{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:37SXUSDXUZ7THWHLEUE6HB6C23","short_pith_number":"pith:37SXUSDX","canonical_record":{"source":{"id":"1711.01294","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-11-03T18:47:14Z","cross_cats_sorted":[],"title_canon_sha256":"0af5be361ef0faaf397dde455d588b9a9cff82eb307067da935672b3b6c8c7aa","abstract_canon_sha256":"9a53bb33b7753204b8b881d558b32ffc783ea3ad2719dde9e902ee313d2ca720"},"schema_version":"1.0"},"canonical_sha256":"dfe57a4877a67f33d8eb2509e387c2d6d03511be484a105bc0b0fa4a18237630","source":{"kind":"arxiv","id":"1711.01294","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.01294","created_at":"2026-05-18T00:31:18Z"},{"alias_kind":"arxiv_version","alias_value":"1711.01294v1","created_at":"2026-05-18T00:31:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.01294","created_at":"2026-05-18T00:31:18Z"},{"alias_kind":"pith_short_12","alias_value":"37SXUSDXUZ7T","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"37SXUSDXUZ7THWHL","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"37SXUSDX","created_at":"2026-05-18T12:30:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:37SXUSDXUZ7THWHLEUE6HB6C23","target":"record","payload":{"canonical_record":{"source":{"id":"1711.01294","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-11-03T18:47:14Z","cross_cats_sorted":[],"title_canon_sha256":"0af5be361ef0faaf397dde455d588b9a9cff82eb307067da935672b3b6c8c7aa","abstract_canon_sha256":"9a53bb33b7753204b8b881d558b32ffc783ea3ad2719dde9e902ee313d2ca720"},"schema_version":"1.0"},"canonical_sha256":"dfe57a4877a67f33d8eb2509e387c2d6d03511be484a105bc0b0fa4a18237630","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:18.255368Z","signature_b64":"pQXDPIU1PXERsHxdaWhV+RPjyNDMjwXCb1PEYnS118YrfGW3Wq6N8BTpqlOMaReg90lIg7fqPmkaAnHrHyWeBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dfe57a4877a67f33d8eb2509e387c2d6d03511be484a105bc0b0fa4a18237630","last_reissued_at":"2026-05-18T00:31:18.254692Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:18.254692Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.01294","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":"2026-05-18T00:31:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vt4en9GkmgUgUsHhFqV4GCSYNE7/dvLEWTVUMFsAJ2SReT32v+XRBCoMI5+9x7Zyi9Gx4bchwUV82PcA32ymCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T17:27:09.789045Z"},"content_sha256":"bc4097952a156de7604cc4c86d38529a0da040fb592542d0547c6805c8394ba0","schema_version":"1.0","event_id":"sha256:bc4097952a156de7604cc4c86d38529a0da040fb592542d0547c6805c8394ba0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:37SXUSDXUZ7THWHLEUE6HB6C23","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Inverses of Cartan Matrices of Lie Algebras and Lie Superalgebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Yangjiang Wei, Yi Ming Zou","submitted_at":"2017-11-03T18:47:14Z","abstract_excerpt":"We derive explicit formulas for the inverses of the Cartan matrices of the simple Lie algebras and the basic classical Lie superalgebras, as well as for their infinite generalizations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.01294","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":"2026-05-18T00:31:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2GV35JwIfzqi4V41VWZi7x02fUABEGvozZFUmn0QU2CqlNTJ/MfcRqGfWlxUtptGBNWFa3OqwEKNo7mu2B9ZDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T17:27:09.789708Z"},"content_sha256":"fc644fdc3cb2768cbd0b68939cb0b33d847ac83b17373c634b5cc79bbaddc552","schema_version":"1.0","event_id":"sha256:fc644fdc3cb2768cbd0b68939cb0b33d847ac83b17373c634b5cc79bbaddc552"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/37SXUSDXUZ7THWHLEUE6HB6C23/bundle.json","state_url":"https://pith.science/pith/37SXUSDXUZ7THWHLEUE6HB6C23/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/37SXUSDXUZ7THWHLEUE6HB6C23/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":"2026-05-24T17:27:09Z","links":{"resolver":"https://pith.science/pith/37SXUSDXUZ7THWHLEUE6HB6C23","bundle":"https://pith.science/pith/37SXUSDXUZ7THWHLEUE6HB6C23/bundle.json","state":"https://pith.science/pith/37SXUSDXUZ7THWHLEUE6HB6C23/state.json","well_known_bundle":"https://pith.science/.well-known/pith/37SXUSDXUZ7THWHLEUE6HB6C23/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:37SXUSDXUZ7THWHLEUE6HB6C23","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":"9a53bb33b7753204b8b881d558b32ffc783ea3ad2719dde9e902ee313d2ca720","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-11-03T18:47:14Z","title_canon_sha256":"0af5be361ef0faaf397dde455d588b9a9cff82eb307067da935672b3b6c8c7aa"},"schema_version":"1.0","source":{"id":"1711.01294","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.01294","created_at":"2026-05-18T00:31:18Z"},{"alias_kind":"arxiv_version","alias_value":"1711.01294v1","created_at":"2026-05-18T00:31:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.01294","created_at":"2026-05-18T00:31:18Z"},{"alias_kind":"pith_short_12","alias_value":"37SXUSDXUZ7T","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"37SXUSDXUZ7THWHL","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"37SXUSDX","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:fc644fdc3cb2768cbd0b68939cb0b33d847ac83b17373c634b5cc79bbaddc552","target":"graph","created_at":"2026-05-18T00:31:18Z","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 derive explicit formulas for the inverses of the Cartan matrices of the simple Lie algebras and the basic classical Lie superalgebras, as well as for their infinite generalizations.","authors_text":"Yangjiang Wei, Yi Ming Zou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-11-03T18:47:14Z","title":"Inverses of Cartan Matrices of Lie Algebras and Lie Superalgebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.01294","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:bc4097952a156de7604cc4c86d38529a0da040fb592542d0547c6805c8394ba0","target":"record","created_at":"2026-05-18T00:31:18Z","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":"9a53bb33b7753204b8b881d558b32ffc783ea3ad2719dde9e902ee313d2ca720","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-11-03T18:47:14Z","title_canon_sha256":"0af5be361ef0faaf397dde455d588b9a9cff82eb307067da935672b3b6c8c7aa"},"schema_version":"1.0","source":{"id":"1711.01294","kind":"arxiv","version":1}},"canonical_sha256":"dfe57a4877a67f33d8eb2509e387c2d6d03511be484a105bc0b0fa4a18237630","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dfe57a4877a67f33d8eb2509e387c2d6d03511be484a105bc0b0fa4a18237630","first_computed_at":"2026-05-18T00:31:18.254692Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:18.254692Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pQXDPIU1PXERsHxdaWhV+RPjyNDMjwXCb1PEYnS118YrfGW3Wq6N8BTpqlOMaReg90lIg7fqPmkaAnHrHyWeBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:18.255368Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.01294","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bc4097952a156de7604cc4c86d38529a0da040fb592542d0547c6805c8394ba0","sha256:fc644fdc3cb2768cbd0b68939cb0b33d847ac83b17373c634b5cc79bbaddc552"],"state_sha256":"e66d96a193ecf1cc717339c526d6ef284b6f7a9d1eba0a446eab0b987bc16cec"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iLQL+O9eounzwA9XUTN95i1T93Z6bQCRwgDwK0REfq1sawN2HZ/fT6nKsFdICotYJFBDE0DUWcHWFdHRQoumCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T17:27:09.792899Z","bundle_sha256":"8badb7c60dee78ee54287b705d9faa3283096ecc0b5d453bc8aa794adbbd25ff"}}