{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:32W4STGWMXQKZX2MWL7MQCZTUM","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":"51b037571e4c0da3495a9e2df08b625207914f8fb6e8f6511f5615066fe97218","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-05-01T10:28:57Z","title_canon_sha256":"283412bea1742c423a4eecf0706f37c6f3fe0e68f4471e40155b0c6b55f5efd6"},"schema_version":"1.0","source":{"id":"1705.00460","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.00460","created_at":"2026-05-17T23:59:25Z"},{"alias_kind":"arxiv_version","alias_value":"1705.00460v2","created_at":"2026-05-17T23:59:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.00460","created_at":"2026-05-17T23:59:25Z"},{"alias_kind":"pith_short_12","alias_value":"32W4STGWMXQK","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"32W4STGWMXQKZX2M","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"32W4STGW","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:1c3aad3b4579fd38f90367dc83e3999a79a87a22453e9682d5201b8e487127f7","target":"graph","created_at":"2026-05-17T23:59:25Z","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":"In this paper, it is proved that a connected 3-dimensional Riemannian manifold or a closed connected semi-Riemannian manifold $M^n$($n>1$) admitting a projective vector field with a non-linearizable singularity is projectively flat.","authors_text":"Tianyu Ma","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-05-01T10:28:57Z","title":"Geodesic rigidity of Levi-Civita connections admitting essential projective vector fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.00460","kind":"arxiv","version":2},"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":"sha256:9bfe2e07f64aa4cfcbda6e8da6701a8457313e03093a29fede3198bd835d9608","target":"record","created_at":"2026-05-17T23:59:25Z","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":"51b037571e4c0da3495a9e2df08b625207914f8fb6e8f6511f5615066fe97218","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-05-01T10:28:57Z","title_canon_sha256":"283412bea1742c423a4eecf0706f37c6f3fe0e68f4471e40155b0c6b55f5efd6"},"schema_version":"1.0","source":{"id":"1705.00460","kind":"arxiv","version":2}},"canonical_sha256":"deadc94cd665e0acdf4cb2fec80b33a311fc4d49ee823cc127f92f30349b432d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"deadc94cd665e0acdf4cb2fec80b33a311fc4d49ee823cc127f92f30349b432d","first_computed_at":"2026-05-17T23:59:25.307334Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:25.307334Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jIeZwmhsFFcCuvBxKzTVm314WdrQb7bTLIPh530gGcQn5OKeC+5HG5bs8WebPqqt5ZdGhkyGyTvFee3SRIaRCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:25.307972Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.00460","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9bfe2e07f64aa4cfcbda6e8da6701a8457313e03093a29fede3198bd835d9608","sha256:1c3aad3b4579fd38f90367dc83e3999a79a87a22453e9682d5201b8e487127f7"],"state_sha256":"e1d4f8fa299bc2c0f21b6cfd4b436f48c07820d22e39ecd83ce81154d60cf05c"}