $3^{3+3}:\\mathrm{SL}_3(3)$, which is isomorphic to a maximal subgroup of the orthogonal group $\\Omega_7(3)$. In particular we show that the algebra is uniquely determined by this subgroup. Conversely, we prove from first principles that the algebra satisfies the Jacobi identity, and thus give an elementary proof of existence of a Lie algebra of type $E_6$. The compact real form of $F_4$ is exhibited as a subalgebra."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.3967","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":"2026-05-18T03:48:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dXzKRZMy2eSDZvAqHH0TXskCUum1L896xUf0yrjdFk5T27coW+D7nt9sY/fFwrFBxODuJO7SbX8LYRLms4A6AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T15:01:49.468536Z"},"content_sha256":"2897b5a74dd248652cb43d7f681f253e6b1eaa341815c09ba57be346114b6b2c","schema_version":"1.0","event_id":"sha256:2897b5a74dd248652cb43d7f681f253e6b1eaa341815c09ba57be346114b6b2c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CPXDZ7R6DBK56WEZIH256HXK22/bundle.json","state_url":"https://pith.science/pith/CPXDZ7R6DBK56WEZIH256HXK22/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CPXDZ7R6DBK56WEZIH256HXK22/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":"2026-05-26T15:01:49Z","links":{"resolver":"https://pith.science/pith/CPXDZ7R6DBK56WEZIH256HXK22","bundle":"https://pith.science/pith/CPXDZ7R6DBK56WEZIH256HXK22/bundle.json","state":"https://pith.science/pith/CPXDZ7R6DBK56WEZIH256HXK22/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CPXDZ7R6DBK56WEZIH256HXK22/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:CPXDZ7R6DBK56WEZIH256HXK22","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":"6181bed4a3e14a6ae661f49843e9cdd17001a69f34be9e2ce6f453793b021caa","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-08-20T10:31:55Z","title_canon_sha256":"1fbc8fe45899bee7b7f570006ffcce3e5678ad5eac3aee0a4b4783dc148d3e8a"},"schema_version":"1.0","source":{"id":"1208.3967","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.3967","created_at":"2026-05-18T03:48:25Z"},{"alias_kind":"arxiv_version","alias_value":"1208.3967v1","created_at":"2026-05-18T03:48:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.3967","created_at":"2026-05-18T03:48:25Z"},{"alias_kind":"pith_short_12","alias_value":"CPXDZ7R6DBK5","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CPXDZ7R6DBK56WEZ","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CPXDZ7R6","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:2897b5a74dd248652cb43d7f681f253e6b1eaa341815c09ba57be346114b6b2c","target":"graph","created_at":"2026-05-18T03:48:25Z","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":"We give a construction of the compact real form of the Lie algebra of type $E_6$, using the finite irreducible subgroup of shape $3^{3+3}:\\mathrm{SL}_3(3)$, which is isomorphic to a maximal subgroup of the orthogonal group $\\Omega_7(3)$. In particular we show that the algebra is uniquely determined by this subgroup. Conversely, we prove from first principles that the algebra satisfies the Jacobi identity, and thus give an elementary proof of existence of a Lie algebra of type $E_6$. The compact real form of $F_4$ is exhibited as a subalgebra.","authors_text":"Robert A. Wilson","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-08-20T10:31:55Z","title":"On the compact real forms of the Lie algebras of type $E_6$ and $F_4$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.3967","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:ba14ddca6d7023a6dfa219dcf81b0a05430ef0272380e9b963fcc498859942fb","target":"record","created_at":"2026-05-18T03:48:25Z","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":"6181bed4a3e14a6ae661f49843e9cdd17001a69f34be9e2ce6f453793b021caa","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-08-20T10:31:55Z","title_canon_sha256":"1fbc8fe45899bee7b7f570006ffcce3e5678ad5eac3aee0a4b4783dc148d3e8a"},"schema_version":"1.0","source":{"id":"1208.3967","kind":"arxiv","version":1}},"canonical_sha256":"13ee3cfe3e1855df589941f5df1eead699f269eda5be882595fe5aaaff247b29","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"13ee3cfe3e1855df589941f5df1eead699f269eda5be882595fe5aaaff247b29","first_computed_at":"2026-05-18T03:48:25.625736Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:48:25.625736Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8UaalFHNhHpE1uwfV60bqYRX1cyGytdj2l+E+5lRXGi9me6zDnxr+xxE6xcdjgoV2L1FP5kuCbm04upq0oPDBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:48:25.626616Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.3967","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba14ddca6d7023a6dfa219dcf81b0a05430ef0272380e9b963fcc498859942fb","sha256:2897b5a74dd248652cb43d7f681f253e6b1eaa341815c09ba57be346114b6b2c"],"state_sha256":"f24133ae94f8165fe01c1ec87c9c9f70e4debefc39e298642e844a9b2d042d50"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZIV50v/fUm1Ns4+6IHpqWHwzig6TR0k3txQd4/5fYiHgd0ro1A08BLLxGgAGzo62+HyYDFVwEXoZzZsPV2+BDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T15:01:49.471486Z","bundle_sha256":"af487878a25ef2a696071d885dd57c196c0be700a941e425e03ccf796f3e164a"}}