{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:V7CGPSMZ32455XUMPEB2XDF72K","short_pith_number":"pith:V7CGPSMZ","canonical_record":{"source":{"id":"1308.4834","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-08-22T12:02:05Z","cross_cats_sorted":[],"title_canon_sha256":"44f03d704d7c4e345adc505a85f74a7016acbda15d425d340595845aa46682d1","abstract_canon_sha256":"3bc902b30afd368cd361e482e9b343bcd6ba6a9a9e38b199a5aa389816a6e7e8"},"schema_version":"1.0"},"canonical_sha256":"afc467c999deb9dede8c7903ab8cbfd2bfbd2404029e0a0af2569980fac17285","source":{"kind":"arxiv","id":"1308.4834","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.4834","created_at":"2026-05-17T23:48:02Z"},{"alias_kind":"arxiv_version","alias_value":"1308.4834v3","created_at":"2026-05-17T23:48:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.4834","created_at":"2026-05-17T23:48:02Z"},{"alias_kind":"pith_short_12","alias_value":"V7CGPSMZ3245","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"V7CGPSMZ32455XUM","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"V7CGPSMZ","created_at":"2026-05-18T12:28:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:V7CGPSMZ32455XUMPEB2XDF72K","target":"record","payload":{"canonical_record":{"source":{"id":"1308.4834","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-08-22T12:02:05Z","cross_cats_sorted":[],"title_canon_sha256":"44f03d704d7c4e345adc505a85f74a7016acbda15d425d340595845aa46682d1","abstract_canon_sha256":"3bc902b30afd368cd361e482e9b343bcd6ba6a9a9e38b199a5aa389816a6e7e8"},"schema_version":"1.0"},"canonical_sha256":"afc467c999deb9dede8c7903ab8cbfd2bfbd2404029e0a0af2569980fac17285","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:02.655173Z","signature_b64":"R7veztRiMFDqMk/t9oG9TCbfUE3q5XJtLx3eCK4u5KRkOBx29slfosgw+hOuXa4++qUGrirkPEaOBC3QY6MZBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"afc467c999deb9dede8c7903ab8cbfd2bfbd2404029e0a0af2569980fac17285","last_reissued_at":"2026-05-17T23:48:02.654645Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:02.654645Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.4834","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:48:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xnW2ZfEvkQYXhLdj8YXg+ZR6GmL53vNeBgho4bcWNoTg5zjuGcOYCWl3GOTSowidm0Ldkv5+AuY64eEjIQ7PBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T05:00:30.920643Z"},"content_sha256":"2100a009d1735cb92713f30b194928b857414c93aebed94ea36e81462a483000","schema_version":"1.0","event_id":"sha256:2100a009d1735cb92713f30b194928b857414c93aebed94ea36e81462a483000"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:V7CGPSMZ32455XUMPEB2XDF72K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Three-dimensional Riemannian manifolds with circulant structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Dimitar Razpopov, Georgi Dzhelepov, Iva Dokuzova","submitted_at":"2013-08-22T12:02:05Z","abstract_excerpt":"We consider a 3-dimensional Riemannian manifold M with two circulant structures -- a metric g and an endomorphism q whose third power is identity. The structure q is compatible with g such that an isometry is induced in any tangent space of M. We obtain some curvature properties of this manifold (M, g, q) and give an explicit example of such a manifold."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.4834","kind":"arxiv","version":3},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:48:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yfEmdrmy/BGGB4CRdY4PiexsxlT1EI+dHXoIEe1l8t60z0sTNAhzSG9mJC469epqB1Zji+CpbhCVtohv7N2hBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T05:00:30.920980Z"},"content_sha256":"017fa4b0a8dcd4e59ff356c10661493bc03a04afa287b60cccdc42a0dceabd9f","schema_version":"1.0","event_id":"sha256:017fa4b0a8dcd4e59ff356c10661493bc03a04afa287b60cccdc42a0dceabd9f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V7CGPSMZ32455XUMPEB2XDF72K/bundle.json","state_url":"https://pith.science