{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:X5TZV2H7K22MO6BY5HHQJIBMBO","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":"c202f2f02ba8fa58884e6d464170ee0ccf78610a7c987c67dce89ee9755e791c","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-01-15T14:12:12Z","title_canon_sha256":"349c236ed58f1f865aaa11372998287427178eb2267f4af2325c89eb651fb0b4"},"schema_version":"1.0","source":{"id":"0901.2267","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0901.2267","created_at":"2026-05-18T04:31:51Z"},{"alias_kind":"arxiv_version","alias_value":"0901.2267v1","created_at":"2026-05-18T04:31:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.2267","created_at":"2026-05-18T04:31:51Z"},{"alias_kind":"pith_short_12","alias_value":"X5TZV2H7K22M","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"X5TZV2H7K22MO6BY","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"X5TZV2H7","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:995e4f62f87aa418a684c10a0c2fddab7b53d07f7ce454d1a5d0a3ecd03dee8b","target":"graph","created_at":"2026-05-18T04:31:51Z","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 provide examples of homogeneous spaces which are neither symmetric spaces nor real cohomology spheres, yet have the property that every invariant metric is geometrically formal. We also extend the known obstructions to geometric formality to some new classes of homogeneous spaces and of biquotients, and to certain sphere bundles.","authors_text":"D. Kotschick, S. Terzic","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-01-15T14:12:12Z","title":"Geometric formality of homogeneous spaces and of biquotients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.2267","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":"sha256:050f7dd4ee996306e41dd0e63d6b5225b436356fc64fc79a1323438ad8d486f5","target":"record","created_at":"2026-05-18T04:31:51Z","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":"c202f2f02ba8fa58884e6d464170ee0ccf78610a7c987c67dce89ee9755e791c","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-01-15T14:12:12Z","title_canon_sha256":"349c236ed58f1f865aaa11372998287427178eb2267f4af2325c89eb651fb0b4"},"schema_version":"1.0","source":{"id":"0901.2267","kind":"arxiv","version":1}},"canonical_sha256":"bf679ae8ff56b4c77838e9cf04a02c0b938ed79b7f78da531b21544e39e58796","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bf679ae8ff56b4c77838e9cf04a02c0b938ed79b7f78da531b21544e39e58796","first_computed_at":"2026-05-18T04:31:51.264043Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:31:51.264043Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0OkGiysFAQmEFQSSU/YAwpf63iM6fxPDOB75/+WXMiwJeAHUXvIBkFLLnBxZ4ttZGo7lAvrNVDRnPOTACt9eCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:31:51.264705Z","signed_message":"canonical_sha256_bytes"},"source_id":"0901.2267","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:050f7dd4ee996306e41dd0e63d6b5225b436356fc64fc79a1323438ad8d486f5","sha256:995e4f62f87aa418a684c10a0c2fddab7b53d07f7ce454d1a5d0a3ecd03dee8b"],"state_sha256":"12e05463acf83259d638978f22f50637e2bcd07191e23bb535e7a81013e07f71"}