{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:G4BHVSVVIJUXIJS2ASTRMKYCPN","short_pith_number":"pith:G4BHVSVV","schema_version":"1.0","canonical_sha256":"37027acab5426974265a04a7162b027b6d405ff72822a44c8b7ee6dee98afa5c","source":{"kind":"arxiv","id":"1504.01498","version":2},"attestation_state":"computed","paper":{"title":"Metrics with Prescribed Ricci Curvature on Homogeneous Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Artem Pulemotov","submitted_at":"2015-04-07T07:12:19Z","abstract_excerpt":"Let $G$ be a compact connected Lie group and $H$ a closed subgroup of $G$. Suppose the homogeneous space $G/H$ is effective and has dimension 3 or higher. Consider a $G$-invariant, symmetric, positive-semidefinite, nonzero (0,2)-tensor field $T$ on $G/H$. Assume that $H$ is a maximal connected Lie subgroup of $G$. We prove the existence of a $G$-invariant Riemannian metric $g$ and a positive number $c$ such that the Ricci curvature of $g$ coincides with $cT$ on $G/H$. Afterwards, we examine what happens when the maximality hypothesis fails to hold."},"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":"1504.01498","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-04-07T07:12:19Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"da92307cacc7397cf8654608789a2c33b528f6615463fcb520d88f34277e0d90","abstract_canon_sha256":"df99d3cc7785fc4eb155d91be5f09ad1976145c0a2c37c57d0e7640c2027874e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:08.624506Z","signature_b64":"ZDeCf0pEK+lzdxb657XsmO/Ks1CVgPJ76U1yyK8r5CrWRW2oV1rrEtRENW/a1ru0aaHSAId94Fz9CP7hVQ1aCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"37027acab5426974265a04a7162b027b6d405ff72822a44c8b7ee6dee98afa5c","last_reissued_at":"2026-05-18T01:12:08.623918Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:08.623918Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Metrics with Prescribed Ricci Curvature on Homogeneous Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Artem Pulemotov","submitted_at":"2015-04-07T07:12:19Z","abstract_excerpt":"Let $G$ be a compact connected Lie group and $H$ a closed subgroup of $G$. Suppose the homogeneous space $G/H$ is effective and has dimension 3 or higher. Consider a $G$-invariant, symmetric, positive-semidefinite, nonzero (0,2)-tensor field $T$ on $G/H$. Assume that $H$ is a maximal connected Lie subgroup of $G$. We prove the existence of a $G$-invariant Riemannian metric $g$ and a positive number $c$ such that the Ricci curvature of $g$ coincides with $cT$ on $G/H$. Afterwards, we examine what happens when the maximality hypothesis fails to hold."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01498","kind":"arxiv","version":2},"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":"1504.01498","created_at":"2026-05-18T01:12:08.624014+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.01498v2","created_at":"2026-05-18T01:12:08.624014+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.01498","created_at":"2026-05-18T01:12:08.624014+00:00"},{"alias_kind":"pith_short_12","alias_value":"G4BHVSVVIJUX","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_16","alias_value":"G4BHVSVVIJUXIJS2","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_8","alias_value":"G4BHVSVV","created_at":"2026-05-18T12:29:22.688609+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/G4BHVSVVIJUXIJS2ASTRMKYCPN","json":"https://pith.science/pith/G4BHVSVVIJUXIJS2ASTRMKYCPN.json","graph_json":"https://pith.science/api/pith-number/G4BHVSVVIJUXIJS2ASTRMKYCPN/graph.json","events_json":"https://pith.science/api/pith-number/G4BHVSVVIJUXIJS2ASTRMKYCPN/events.json","paper":"https://pith.science/paper/G4BHVSVV"},"agent_actions":{"view_html":"https://pith.science/pith/G4BHVSVVIJUXIJS2ASTRMKYCPN","download_json":"https://pith.science/pith/G4BHVSVVIJUXIJS2ASTRMKYCPN.json","view_paper":"https://pith.science/paper/G4BHVSVV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.01498&json=true","fetch_graph":"https://pith.science/api/pith-number/G4BHVSVVIJUXIJS2ASTRMKYCPN/graph.json","fetch_events":"https://pith.science/api/pith-number/G4BHVSVVIJUXIJS2ASTRMKYCPN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/G4BHVSVVIJUXIJS2ASTRMKYCPN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/G4BHVSVVIJUXIJS2ASTRMKYCPN/action/storage_attestation","attest_author":"https://pith.science/pith/G4BHVSVVIJUXIJS2ASTRMKYCPN/action/author_attestation","sign_citation":"https://pith.science/pith/G4BHVSVVIJUXIJS2ASTRMKYCPN/action/citation_signature","submit_replication":"https://pith.science/pith/G4BHVSVVIJUXIJS2ASTRMKYCPN/action/replication_record"}},"created_at":"2026-05-18T01:12:08.624014+00:00","updated_at":"2026-05-18T01:12:08.624014+00:00"}