{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:PNZUI7ZBZHKTREUPSULLSZEL72","short_pith_number":"pith:PNZUI7ZB","schema_version":"1.0","canonical_sha256":"7b73447f21c9d538928f9516b9648bfe8acd2b4beb43778861e773b58243dfa8","source":{"kind":"arxiv","id":"1105.3081","version":1},"attestation_state":"computed","paper":{"title":"A Classification of Riemannian manifolds of quasi-constant sectional curvatures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Georgi Ganchev, Vesselka Mihova","submitted_at":"2011-05-16T12:46:05Z","abstract_excerpt":"Riemannian manifolds of quasi-constant sectional curvatures (QC-manifolds) are divided into two basic classes: with positive or negative horizontal sectional curvatures. We prove that the Riemannian QC-manifolds with positive horizontal sectional curvatures are locally equivalent to canal hypersurfaces in Euclidean space, while the Riemannian QC-manifolds with negative horizontal sectional curvatures are locally equivalent to canal space-like hypersurfaces in Minkowski space. We prove that the local theory of conformally flat Riemannian manifolds, which can be locally isometrically embedded as"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1105.3081","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-05-16T12:46:05Z","cross_cats_sorted":[],"title_canon_sha256":"d9d0cdf750628eefb36258e0b396bdc0add56ca3ffa4d554215018cfb5ad6e55","abstract_canon_sha256":"3adbfe7087f373afa7b410b6921f524115ddd247738252ea651b2ecbe1731ef0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:13.056915Z","signature_b64":"DqKLbgAc/uZvK+srV6w61ZlwziU+ljZcaBjDopZi8Fv4DlRaSO0Wt+RmaY90VhbgzIpnJXdgfxBEoLrhtRA2BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7b73447f21c9d538928f9516b9648bfe8acd2b4beb43778861e773b58243dfa8","last_reissued_at":"2026-05-18T01:24:13.056411Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:13.056411Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Classification of Riemannian manifolds of quasi-constant sectional curvatures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Georgi Ganchev, Vesselka Mihova","submitted_at":"2011-05-16T12:46:05Z","abstract_excerpt":"Riemannian manifolds of quasi-constant sectional curvatures (QC-manifolds) are divided into two basic classes: with positive or negative horizontal sectional curvatures. We prove that the Riemannian QC-manifolds with positive horizontal sectional curvatures are locally equivalent to canal hypersurfaces in Euclidean space, while the Riemannian QC-manifolds with negative horizontal sectional curvatures are locally equivalent to canal space-like hypersurfaces in Minkowski space. We prove that the local theory of conformally flat Riemannian manifolds, which can be locally isometrically embedded as"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.3081","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1105.3081","created_at":"2026-05-18T01:24:13.056515+00:00"},{"alias_kind":"arxiv_version","alias_value":"1105.3081v1","created_at":"2026-05-18T01:24:13.056515+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.3081","created_at":"2026-05-18T01:24:13.056515+00:00"},{"alias_kind":"pith_short_12","alias_value":"PNZUI7ZBZHKT","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_16","alias_value":"PNZUI7ZBZHKTREUP","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_8","alias_value":"PNZUI7ZB","created_at":"2026-05-18T12:26:39.201973+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PNZUI7ZBZHKTREUPSULLSZEL72","json":"https://pith.science/pith/PNZUI7ZBZHKTREUPSULLSZEL72.json","graph_json":"https://pith.science/api/pith-number/PNZUI7ZBZHKTREUPSULLSZEL72/graph.json","events_json":"https://pith.science/api/pith-number/PNZUI7ZBZHKTREUPSULLSZEL72/events.json","paper":"https://pith.science/paper/PNZUI7ZB"},"agent_actions":{"view_html":"https://pith.science/pith/PNZUI7ZBZHKTREUPSULLSZEL72","download_json":"https://pith.science/pith/PNZUI7ZBZHKTREUPSULLSZEL72.json","view_paper":"https://pith.science/paper/PNZUI7ZB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1105.3081&json=true","fetch_graph":"https://pith.science/api/pith-number/PNZUI7ZBZHKTREUPSULLSZEL72/graph.json","fetch_events":"https://pith.science/api/pith-number/PNZUI7ZBZHKTREUPSULLSZEL72/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PNZUI7ZBZHKTREUPSULLSZEL72/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PNZUI7ZBZHKTREUPSULLSZEL72/action/storage_attestation","attest_author":"https://pith.science/pith/PNZUI7ZBZHKTREUPSULLSZEL72/action/author_attestation","sign_citation":"https://pith.science/pith/PNZUI7ZBZHKTREUPSULLSZEL72/action/citation_signature","submit_replication":"https://pith.science/pith/PNZUI7ZBZHKTREUPSULLSZEL72/action/replication_record"}},"created_at":"2026-05-18T01:24:13.056515+00:00","updated_at":"2026-05-18T01:24:13.056515+00:00"}