{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:HXEQTSGJM3OWTKFSKTJUTQ7FI6","short_pith_number":"pith:HXEQTSGJ","canonical_record":{"source":{"id":"0712.1398","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2007-12-10T06:12:26Z","cross_cats_sorted":[],"title_canon_sha256":"e9ee772b5dd8a0260c257d54a6013912e986ebf1e9a4752a37c3b4b7b13f7b21","abstract_canon_sha256":"f9e88620bb3433684d7b204b5f3a079f80fdcceabcb41aa3b4746b21487f3186"},"schema_version":"1.0"},"canonical_sha256":"3dc909c8c966dd69a8b254d349c3e547967b204171a1cfadd78261124cb439b9","source":{"kind":"arxiv","id":"0712.1398","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0712.1398","created_at":"2026-05-18T03:49:20Z"},{"alias_kind":"arxiv_version","alias_value":"0712.1398v2","created_at":"2026-05-18T03:49:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0712.1398","created_at":"2026-05-18T03:49:20Z"},{"alias_kind":"pith_short_12","alias_value":"HXEQTSGJM3OW","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"HXEQTSGJM3OWTKFS","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"HXEQTSGJ","created_at":"2026-05-18T12:25:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:HXEQTSGJM3OWTKFSKTJUTQ7FI6","target":"record","payload":{"canonical_record":{"source":{"id":"0712.1398","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2007-12-10T06:12:26Z","cross_cats_sorted":[],"title_canon_sha256":"e9ee772b5dd8a0260c257d54a6013912e986ebf1e9a4752a37c3b4b7b13f7b21","abstract_canon_sha256":"f9e88620bb3433684d7b204b5f3a079f80fdcceabcb41aa3b4746b21487f3186"},"schema_version":"1.0"},"canonical_sha256":"3dc909c8c966dd69a8b254d349c3e547967b204171a1cfadd78261124cb439b9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:49:20.180545Z","signature_b64":"ijMKERPpu2vUPGHXaAyTtq0O4UawQKKt3kyP8QalrZpH6vmLHXOh72l+uDQRxO80wzPotVE5MBhs5ObZGwkuDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3dc909c8c966dd69a8b254d349c3e547967b204171a1cfadd78261124cb439b9","last_reissued_at":"2026-05-18T03:49:20.179975Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:49:20.179975Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0712.1398","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":"2026-05-18T03:49:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XpCVbZtWWKzL/VSXGjHMKRdJznsC0dOSciTGjmmjtltuCJdbuIDOJg8kZhiN3hlamgYwYxFUD9strtZz5c/LAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T19:59:34.976057Z"},"content_sha256":"59c4c15f95a811c6be9e45ade371c3c8b5f3ccc7ff0dc28d17da93c5354e5cbf","schema_version":"1.0","event_id":"sha256:59c4c15f95a811c6be9e45ade371c3c8b5f3ccc7ff0dc28d17da93c5354e5cbf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:HXEQTSGJM3OWTKFSKTJUTQ7FI6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Prolongations of Lie algebras and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Paul-Andi Nagy","submitted_at":"2007-12-10T06:12:26Z","abstract_excerpt":"We study the skew-symmetric prolongation of a Lie subalgebra $\\g \\subseteq \\mathfrak{so}(n)$, in other words the intersection $\\Lambda^3 \\cap (\\Lambda^1 \\otimes \\g)$.We compute this space in full generality. Applications include uniqueness results for connections with skew-symmetric torsion and also the proof of the Euclidean version of a conjecture posed in \\cite{ofarill} concerning a class of Pl\\\"ucker-type embeddings. We also derive a classification of the metric k-Lie algebras (or Filipov algebras), in positive signature and finite dimension. Prolongations of Lie algebras can also be used "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0712.1398","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":""},"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":"2026-05-18T03:49:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AULt7uMcNmXMGozPJ+ZEFLZR9efTS07Ji4R3c4Jwa1tVBiblOhNlxttvJwf6WJIs4m5kazYkxpId0KXTV/jpCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T19:59:34.976753Z"},"content_sha256":"81c5286c792a7184ffc0070861344b02077c1320c5c3f7be897c0727c1d73fa2","schema_version":"1.0","event_id":"sha256:81c5286c792a7184ffc0070861344b02077c1320c5c3f7be897c0727c1d73fa2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HXEQTSGJM3OWTKFSKTJUTQ7FI6/bundle.json