{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:JKDHBQBQH5ZECGQ54TG7AHP65O","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":"f7fb7b3f2bc4171261e35360ce8e61b3ae4a8719ea29ef456abd397b590fd01e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-08-05T14:02:37Z","title_canon_sha256":"8909e02799eed109a1b917038eb280d649889d2d64167c0a7b11552901dad2fd"},"schema_version":"1.0","source":{"id":"1408.0975","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.0975","created_at":"2026-05-18T01:29:05Z"},{"alias_kind":"arxiv_version","alias_value":"1408.0975v3","created_at":"2026-05-18T01:29:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.0975","created_at":"2026-05-18T01:29:05Z"},{"alias_kind":"pith_short_12","alias_value":"JKDHBQBQH5ZE","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"JKDHBQBQH5ZECGQ5","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"JKDHBQBQ","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:1dfe436588bfbcdde8d67b03a54cd7e29517bd4734fa637573b3d0973fde1ee8","target":"graph","created_at":"2026-05-18T01:29:05Z","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 compact connected Lie group $G$ we study the class of bi-invariant affine connections whose geodesics through $e\\in G$ are the 1-parameter subgroups. We show that the bi-invariant affine connections which induce derivations on the corresponding Lie algebra $\\frak{g}$ coincide with the bi-invariant metric connections. Next we describe the geometry of a naturally reductive space $(M=G/K, g)$ endowed with a family of $G$-invariant connections $\\nabla^{\\alpha}$ whose torsion is a multiple of the torsion of the canonical connection $\\nabla^{c}$. For the spheres ${\\rm S}^{6}$ and ${\\rm S}^{7}$","authors_text":"Ioannis Chrysikos","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-08-05T14:02:37Z","title":"Invariant connections with skew-torsion and $\\nabla$-Einstein manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.0975","kind":"arxiv","version":3},"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":"sha256:15d5ca857c7214ce831b27509c5fa749f5e1ef4f07cac539d9b8c81b7a9b45aa","target":"record","created_at":"2026-05-18T01:29:05Z","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":"f7fb7b3f2bc4171261e35360ce8e61b3ae4a8719ea29ef456abd397b590fd01e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-08-05T14:02:37Z","title_canon_sha256":"8909e02799eed109a1b917038eb280d649889d2d64167c0a7b11552901dad2fd"},"schema_version":"1.0","source":{"id":"1408.0975","kind":"arxiv","version":3}},"canonical_sha256":"4a8670c0303f72411a1de4cdf01dfeeba6d05a0cbee6382734f00e3cadbe3104","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4a8670c0303f72411a1de4cdf01dfeeba6d05a0cbee6382734f00e3cadbe3104","first_computed_at":"2026-05-18T01:29:05.409463Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:29:05.409463Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KKlUzdWCUL48wCIpfLzyioFPw3m8ZKxxylFG37i5vFVxcwRcjzHnCSRxZJYESZgA7TDeYnnuZspvetbW8/lhDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:29:05.410177Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.0975","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:15d5ca857c7214ce831b27509c5fa749f5e1ef4f07cac539d9b8c81b7a9b45aa","sha256:1dfe436588bfbcdde8d67b03a54cd7e29517bd4734fa637573b3d0973fde1ee8"],"state_sha256":"a5ab3e6536cde7227254159cee3e9a072ec761be774bcffb7e3186a8fc96d02e"}