{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:OULP4TKMJ6IPSEZDTYX5D7DGU3","short_pith_number":"pith:OULP4TKM","canonical_record":{"source":{"id":"1911.06575","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-11-15T11:40:22Z","cross_cats_sorted":["hep-th","math-ph","math.MP"],"title_canon_sha256":"4192e658739ad40f26e610a609840179eaeedfc083a9ae1f882fd1bcf13ee187","abstract_canon_sha256":"e3ad1156dc73834f018745cb51cfb62d45970843d13a78686e1d71237d786479"},"schema_version":"1.0"},"canonical_sha256":"7516fe4d4c4f90f913239e2fd1fc66a6f427033f6bc7d405e0027858a4650316","source":{"kind":"arxiv","id":"1911.06575","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1911.06575","created_at":"2026-07-05T01:04:07Z"},{"alias_kind":"arxiv_version","alias_value":"1911.06575v2","created_at":"2026-07-05T01:04:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1911.06575","created_at":"2026-07-05T01:04:07Z"},{"alias_kind":"pith_short_12","alias_value":"OULP4TKMJ6IP","created_at":"2026-07-05T01:04:07Z"},{"alias_kind":"pith_short_16","alias_value":"OULP4TKMJ6IPSEZD","created_at":"2026-07-05T01:04:07Z"},{"alias_kind":"pith_short_8","alias_value":"OULP4TKM","created_at":"2026-07-05T01:04:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:OULP4TKMJ6IPSEZDTYX5D7DGU3","target":"record","payload":{"canonical_record":{"source":{"id":"1911.06575","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-11-15T11:40:22Z","cross_cats_sorted":["hep-th","math-ph","math.MP"],"title_canon_sha256":"4192e658739ad40f26e610a609840179eaeedfc083a9ae1f882fd1bcf13ee187","abstract_canon_sha256":"e3ad1156dc73834f018745cb51cfb62d45970843d13a78686e1d71237d786479"},"schema_version":"1.0"},"canonical_sha256":"7516fe4d4c4f90f913239e2fd1fc66a6f427033f6bc7d405e0027858a4650316","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:04:07.115785Z","signature_b64":"VcSefnIj12YqV4yzT+4a4YzKvTQ1vdKd+yW8jO3oHk+8tijCQGo/Dl4AvLuUnqn9k51z96dX7Zl1tJ2PUkR9CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7516fe4d4c4f90f913239e2fd1fc66a6f427033f6bc7d405e0027858a4650316","last_reissued_at":"2026-07-05T01:04:07.115321Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:04:07.115321Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1911.06575","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T01:04:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ssjkvJ5NB8e7ROywz21CvRUMaLzYxvmJC0/ltn5i1PTuyDfoN6T4qPFq906zO/o769nOyaDjepmQdMxQ3K06AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T04:42:48.172551Z"},"content_sha256":"1d90ee667dee7ac2a4a1f9edb22e28b503e81f21fd7d94f36ed9aaedd12bd489","schema_version":"1.0","event_id":"sha256:1d90ee667dee7ac2a4a1f9edb22e28b503e81f21fd7d94f36ed9aaedd12bd489"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:OULP4TKMJ6IPSEZDTYX5D7DGU3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Real forms of embeddings of maximal reductive subalgebras of the complex simple Lie algebras of rank up to 8","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"math.RA","authors_text":"Alessio Marrani, Willem A. de Graaf","submitted_at":"2019-11-15T11:40:22Z","abstract_excerpt":"We give tables of noncompact real forms of maximal reductive subalgebras of complex simple Lie algebras of rank up to 8. These were obtained by computational methods that we briefly describe. We also discuss applications in theoretical physics of these embeddings."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.06575","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1911.06575/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T01:04:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NlkEKfk8dT+wJBjAYjOXgYyDCTOR021Fx2YtqduA4jFr06NvqAahyO0CQda4NLVG+ZCn9Q6mHm3+g292ZRV0DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T04:42:48.173079Z"},"content_sha256":"0d08a186b163168e9cfc586c6b091b90784f145620ab158049a5e4e2f19c57fc","schema_version":"1.0","event_id":"sha256:0d08a186b163168e9cfc586c6b091b90784f145620ab158049a5e4e2f19c57fc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OULP4TKMJ6IPSEZDTYX5D7DGU3/bundle.json","state_url":"https://pith.science