{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:3WHX5TQ253YUIJ3ZBNLCA3ZPWE","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":"cc0feff79e69f35a396ce8776b5a2421db842ad8316307e003a6140c7916f151","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-06-17T16:35:46Z","title_canon_sha256":"2bb2ee090dbed0be13250c1195f5f194cdbcc70d60ac141ed9ee5a29df698d07"},"schema_version":"1.0","source":{"id":"1206.3766","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.3766","created_at":"2026-05-18T03:53:18Z"},{"alias_kind":"arxiv_version","alias_value":"1206.3766v1","created_at":"2026-05-18T03:53:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.3766","created_at":"2026-05-18T03:53:18Z"},{"alias_kind":"pith_short_12","alias_value":"3WHX5TQ253YU","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"3WHX5TQ253YUIJ3Z","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"3WHX5TQ2","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:efcf67445ba699b534212e010bf242be9cb383d880013783a51f6275db19d3e2","target":"graph","created_at":"2026-05-18T03:53:18Z","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":"If $\\pi :M\\rightarrow B$ is a Riemannian Submersion and $M$ has positive sectional curvature, O'Neill's Horizontal Curvature Equation shows that $B$ must also have positive curvature. We show there are Riemannian submersions from compact manifolds with positive Ricci curvature to manifolds that have small neighborhoods of (arbitrarily) negative Ricci curvature, but that there are no Riemannian submersions from manifolds with positive Ricci curvature to manifolds with nonpositive Ricci curvature.","authors_text":"Curtis Pro, Frederick Wilhelm","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-06-17T16:35:46Z","title":"Riemannian Submersions Need Not Preserve Positive Ricci Curvature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.3766","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:f95b0bff52b21341c560c9c71e313907a233f230286e8efc8f35eb89992e5288","target":"record","created_at":"2026-05-18T03:53:18Z","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":"cc0feff79e69f35a396ce8776b5a2421db842ad8316307e003a6140c7916f151","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-06-17T16:35:46Z","title_canon_sha256":"2bb2ee090dbed0be13250c1195f5f194cdbcc70d60ac141ed9ee5a29df698d07"},"schema_version":"1.0","source":{"id":"1206.3766","kind":"arxiv","version":1}},"canonical_sha256":"dd8f7ece1aeef14427790b56206f2fb1039344063bedff9c46db0a2fc2c56417","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dd8f7ece1aeef14427790b56206f2fb1039344063bedff9c46db0a2fc2c56417","first_computed_at":"2026-05-18T03:53:18.793624Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:53:18.793624Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O4d5sDf5fhp0FaLrRrZPt9aJzfpavg6EYTam0zmRcUXXmomfqDjP/rV/96oJ35LztkZksuYYZEKxb6hxMHEoCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:53:18.794236Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.3766","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f95b0bff52b21341c560c9c71e313907a233f230286e8efc8f35eb89992e5288","sha256:efcf67445ba699b534212e010bf242be9cb383d880013783a51f6275db19d3e2"],"state_sha256":"a9a990e9d6713b709e8e2062864239bfc85e14e35e655843a16f6023dc6d2aeb"}