{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:GHTLLF3M7CQJG6D5M55C5HH3LB","short_pith_number":"pith:GHTLLF3M","canonical_record":{"source":{"id":"math-ph/0510013","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2005-10-03T16:11:36Z","cross_cats_sorted":["math.MP","math.RT"],"title_canon_sha256":"f9c4d73959ccec6d2795cf55f2a8413b57705d9469d81262cba7f97f6d9b8da4","abstract_canon_sha256":"5d183cd335a4d26a763e03c4666869daa2989527c85b8a500e1dc78693357977"},"schema_version":"1.0"},"canonical_sha256":"31e6b5976cf8a093787d677a2e9cfb587d25cf7f69ed9907b45e859b4f161dba","source":{"kind":"arxiv","id":"math-ph/0510013","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0510013","created_at":"2026-05-18T01:05:30Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0510013v1","created_at":"2026-05-18T01:05:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0510013","created_at":"2026-05-18T01:05:30Z"},{"alias_kind":"pith_short_12","alias_value":"GHTLLF3M7CQJ","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"GHTLLF3M7CQJG6D5","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"GHTLLF3M","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:GHTLLF3M7CQJG6D5M55C5HH3LB","target":"record","payload":{"canonical_record":{"source":{"id":"math-ph/0510013","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2005-10-03T16:11:36Z","cross_cats_sorted":["math.MP","math.RT"],"title_canon_sha256":"f9c4d73959ccec6d2795cf55f2a8413b57705d9469d81262cba7f97f6d9b8da4","abstract_canon_sha256":"5d183cd335a4d26a763e03c4666869daa2989527c85b8a500e1dc78693357977"},"schema_version":"1.0"},"canonical_sha256":"31e6b5976cf8a093787d677a2e9cfb587d25cf7f69ed9907b45e859b4f161dba","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:30.068385Z","signature_b64":"Dt01M3+vqj4VgEHeCNz+iUi/KzKzXSYXVRuQHuFEorp0h61J/ldKr5Qhxq4hD8K1JFoV9PXMOczMM8HM4qIpDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"31e6b5976cf8a093787d677a2e9cfb587d25cf7f69ed9907b45e859b4f161dba","last_reissued_at":"2026-05-18T01:05:30.067904Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:30.067904Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math-ph/0510013","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":"2026-05-18T01:05:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KmdcL/HQ0bQBlvYyJDIw5Dzln04YfDVZCE/06X4mhRrTrSpobxnXKN3NY4acWY7h69uL9eS6HrV9/PUyg/mnCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T23:40:57.361774Z"},"content_sha256":"e434654d0f504c9ad8a8d9493da350a1db68d7f3b6a6a4010a5c6640e76ce1a6","schema_version":"1.0","event_id":"sha256:e434654d0f504c9ad8a8d9493da350a1db68d7f3b6a6a4010a5c6640e76ce1a6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:GHTLLF3M7CQJG6D5M55C5HH3LB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Defining relations associated with the principal sl(2)-subalgebras of simple Lie algebras","license":"","headline":"","cross_cats":["math.MP","math.RT"],"primary_cat":"math-ph","authors_text":"Dimitry Leites, Pavel Grozman","submitted_at":"2005-10-03T16:11:36Z","abstract_excerpt":"The notion of defining relations is well-defined for any nilpotent Lie algebra. Therefore a conventional way to present a simple Lie algebra G is by splitting it into the direct sum of a commutative Cartan subalgebra and two maximal nilpotent subalgebras (positive and negative) and together the generators of both these nilpotent subalgebras together generate G. Though there are many relations between these generators, they are neat (Serre relations).\n  It is possible to determine the relations for generators of different type, e.g, with the principal embeddings of sl(2) into G one can associat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0510013","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":"2026-05-18T01:05:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wHJw7Hl46PyQTDznPK3SH4riLD03tDq0oQ8k7+ECCX/wprESAkiLATSr59LdNXyY5p+qfVPpvOA2r/Oib5dxDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T23:40:57.362123Z"},"content_sha256":"e130af1413ab5ed3b02ec6b4096d2b0f5879792fc32a55a2027198cf52e01cef","schema_version":"1.0","event_id":"sha256:e130af1413ab5ed3b02ec6b4096d2b0f5879792fc32a55a2027198cf52e01cef"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GHTLLF3M7CQJG6D5M55C5HH3LB/bundle.json","state_url":"https://pith.science/pith/GHTLLF3M7CQJG6D5M55C5HH3LB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GHTLLF3M7CQJG6D5M55C5HH3LB/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":"2026-06-30T23:40:57Z","links":{"resolver":"https://pith.science/pith/GHTLLF3M7CQJG6D5M55C5HH3LB","bundle":"https://pith.science/pith/GHTLLF3M7CQJG6D5M55C5HH3LB/bundle.json","state":"https://pith.science/pith/GHTLLF3M7CQJG6D5M55C5HH3LB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GHTLLF3M7CQJG6D5M55C5HH3LB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:GHTLLF3M7CQJG6D5M55C5HH3LB","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":"5d183cd335a4d26a763e03c4666869daa2989527c85b8a500e1dc78693357977","cross_cats_sorted":["math.MP","math.RT"],"license":"","primary_cat":"math-ph","submitted_at":"2005-10-03T16:11:36Z","title_canon_sha256":"f9c4d73959ccec6d2795cf55f2a8413b57705d9469d81262cba7f97f6d9b8da4"},"schema_version":"1.0","source":{"id":"math-ph/0510013","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0510013","created_at":"2026-05-18T01:05:30Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0510013v1","created_at":"2026-05-18T01:05:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0510013","created_at":"2026-05-18T01:05:30Z"},{"alias_kind":"pith_short_12","alias_value":"GHTLLF3M7CQJ","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"GHTLLF3M7CQJG6D5","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"GHTLLF3M","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:e130af1413ab5ed3b02ec6b4096d2b0f5879792fc32a55a2027198cf52e01cef","target":"graph","created_at":"2026-05-18T01:05:30Z","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":"The notion of defining relations is well-defined for any nilpotent Lie algebra. Therefore a conventional way to present a simple Lie algebra G is by splitting it into the direct sum of a commutative Cartan subalgebra and two maximal nilpotent subalgebras (positive and negative) and together the generators of both these nilpotent subalgebras together generate G. Though there are many relations between these generators, they are neat (Serre relations).\n  It is possible to determine the relations for generators of different type, e.g, with the principal embeddings of sl(2) into G one can associat","authors_text":"Dimitry Leites, Pavel Grozman","cross_cats":["math.MP","math.RT"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2005-10-03T16:11:36Z","title":"Defining relations associated with the principal sl(2)-subalgebras of simple Lie algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0510013","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:e434654d0f504c9ad8a8d9493da350a1db68d7f3b6a6a4010a5c6640e76ce1a6","target":"record","created_at":"2026-05-18T01:05:30Z","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":"5d183cd335a4d26a763e03c4666869daa2989527c85b8a500e1dc78693357977","cross_cats_sorted":["math.MP","math.RT"],"license":"","primary_cat":"math-ph","submitted_at":"2005-10-03T16:11:36Z","title_canon_sha256":"f9c4d73959ccec6d2795cf55f2a8413b57705d9469d81262cba7f97f6d9b8da4"},"schema_version":"1.0","source":{"id":"math-ph/0510013","kind":"arxiv","version":1}},"canonical_sha256":"31e6b5976cf8a093787d677a2e9cfb587d25cf7f69ed9907b45e859b4f161dba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"31e6b5976cf8a093787d677a2e9cfb587d25cf7f69ed9907b45e859b4f161dba","first_computed_at":"2026-05-18T01:05:30.067904Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:30.067904Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Dt01M3+vqj4VgEHeCNz+iUi/KzKzXSYXVRuQHuFEorp0h61J/ldKr5Qhxq4hD8K1JFoV9PXMOczMM8HM4qIpDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:30.068385Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0510013","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e434654d0f504c9ad8a8d9493da350a1db68d7f3b6a6a4010a5c6640e76ce1a6","sha256:e130af1413ab5ed3b02ec6b4096d2b0f5879792fc32a55a2027198cf52e01cef"],"state_sha256":"8c966df22cdff316683fd9d951d17b32b046bcc2f2c9f68eaf7345dcd0362303"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kPv6QhcGnlgqU2iRAwQ9e1u52Ma/Odmqws/SU4RE78Nl/P2yFve9cEHMh0yFCWyHoWBBsdNyzklWTxXTnpuGDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T23:40:57.364119Z","bundle_sha256":"9689eaebc4d4baada802ab8e8e2808e7a33b7545b7ad8084bde95cc85cdae1e1"}}