/pith/OULP4TKMJ6IPSEZDTYX5D7DGU3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OULP4TKMJ6IPSEZDTYX5D7DGU3/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":"2026-08-04T04:42:48Z","links":{"resolver":"https://pith.science/pith/OULP4TKMJ6IPSEZDTYX5D7DGU3","bundle":"https://pith.science/pith/OULP4TKMJ6IPSEZDTYX5D7DGU3/bundle.json","state":"https://pith.science/pith/OULP4TKMJ6IPSEZDTYX5D7DGU3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OULP4TKMJ6IPSEZDTYX5D7DGU3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:OULP4TKMJ6IPSEZDTYX5D7DGU3","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":"e3ad1156dc73834f018745cb51cfb62d45970843d13a78686e1d71237d786479","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-11-15T11:40:22Z","title_canon_sha256":"4192e658739ad40f26e610a609840179eaeedfc083a9ae1f882fd1bcf13ee187"},"schema_version":"1.0","source":{"id":"1911.06575","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1911.06575","created_at":"2026-07-05T01:04:07Z"},{"alias_kind":"arxiv_version","alias_value":"1911.06575v2","created_at":"2026-07-05T01:04:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1911.06575","created_at":"2026-07-05T01:04:07Z"},{"alias_kind":"pith_short_12","alias_value":"OULP4TKMJ6IP","created_at":"2026-07-05T01:04:07Z"},{"alias_kind":"pith_short_16","alias_value":"OULP4TKMJ6IPSEZD","created_at":"2026-07-05T01:04:07Z"},{"alias_kind":"pith_short_8","alias_value":"OULP4TKM","created_at":"2026-07-05T01:04:07Z"}],"graph_snapshots":[{"event_id":"sha256:0d08a186b163168e9cfc586c6b091b90784f145620ab158049a5e4e2f19c57fc","target":"graph","created_at":"2026-07-05T01:04:07Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1911.06575/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We give tables of noncompact real forms of maximal reductive subalgebras of complex simple Lie algebras of rank up to 8. These were obtained by computational methods that we briefly describe. We also discuss applications in theoretical physics of these embeddings.","authors_text":"Alessio Marrani, Willem A. de Graaf","cross_cats":["hep-th","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-11-15T11:40:22Z","title":"Real forms of embeddings of maximal reductive subalgebras of the complex simple Lie algebras of rank up to 8"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.06575","kind":"arxiv","version":2},"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":"sha256:1d90ee667dee7ac2a4a1f9edb22e28b503e81f21fd7d94f36ed9aaedd12bd489","target":"record","created_at":"2026-07-05T01:04:07Z","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":"e3ad1156dc73834f018745cb51cfb62d45970843d13a78686e1d71237d786479","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-11-15T11:40:22Z","title_canon_sha256":"4192e658739ad40f26e610a609840179eaeedfc083a9ae1f882fd1bcf13ee187"},"schema_version":"1.0","source":{"id":"1911.06575","kind":"arxiv","version":2}},"canonical_sha256":"7516fe4d4c4f90f913239e2fd1fc66a6f427033f6bc7d405e0027858a4650316","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7516fe4d4c4f90f913239e2fd1fc66a6f427033f6bc7d405e0027858a4650316","first_computed_at":"2026-07-05T01:04:07.115321Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:04:07.115321Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VcSefnIj12YqV4yzT+4a4YzKvTQ1vdKd+yW8jO3oHk+8tijCQGo/Dl4AvLuUnqn9k51z96dX7Zl1tJ2PUkR9CQ==","signature_status":"signed_v1","signed_at":"2026-07-05T01:04:07.115785Z","signed_message":"canonical_sha256_bytes"},"source_id":"1911.06575","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1d90ee667dee7ac2a4a1f9edb22e28b503e81f21fd7d94f36ed9aaedd12bd489","sha256:0d08a186b163168e9cfc586c6b091b90784f145620ab158049a5e4e2f19c57fc"],"state_sha256":"05dc7b2313c681f19b4308dd9b03a32708ebc7644c26fdd52d67f60ebb115e68"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mDoIKBXPjr1ek3UHFI1JqBcgUTF/1C6ODcAM0E1prkheDUZ4h80XzKv9gAP0FUoOKg6MJNyvtvxotSteR4ePBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T04:42:48.178647Z","bundle_sha256":"8fb55eef2c87ff35eb7075953c5a77bdd239297857bc993e308bc09e0b428352"}}