{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:MU2WKTNXB5BMTMWU5LBVRGY4L4","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":"0cdd65fe14149bd359c22512717e4cbef11794e9aeedf4c3aab168bd8d7a16e7","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2016-07-19T15:58:09Z","title_canon_sha256":"b4b084fa0d5ff2fc0473dacbf3e203757e3db0dee007d2fee530e1a3d4c355e9"},"schema_version":"1.0","source":{"id":"1607.05644","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.05644","created_at":"2026-05-18T00:24:35Z"},{"alias_kind":"arxiv_version","alias_value":"1607.05644v1","created_at":"2026-05-18T00:24:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.05644","created_at":"2026-05-18T00:24:35Z"},{"alias_kind":"pith_short_12","alias_value":"MU2WKTNXB5BM","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MU2WKTNXB5BMTMWU","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MU2WKTNX","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:f1b7cc4c713297765a350138d418034e459a1fb34e30cfe60f077efd7a6627f1","target":"graph","created_at":"2026-05-18T00:24:35Z","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":"A manifold is locally \\emph{$k$-fold symmetric}, if for any point and any $k$-dimensional vector subspace tangent to this point there exists a local isometry such that this point is a fixed point and the differential of the isometry restricted to that $k$-dimensional vector subspace is minus the identity. We show that for $k \\ge 2$, Riemannian, pseudoriemannian and Finslerian locally $k$-fold symmetric manifolds are locally symmetric.","authors_text":"ShaoQiang Deng, Vladimir S. Matveev","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2016-07-19T15:58:09Z","title":"Locally 2-fold symmetric manifolds are locally symmetric"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.05644","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":"sha256:41104f35ad354819c499ae4a33a26c4db6f5e483bbcf6f811b2a035e340e800d","target":"record","created_at":"2026-05-18T00:24:35Z","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":"0cdd65fe14149bd359c22512717e4cbef11794e9aeedf4c3aab168bd8d7a16e7","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2016-07-19T15:58:09Z","title_canon_sha256":"b4b084fa0d5ff2fc0473dacbf3e203757e3db0dee007d2fee530e1a3d4c355e9"},"schema_version":"1.0","source":{"id":"1607.05644","kind":"arxiv","version":1}},"canonical_sha256":"6535654db70f42c9b2d4eac3589b1c5f231ae287302e5bc2aa51e613d5f314ea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6535654db70f42c9b2d4eac3589b1c5f231ae287302e5bc2aa51e613d5f314ea","first_computed_at":"2026-05-18T00:24:35.563035Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:35.563035Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O8bpMwpxWtZ9zD65VUb3+dt3kLW0kF+fe43p4yXTdaj4CmW7a5U78DJhKKH2IGVMRze+TuO/4f7aCI8cxy5UAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:35.563459Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.05644","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:41104f35ad354819c499ae4a33a26c4db6f5e483bbcf6f811b2a035e340e800d","sha256:f1b7cc4c713297765a350138d418034e459a1fb34e30cfe60f077efd7a6627f1"],"state_sha256":"2f45a99a14c09ade9709c22b2f354c911c17600085eaabb3bf555a263f1fecdc"}