{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:TQCHYAMZMDXTVEUPF3PJ4N5QGA","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":"454de566342f08cbdbd0f3b8bc8aad170e52b2781a8c041a557b7689f0ad35c3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-03-09T23:34:12Z","title_canon_sha256":"cf72589355847580f1d0586bf6cd001c684575dac9e8b51b49a1cf8e73506ade"},"schema_version":"1.0","source":{"id":"1403.2117","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.2117","created_at":"2026-05-18T00:14:16Z"},{"alias_kind":"arxiv_version","alias_value":"1403.2117v1","created_at":"2026-05-18T00:14:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.2117","created_at":"2026-05-18T00:14:16Z"},{"alias_kind":"pith_short_12","alias_value":"TQCHYAMZMDXT","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"TQCHYAMZMDXTVEUP","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"TQCHYAMZ","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:34d041fc3663d1e427831def9ef9afeac60155666b66b0d5d4e6649891e82d61","target":"graph","created_at":"2026-05-18T00:14:16Z","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 begin a systematic study of a curvature condition (strongly positive curvature) which lies strictly between positive curvature operator and positive sectional curvature, and stems from the work of Thorpe in the 1970s. We prove that this condition is preserved under Riemannian submersions and Cheeger deformations, and that most compact homogeneous spaces with positive sectional curvature satisfy it.","authors_text":"Renato G. Bettiol, Ricardo A. E. Mendes","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-03-09T23:34:12Z","title":"Strongly positive curvature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.2117","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:be429d13cea6924c12268aefbe0feab9ded5911c9bb8a2bce8e82feb295258e8","target":"record","created_at":"2026-05-18T00:14:16Z","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":"454de566342f08cbdbd0f3b8bc8aad170e52b2781a8c041a557b7689f0ad35c3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-03-09T23:34:12Z","title_canon_sha256":"cf72589355847580f1d0586bf6cd001c684575dac9e8b51b49a1cf8e73506ade"},"schema_version":"1.0","source":{"id":"1403.2117","kind":"arxiv","version":1}},"canonical_sha256":"9c047c019960ef3a928f2ede9e37b0303fb603925a15e4f139853a5f13d0e7ef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c047c019960ef3a928f2ede9e37b0303fb603925a15e4f139853a5f13d0e7ef","first_computed_at":"2026-05-18T00:14:16.847296Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:16.847296Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"871hoy9SG37PgvZ+0Q7w7jC5aFh4tvvXXS7xDM9tXgaVzSAw7A/eUISma8f6PEZFocERpmTJUr1WIhwDKWz7Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:16.847840Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.2117","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:be429d13cea6924c12268aefbe0feab9ded5911c9bb8a2bce8e82feb295258e8","sha256:34d041fc3663d1e427831def9ef9afeac60155666b66b0d5d4e6649891e82d61"],"state_sha256":"df994bdb8dac6cd3392fbf7326c6a42e26c76da7a9f619e96eb1552401e94219"}