{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:3BNYU3DK6LUWN3XM2MCWXLDK4K","short_pith_number":"pith:3BNYU3DK","canonical_record":{"source":{"id":"1407.7850","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-07-29T19:58:47Z","cross_cats_sorted":[],"title_canon_sha256":"92a0932b8dd1d2510457a53a915743e1d4875e00d8c9debe974934b76ad1428b","abstract_canon_sha256":"f26e650166abeff1eba6f0d2998a4a2b0b55e10430c1dfe6be85877751b82467"},"schema_version":"1.0"},"canonical_sha256":"d85b8a6c6af2e966eeecd3056bac6ae2bcd96b63589403724eeb14ac1b913bd0","source":{"kind":"arxiv","id":"1407.7850","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.7850","created_at":"2026-05-18T02:46:15Z"},{"alias_kind":"arxiv_version","alias_value":"1407.7850v1","created_at":"2026-05-18T02:46:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.7850","created_at":"2026-05-18T02:46:15Z"},{"alias_kind":"pith_short_12","alias_value":"3BNYU3DK6LUW","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3BNYU3DK6LUWN3XM","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3BNYU3DK","created_at":"2026-05-18T12:28:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:3BNYU3DK6LUWN3XM2MCWXLDK4K","target":"record","payload":{"canonical_record":{"source":{"id":"1407.7850","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-07-29T19:58:47Z","cross_cats_sorted":[],"title_canon_sha256":"92a0932b8dd1d2510457a53a915743e1d4875e00d8c9debe974934b76ad1428b","abstract_canon_sha256":"f26e650166abeff1eba6f0d2998a4a2b0b55e10430c1dfe6be85877751b82467"},"schema_version":"1.0"},"canonical_sha256":"d85b8a6c6af2e966eeecd3056bac6ae2bcd96b63589403724eeb14ac1b913bd0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:46:15.367449Z","signature_b64":"f657S08z4kdEcapdTs2BLPETTVe8rswv7WJNJsKV1z7uHyCmlccbHzLjiFT/6AO/svrs/fcLU2dT/dFRcQcvCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d85b8a6c6af2e966eeecd3056bac6ae2bcd96b63589403724eeb14ac1b913bd0","last_reissued_at":"2026-05-18T02:46:15.366811Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:46:15.366811Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.7850","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":"2026-05-18T02:46:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jvAarYD7LL/zuQmUwMD+dkL5Z6cCoa+6exUQkdZB1Y+y6Xd53hHx6kvHxr9rs6eNe3xUH7nialPlnPVZB5ZuDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T16:56:17.115147Z"},"content_sha256":"17e4b5f60d93d55f3974f1b962b575627fc5c91b8d475e27adac19544e5611f6","schema_version":"1.0","event_id":"sha256:17e4b5f60d93d55f3974f1b962b575627fc5c91b8d475e27adac19544e5611f6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:3BNYU3DK6LUWN3XM2MCWXLDK4K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Regular subalgebras and nilpotent orbits of real graded Lie algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"H. Dietrich, Paolo Faccin, Willem A. de Graaf","submitted_at":"2014-07-29T19:58:47Z","abstract_excerpt":"For a semisimple Lie algebra over the complex numbers, Dynkin (1952) developed an algorithm to classify the regular semisimple subalgebras, up to conjugacy by the inner automorphism group. For a graded semisimple Lie algebra over the complex numbers, Vinberg (1979) showed that a classification of a certain type of regular subalgebras (called carrier algebras) yields a classification of the nilpotent orbits in a homogeneous component of that Lie algebra. Here we consider these problems for (graded) semisimple Lie algebras over the real numbers. First, we describe an algorithm to classify the re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.7850","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":"2026-05-18T02:46:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"barZ2qac1c1y/GhQ/HHd7sdV9dEp2ip+lLFgfYeYtZ34pwmyX7sUtioGmaDaP+TwC8mpUFr/5xHnLyiuFZHwBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T16:56:17.115510Z"},"content_sha256":"d2ad29c95b78ddaa42bec952f0dbae90ab453e7661e8fb8404d473d1275eca94","schema_version":"1.0","event_id":"sha256:d2ad29c95b78ddaa42bec952f0dbae90ab453e7661e8fb8404d473d1275eca94"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3BNYU3DK6LUWN3XM2MCWXLDK4K/bundle.json","state_url":"https://pith.science/pith/3BNYU3DK6LUWN3XM2MCWXLDK4K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3BNYU3DK6LUWN3XM2MCWXLDK4K/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":"2026-05-19T16:56:17Z","links":{"resolver":"https://pith.science/pith/3BNYU3DK6LUWN3XM2MCWXLDK4K","bundle":"https://pith.science/pith/3BNYU3DK6LUWN3XM2MCWXLDK4K/bundle.json","state":"https://pith.science/pith/3BNYU3DK6LUWN3XM2MCWXLDK4K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3BNYU3DK6LUWN3XM2MCWXLDK4K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:3BNYU3DK6LUWN3XM2MCWXLDK4K","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":"f26e650166abeff1eba6f0d2998a4a2b0b55e10430c1dfe6be85877751b82467","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-07-29T19:58:47Z","title_canon_sha256":"92a0932b8dd1d2510457a53a915743e1d4875e00d8c9debe974934b76ad1428b"},"schema_version":"1.0","source":{"id":"1407.7850","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.7850","created_at":"2026-05-18T02:46:15Z"},{"alias_kind":"arxiv_version","alias_value":"1407.7850v1","created_at":"2026-05-18T02:46:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.7850","created_at":"2026-05-18T02:46:15Z"},{"alias_kind":"pith_short_12","alias_value":"3BNYU3DK6LUW","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3BNYU3DK6LUWN3XM","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3BNYU3DK","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:d2ad29c95b78ddaa42bec952f0dbae90ab453e7661e8fb8404d473d1275eca94","target":"graph","created_at":"2026-05-18T02:46:15Z","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":"For a semisimple Lie algebra over the complex numbers, Dynkin (1952) developed an algorithm to classify the regular semisimple subalgebras, up to conjugacy by the inner automorphism group. For a graded semisimple Lie algebra over the complex numbers, Vinberg (1979) showed that a classification of a certain type of regular subalgebras (called carrier algebras) yields a classification of the nilpotent orbits in a homogeneous component of that Lie algebra. Here we consider these problems for (graded) semisimple Lie algebras over the real numbers. First, we describe an algorithm to classify the re","authors_text":"H. Dietrich, Paolo Faccin, Willem A. de Graaf","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-07-29T19:58:47Z","title":"Regular subalgebras and nilpotent orbits of real graded Lie algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.7850","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":"sha256:17e4b5f60d93d55f3974f1b962b575627fc5c91b8d475e27adac19544e5611f6","target":"record","created_at":"2026-05-18T02:46:15Z","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":"f26e650166abeff1eba6f0d2998a4a2b0b55e10430c1dfe6be85877751b82467","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-07-29T19:58:47Z","title_canon_sha256":"92a0932b8dd1d2510457a53a915743e1d4875e00d8c9debe974934b76ad1428b"},"schema_version":"1.0","source":{"id":"1407.7850","kind":"arxiv","version":1}},"canonical_sha256":"d85b8a6c6af2e966eeecd3056bac6ae2bcd96b63589403724eeb14ac1b913bd0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d85b8a6c6af2e966eeecd3056bac6ae2bcd96b63589403724eeb14ac1b913bd0","first_computed_at":"2026-05-18T02:46:15.366811Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:46:15.366811Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f657S08z4kdEcapdTs2BLPETTVe8rswv7WJNJsKV1z7uHyCmlccbHzLjiFT/6AO/svrs/fcLU2dT/dFRcQcvCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:46:15.367449Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.7850","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:17e4b5f60d93d55f3974f1b962b575627fc5c91b8d475e27adac19544e5611f6","sha256:d2ad29c95b78ddaa42bec952f0dbae90ab453e7661e8fb8404d473d1275eca94"],"state_sha256":"e2c53f61299122beb8c48c295132cf243f3f0b3b08bde597098d99432acd9187"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aM3Q80yaKbkajstg1DJD1ZkHGslfrkcipP/ZmFH1n67SG7SWH9lLeMsu0t4FT1t6rESbbdAnndnyvsFvnjMPAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-19T16:56:17.117485Z","bundle_sha256":"d51238b54a6aeceac627f8bf13ad7e7f16b72ec12a49f5d6d9180357fb74984e"}}