{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:MVIBNY2SDMJHRDZ3NEWLOMXIDY","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":"9f1d5ce97378670aeb89bf3a342014b9c76952007b61c15438a2ce855874d86e","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-12-01T14:47:19Z","title_canon_sha256":"7c54503c96a70da84bb734a145833e9011f53e57b467b2c95dd32ee537545bc0"},"schema_version":"1.0","source":{"id":"0912.0169","kind":"arxiv","version":7}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.0169","created_at":"2026-05-18T03:49:46Z"},{"alias_kind":"arxiv_version","alias_value":"0912.0169v7","created_at":"2026-05-18T03:49:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.0169","created_at":"2026-05-18T03:49:46Z"},{"alias_kind":"pith_short_12","alias_value":"MVIBNY2SDMJH","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"MVIBNY2SDMJHRDZ3","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"MVIBNY2S","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:68895e82b8228e93ed7fcecbf9cfdd3d29843feda9cc4761a447183ef567e0db","target":"graph","created_at":"2026-05-18T03:49:46Z","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":"In this note we classify all homogeneous spaces $G/H$ admitting a $G$-invariant $G_2$-structure, assuming that $G$ is a compact Lie group and $G$ acts effectively on $G/H$. They include a subclass of all homogeneous spaces $G/H$ with a $G$-invariant $\\tilde G_2$-structure, where $G$ is a compact Lie group. There are many new examples with nontrivial fundamental group. We study a subclass of homogeneous spaces of high rigidity and low rigidity and show that they admit families of invariant coclosed $G_2$-structures (resp. $\\tilde G_2$-structures).","authors_text":"Hong Van Le, Mobeen Munir","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-12-01T14:47:19Z","title":"Classification of compact homogeneous spaces with invariant $G_2$-structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.0169","kind":"arxiv","version":7},"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:e9cbfbb0a59f61f6fa092b2fa4c0ae3e5242a775ec967bddce8e3acefe3edc29","target":"record","created_at":"2026-05-18T03:49:46Z","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":"9f1d5ce97378670aeb89bf3a342014b9c76952007b61c15438a2ce855874d86e","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-12-01T14:47:19Z","title_canon_sha256":"7c54503c96a70da84bb734a145833e9011f53e57b467b2c95dd32ee537545bc0"},"schema_version":"1.0","source":{"id":"0912.0169","kind":"arxiv","version":7}},"canonical_sha256":"655016e3521b12788f3b692cb732e81e05aacbd173aa573cf090f994ee6c2e0c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"655016e3521b12788f3b692cb732e81e05aacbd173aa573cf090f994ee6c2e0c","first_computed_at":"2026-05-18T03:49:46.040707Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:49:46.040707Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LAZya1U0ec3myatjzYb2Vr4zeH9Db8kVm1xfekgP02VWMGD8ZkzfAjD76DbKsPioo/rd0Ask9QMS29G2SexFAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:49:46.041435Z","signed_message":"canonical_sha256_bytes"},"source_id":"0912.0169","source_kind":"arxiv","source_version":7}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e9cbfbb0a59f61f6fa092b2fa4c0ae3e5242a775ec967bddce8e3acefe3edc29","sha256:68895e82b8228e93ed7fcecbf9cfdd3d29843feda9cc4761a447183ef567e0db"],"state_sha256":"a5bacb2dd9f9814ee6a0aa936a64520d08a9f4e9aee7e468ee605b0df6269a44"}