{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:2K5M6XT4JPVPBFM5IFQERIAP6S","short_pith_number":"pith:2K5M6XT4","schema_version":"1.0","canonical_sha256":"d2bacf5e7c4beaf0959d416048a00ff4887c60a7a3a477078d09a2f9199d3434","source":{"kind":"arxiv","id":"1002.0505","version":1},"attestation_state":"computed","paper":{"title":"Curvature operators and scalar curvature invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"gr-qc","authors_text":"A. Coley, S. Hervik","submitted_at":"2010-02-02T15:07:15Z","abstract_excerpt":"We continue the study of the question of when a pseudo-Riemannain manifold can be locally characterised by its scalar polynomial curvature invariants (constructed from the Riemann tensor and its covariant derivatives). We make further use of alignment theory and the bivector form of the Weyl operator in higher dimensions, and introduce the important notions of diagonalisability and (complex) analytic metric extension. We show that if there exists an analytic metric extension of an arbitrary dimensional space of any signature to a Riemannian space (of Euclidean signature), then that space is ch"},"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":"1002.0505","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-02-02T15:07:15Z","cross_cats_sorted":["hep-th","math-ph","math.MP"],"title_canon_sha256":"defbf88526ec323631129398d1373ae28a4f9d2bc73f1fa48603d7e9d0e1a36c","abstract_canon_sha256":"5b21a5746c3e6b4b167b7f917cfe2b776428d1afd699aa06b1e37912749cd0e6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:09:20.897310Z","signature_b64":"MdqFVTdPtN/zPocHREow599eGqlxpZfsAmRQ676ZlEcGpJzwzxwL0xE5w/k4NdEKNAHFNk9WMS0wB/HLWhqsAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d2bacf5e7c4beaf0959d416048a00ff4887c60a7a3a477078d09a2f9199d3434","last_reissued_at":"2026-05-18T02:09:20.896856Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:09:20.896856Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Curvature operators and scalar curvature invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"gr-qc","authors_text":"A. Coley, S. Hervik","submitted_at":"2010-02-02T15:07:15Z","abstract_excerpt":"We continue the study of the question of when a pseudo-Riemannain manifold can be locally characterised by its scalar polynomial curvature invariants (constructed from the Riemann tensor and its covariant derivatives). We make further use of alignment theory and the bivector form of the Weyl operator in higher dimensions, and introduce the important notions of diagonalisability and (complex) analytic metric extension. We show that if there exists an analytic metric extension of an arbitrary dimensional space of any signature to a Riemannian space (of Euclidean signature), then that space is ch"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.0505","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":"1002.0505","created_at":"2026-05-18T02:09:20.896922+00:00"},{"alias_kind":"arxiv_version","alias_value":"1002.0505v1","created_at":"2026-05-18T02:09:20.896922+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.0505","created_at":"2026-05-18T02:09:20.896922+00:00"},{"alias_kind":"pith_short_12","alias_value":"2K5M6XT4JPVP","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_16","alias_value":"2K5M6XT4JPVPBFM5","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_8","alias_value":"2K5M6XT4","created_at":"2026-05-18T12:26:03.138858+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/2K5M6XT4JPVPBFM5IFQERIAP6S","json":"https://pith.science/pith/2K5M6XT4JPVPBFM5IFQERIAP6S.json","graph_json":"https://pith.science/api/pith-number/2K5M6XT4JPVPBFM5IFQERIAP6S/graph.json","events_json":"https://pith.science/api/pith-number/2K5M6XT4JPVPBFM5IFQERIAP6S/events.json","paper":"https://pith.science/paper/2K5M6XT4"},"agent_actions":{"view_html":"https://pith.science/pith/2K5M6XT4JPVPBFM5IFQERIAP6S","download_json":"https://pith.science/pith/2K5M6XT4JPVPBFM5IFQERIAP6S.json","view_paper":"https://pith.science/paper/2K5M6XT4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1002.0505&json=true","fetch_graph":"https://pith.science/api/pith-number/2K5M6XT4JPVPBFM5IFQERIAP6S/graph.json","fetch_events":"https://pith.science/api/pith-number/2K5M6XT4JPVPBFM5IFQERIAP6S/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2K5M6XT4JPVPBFM5IFQERIAP6S/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2K5M6XT4JPVPBFM5IFQERIAP6S/action/storage_attestation","attest_author":"https://pith.science/pith/2K5M6XT4JPVPBFM5IFQERIAP6S/action/author_attestation","sign_citation":"https://pith.science/pith/2K5M6XT4JPVPBFM5IFQERIAP6S/action/citation_signature","submit_replication":"https://pith.science/pith/2K5M6XT4JPVPBFM5IFQERIAP6S/action/replication_record"}},"created_at":"2026-05-18T02:09:20.896922+00:00","updated_at":"2026-05-18T02:09:20.896922+00:00"}