","state_url":"https://pith.science/pith/HXEQTSGJM3OWTKFSKTJUTQ7FI6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HXEQTSGJM3OWTKFSKTJUTQ7FI6/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":"2026-06-05T19:59:34Z","links":{"resolver":"https://pith.science/pith/HXEQTSGJM3OWTKFSKTJUTQ7FI6","bundle":"https://pith.science/pith/HXEQTSGJM3OWTKFSKTJUTQ7FI6/bundle.json","state":"https://pith.science/pith/HXEQTSGJM3OWTKFSKTJUTQ7FI6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HXEQTSGJM3OWTKFSKTJUTQ7FI6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:HXEQTSGJM3OWTKFSKTJUTQ7FI6","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":"f9e88620bb3433684d7b204b5f3a079f80fdcceabcb41aa3b4746b21487f3186","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2007-12-10T06:12:26Z","title_canon_sha256":"e9ee772b5dd8a0260c257d54a6013912e986ebf1e9a4752a37c3b4b7b13f7b21"},"schema_version":"1.0","source":{"id":"0712.1398","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0712.1398","created_at":"2026-05-18T03:49:20Z"},{"alias_kind":"arxiv_version","alias_value":"0712.1398v2","created_at":"2026-05-18T03:49:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0712.1398","created_at":"2026-05-18T03:49:20Z"},{"alias_kind":"pith_short_12","alias_value":"HXEQTSGJM3OW","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"HXEQTSGJM3OWTKFS","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"HXEQTSGJ","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:81c5286c792a7184ffc0070861344b02077c1320c5c3f7be897c0727c1d73fa2","target":"graph","created_at":"2026-05-18T03:49:20Z","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 study the skew-symmetric prolongation of a Lie subalgebra $\\g \\subseteq \\mathfrak{so}(n)$, in other words the intersection $\\Lambda^3 \\cap (\\Lambda^1 \\otimes \\g)$.We compute this space in full generality. Applications include uniqueness results for connections with skew-symmetric torsion and also the proof of the Euclidean version of a conjecture posed in \\cite{ofarill} concerning a class of Pl\\\"ucker-type embeddings. We also derive a classification of the metric k-Lie algebras (or Filipov algebras), in positive signature and finite dimension. Prolongations of Lie algebras can also be used ","authors_text":"Paul-Andi Nagy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2007-12-10T06:12:26Z","title":"Prolongations of Lie algebras and applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0712.1398","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":"sha256:59c4c15f95a811c6be9e45ade371c3c8b5f3ccc7ff0dc28d17da93c5354e5cbf","target":"record","created_at":"2026-05-18T03:49:20Z","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":"f9e88620bb3433684d7b204b5f3a079f80fdcceabcb41aa3b4746b21487f3186","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2007-12-10T06:12:26Z","title_canon_sha256":"e9ee772b5dd8a0260c257d54a6013912e986ebf1e9a4752a37c3b4b7b13f7b21"},"schema_version":"1.0","source":{"id":"0712.1398","kind":"arxiv","version":2}},"canonical_sha256":"3dc909c8c966dd69a8b254d349c3e547967b204171a1cfadd78261124cb439b9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3dc909c8c966dd69a8b254d349c3e547967b204171a1cfadd78261124cb439b9","first_computed_at":"2026-05-18T03:49:20.179975Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:49:20.179975Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ijMKERPpu2vUPGHXaAyTtq0O4UawQKKt3kyP8QalrZpH6vmLHXOh72l+uDQRxO80wzPotVE5MBhs5ObZGwkuDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:49:20.180545Z","signed_message":"canonical_sha256_bytes"},"source_id":"0712.1398","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:59c4c15f95a811c6be9e45ade371c3c8b5f3ccc7ff0dc28d17da93c5354e5cbf","sha256:81c5286c792a7184ffc0070861344b02077c1320c5c3f7be897c0727c1d73fa2"],"state_sha256":"9c78ac1f74faf06e9f69c1fd4b9b21b964958ae29c182cd07a9f427dea97b521"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RdhxbbPizxNyyqIn+zqHkL3q5CVk/dAlCdbyMEB/XYokii4I95Mw4/jwGpZR3u34dg5PfmKSn9yaGEQGpWnJDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T19:59:34.980916Z","bundle_sha256":"37e627ca84210335c9ef753603691b3828d20e61e594c444a0f36ea146f1797a"}}