{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:6VV2TL6RQ7WVW42I4GKUVV75SV","short_pith_number":"pith:6VV2TL6R","schema_version":"1.0","canonical_sha256":"f56ba9afd187ed5b7348e1954ad7fd9543ad46f0187579d3b44745928ed526c3","source":{"kind":"arxiv","id":"1110.1820","version":1},"attestation_state":"computed","paper":{"title":"On the geometry of four dimensional Riemannian manifold with a circulant metric and a circulant affinor structure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Dimitar Razpopov","submitted_at":"2011-10-09T10:50:12Z","abstract_excerpt":"We consider a four dimensional Riemannian manifold M with a metric g and an affinor structure q. We note the local coordinates of g and q are circulant matrices. Their first orders are (A, B, C, B), A, B, C \\in FM and (0, 1, 0, 0), respectively.\n  Let \\nabla be the connection of g. Further, let mu_{1}, mu_{2},mu_{3}, mu_{4}, mu_{5}, mu_{6} be the sectional curvatures of 2-sections {x, qx}, {x, q^{2}x}, {q^{3}x, x}, {qx, q^{2}x}, {qx, q^{3}x}, {q^{2}x, q^{3}x} for arbitrary vector x in T_{p}M$, p is in M . Then we have that q^{4}=E; g(qx, qy)=g(x,y), x, y are in chiM.\n  The main results of the "},"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":"1110.1820","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-10-09T10:50:12Z","cross_cats_sorted":[],"title_canon_sha256":"3260db249b80ea0f593d682fa4258e7133eda49d63ea65c6bfe32988b8c5440e","abstract_canon_sha256":"1a603c92b6d9c842395a0e095fd32ccb5fd91e77eabacae34f473bca8766c4ed"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:01.584534Z","signature_b64":"zOtTWIn5uL6D1yBx8iFDYxEiLK9Wysxz7v5NRtersy6ygmw+GyPEGjunUU9CAvf2IZ1SVbcLaJpxbprPq6//CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f56ba9afd187ed5b7348e1954ad7fd9543ad46f0187579d3b44745928ed526c3","last_reissued_at":"2026-05-18T01:17:01.583908Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:01.583908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the geometry of four dimensional Riemannian manifold with a circulant metric and a circulant affinor structure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Dimitar Razpopov","submitted_at":"2011-10-09T10:50:12Z","abstract_excerpt":"We consider a four dimensional Riemannian manifold M with a metric g and an affinor structure q. We note the local coordinates of g and q are circulant matrices. Their first orders are (A, B, C, B), A, B, C \\in FM and (0, 1, 0, 0), respectively.\n  Let \\nabla be the connection of g. Further, let mu_{1}, mu_{2},mu_{3}, mu_{4}, mu_{5}, mu_{6} be the sectional curvatures of 2-sections {x, qx}, {x, q^{2}x}, {q^{3}x, x}, {qx, q^{2}x}, {qx, q^{3}x}, {q^{2}x, q^{3}x} for arbitrary vector x in T_{p}M$, p is in M . Then we have that q^{4}=E; g(qx, qy)=g(x,y), x, y are in chiM.\n  The main results of the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1820","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":"1110.1820","created_at":"2026-05-18T01:17:01.583998+00:00"},{"alias_kind":"arxiv_version","alias_value":"1110.1820v1","created_at":"2026-05-18T01:17:01.583998+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.1820","created_at":"2026-05-18T01:17:01.583998+00:00"},{"alias_kind":"pith_short_12","alias_value":"6VV2TL6RQ7WV","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_16","alias_value":"6VV2TL6RQ7WVW42I","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_8","alias_value":"6VV2TL6R","created_at":"2026-05-18T12:26:22.705136+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/6VV2TL6RQ7WVW42I4GKUVV75SV","json":"https://pith.science/pith/6VV2TL6RQ7WVW42I4GKUVV75SV.json","graph_json":"https://pith.science/api/pith-number/6VV2TL6RQ7WVW42I4GKUVV75SV/graph.json","events_json":"https://pith.science/api/pith-number/6VV2TL6RQ7WVW42I4GKUVV75SV/events.json","paper":"https://pith.science/paper/6VV2TL6R"},"agent_actions":{"view_html":"https://pith.science/pith/6VV2TL6RQ7WVW42I4GKUVV75SV","download_json":"https://pith.science/pith/6VV2TL6RQ7WVW42I4GKUVV75SV.json","view_paper":"https://pith.science/paper/6VV2TL6R","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1110.1820&json=true","fetch_graph":"https://pith.science/api/pith-number/6VV2TL6RQ7WVW42I4GKUVV75SV/graph.json","fetch_events":"https://pith.science/api/pith-number/6VV2TL6RQ7WVW42I4GKUVV75SV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6VV2TL6RQ7WVW42I4GKUVV75SV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6VV2TL6RQ7WVW42I4GKUVV75SV/action/storage_attestation","attest_author":"https://pith.science/pith/6VV2TL6RQ7WVW42I4GKUVV75SV/action/author_attestation","sign_citation":"https://pith.science/pith/6VV2TL6RQ7WVW42I4GKUVV75SV/action/citation_signature","submit_replication":"https://pith.science/pith/6VV2TL6RQ7WVW42I4GKUVV75SV/action/replication_record"}},"created_at":"2026-05-18T01:17:01.583998+00:00","updated_at":"2026-05-18T01:17:01.583998+00:00"}