/pith/V7CGPSMZ32455XUMPEB2XDF72K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V7CGPSMZ32455XUMPEB2XDF72K/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-29T05:00:30Z","links":{"resolver":"https://pith.science/pith/V7CGPSMZ32455XUMPEB2XDF72K","bundle":"https://pith.science/pith/V7CGPSMZ32455XUMPEB2XDF72K/bundle.json","state":"https://pith.science/pith/V7CGPSMZ32455XUMPEB2XDF72K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V7CGPSMZ32455XUMPEB2XDF72K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:V7CGPSMZ32455XUMPEB2XDF72K","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":"3bc902b30afd368cd361e482e9b343bcd6ba6a9a9e38b199a5aa389816a6e7e8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-08-22T12:02:05Z","title_canon_sha256":"44f03d704d7c4e345adc505a85f74a7016acbda15d425d340595845aa46682d1"},"schema_version":"1.0","source":{"id":"1308.4834","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.4834","created_at":"2026-05-17T23:48:02Z"},{"alias_kind":"arxiv_version","alias_value":"1308.4834v3","created_at":"2026-05-17T23:48:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.4834","created_at":"2026-05-17T23:48:02Z"},{"alias_kind":"pith_short_12","alias_value":"V7CGPSMZ3245","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"V7CGPSMZ32455XUM","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"V7CGPSMZ","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:017fa4b0a8dcd4e59ff356c10661493bc03a04afa287b60cccdc42a0dceabd9f","target":"graph","created_at":"2026-05-17T23:48:02Z","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 consider a 3-dimensional Riemannian manifold M with two circulant structures -- a metric g and an endomorphism q whose third power is identity. The structure q is compatible with g such that an isometry is induced in any tangent space of M. We obtain some curvature properties of this manifold (M, g, q) and give an explicit example of such a manifold.","authors_text":"Dimitar Razpopov, Georgi Dzhelepov, Iva Dokuzova","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-08-22T12:02:05Z","title":"Three-dimensional Riemannian manifolds with circulant structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.4834","kind":"arxiv","version":3},"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":"sha256:2100a009d1735cb92713f30b194928b857414c93aebed94ea36e81462a483000","target":"record","created_at":"2026-05-17T23:48:02Z","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":"3bc902b30afd368cd361e482e9b343bcd6ba6a9a9e38b199a5aa389816a6e7e8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-08-22T12:02:05Z","title_canon_sha256":"44f03d704d7c4e345adc505a85f74a7016acbda15d425d340595845aa46682d1"},"schema_version":"1.0","source":{"id":"1308.4834","kind":"arxiv","version":3}},"canonical_sha256":"afc467c999deb9dede8c7903ab8cbfd2bfbd2404029e0a0af2569980fac17285","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"afc467c999deb9dede8c7903ab8cbfd2bfbd2404029e0a0af2569980fac17285","first_computed_at":"2026-05-17T23:48:02.654645Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:02.654645Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"R7veztRiMFDqMk/t9oG9TCbfUE3q5XJtLx3eCK4u5KRkOBx29slfosgw+hOuXa4++qUGrirkPEaOBC3QY6MZBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:02.655173Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.4834","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2100a009d1735cb92713f30b194928b857414c93aebed94ea36e81462a483000","sha256:017fa4b0a8dcd4e59ff356c10661493bc03a04afa287b60cccdc42a0dceabd9f"],"state_sha256":"56cdabde9c6f88f07eb6ad5d8f8c8732d9c96f12b1ffda15bbdf68d2ee7876d3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TaZfuuYZHaxKZYIIl6GmF3Zkj/P+tBPah4OgnEDrHm3fBluDKdr5U1a1Aw2l39HnaisIKbbdeXu4mZMEvEqeBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T05:00:30.923060Z","bundle_sha256":"77fb34267bd52352877aaa12bc53a895372cf263ff5b4ad0db7618fc209ad43d"}}