{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:JEHBKEJHHQQ2AQZPOHLVH4BSRF","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":"82a2fa0520002acbe7831f49ec0f87f448b051359f2d10a0bf91577fc2232508","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-10-22T06:26:47Z","title_canon_sha256":"cb9f687feae84417effe757ca17f499b3e5f0d5f7744b3882652bf6b86e8a382"},"schema_version":"1.0","source":{"id":"1010.4620","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.4620","created_at":"2026-05-18T04:36:50Z"},{"alias_kind":"arxiv_version","alias_value":"1010.4620v2","created_at":"2026-05-18T04:36:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.4620","created_at":"2026-05-18T04:36:50Z"},{"alias_kind":"pith_short_12","alias_value":"JEHBKEJHHQQ2","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"JEHBKEJHHQQ2AQZP","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"JEHBKEJH","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:437d9a8b0b3da549d1d3404f516374b3a966ad0e5916f5d5df6e6a31c887e18b","target":"graph","created_at":"2026-05-18T04:36:50Z","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 article, we study complete pseudo-Riemannian manifolds whose cone admits a parallel symmetric 2-tensorfield. The situation splits in three cases: nilpotent, decomposable or complex Riemannian. In the complex Riemannian and decomposable cases we provide a classification. In the nilpotent case, we are able to describe completely only a dense open subset of the manifold. To conclude, we give examples with non-constant curvature in the nilpotent case.","authors_text":"Pierre Mounoud (IMB)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-10-22T06:26:47Z","title":"On parallel and symmetric 2-tensorfields on cones over pseudo-Riemannian manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.4620","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:adcedb00c7b664423763a0c57b35b24602ee2e95e36d33b8962a3291d5aa6c34","target":"record","created_at":"2026-05-18T04:36:50Z","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":"82a2fa0520002acbe7831f49ec0f87f448b051359f2d10a0bf91577fc2232508","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-10-22T06:26:47Z","title_canon_sha256":"cb9f687feae84417effe757ca17f499b3e5f0d5f7744b3882652bf6b86e8a382"},"schema_version":"1.0","source":{"id":"1010.4620","kind":"arxiv","version":2}},"canonical_sha256":"490e1511273c21a0432f71d753f0328948b12b459019e56dfd6174c79d71fd1f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"490e1511273c21a0432f71d753f0328948b12b459019e56dfd6174c79d71fd1f","first_computed_at":"2026-05-18T04:36:50.024404Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:36:50.024404Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EkhEp1lO0oATnC58oexFgBupAWoc2sraX5htX//gFoX4LHF1l/L4V7IzAAU6mW9ZYX20OsCe8gYiZuqm5tIoCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:36:50.024925Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.4620","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:adcedb00c7b664423763a0c57b35b24602ee2e95e36d33b8962a3291d5aa6c34","sha256:437d9a8b0b3da549d1d3404f516374b3a966ad0e5916f5d5df6e6a31c887e18b"],"state_sha256":"b2b2c60b2d69747007ff6d04d5dbef8522f033021cbd35d25f2be73ca493dd14"}