{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:767YOFH7XT43BJBSPVWRQN7VZT","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":"56b57dfa49058d7db082db649a4456bf61bd8c7c5c7599cff28aaca128b4c9ba","cross_cats_sorted":[],"license":"","primary_cat":"math.DG","submitted_at":"2000-07-20T00:52:01Z","title_canon_sha256":"5b6ff1e16c0b5acfccba22a12f2d821b09378b8b966a7b4828c1a3d15e66f6a0"},"schema_version":"1.0","source":{"id":"math/0007122","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0007122","created_at":"2026-05-17T23:56:49Z"},{"alias_kind":"arxiv_version","alias_value":"math/0007122v3","created_at":"2026-05-17T23:56:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0007122","created_at":"2026-05-17T23:56:49Z"},{"alias_kind":"pith_short_12","alias_value":"767YOFH7XT43","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"767YOFH7XT43BJBS","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"767YOFH7","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:01098d54fccaea39b34c078d55be00a7c0d2990f687b52a1963f0bcad013f3f9","target":"graph","created_at":"2026-05-17T23:56:49Z","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":"It is proved that a compact Kahler manifold whose Ricci tensor has two distinct, constant, non-negative eigenvalues is locally the product of two Kahler-Einstein manifolds. A stronger result is established for the case of Kahler surfaces. Irreducible Kahler manifolds with two distinct, constant eigenvalues of the Ricci tensor are shown to exist in various situations: there are homogeneous examples of any complex dimension n > 1, if one eigenvalue is negative and the other positive or zero, and of any complex dimension n > 2, if the both eigenvalues are negative; there are non-homogeneous examp","authors_text":"Andrei Moroianu, Tedi Draghici, Vestislav Apostolov","cross_cats":[],"headline":"","license":"","primary_cat":"math.DG","submitted_at":"2000-07-20T00:52:01Z","title":"A splitting theorem for Kahler manifolds whose Ricci tensors have constant eigenvalues"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0007122","kind":"arxiv","version":3},"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:ffd1da8d46af0c64d648489933b3b926287c1dd27bedc370c4ed823b063139d8","target":"record","created_at":"2026-05-17T23:56:49Z","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":"56b57dfa49058d7db082db649a4456bf61bd8c7c5c7599cff28aaca128b4c9ba","cross_cats_sorted":[],"license":"","primary_cat":"math.DG","submitted_at":"2000-07-20T00:52:01Z","title_canon_sha256":"5b6ff1e16c0b5acfccba22a12f2d821b09378b8b966a7b4828c1a3d15e66f6a0"},"schema_version":"1.0","source":{"id":"math/0007122","kind":"arxiv","version":3}},"canonical_sha256":"ffbf8714ffbcf9b0a4327d6d1837f5ccfe6c1d3417a7ad2a7027c136038c0213","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ffbf8714ffbcf9b0a4327d6d1837f5ccfe6c1d3417a7ad2a7027c136038c0213","first_computed_at":"2026-05-17T23:56:49.294031Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:49.294031Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Oen3F1mSz72CxZa2v8FxDGNVgc137w373BxrW4mlDVyZbIRojUebzxc0iSHdSF9Y2pplH4ABjVWfVL4uFJSlDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:49.294501Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0007122","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ffd1da8d46af0c64d648489933b3b926287c1dd27bedc370c4ed823b063139d8","sha256:01098d54fccaea39b34c078d55be00a7c0d2990f687b52a1963f0bcad013f3f9"],"state_sha256":"e60f68d4b5a499fd7ba526133144bea93cfc32c01e26a59e136c17e948a1861c"}