{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:S634F3BXDEGDVTEPBSS7IVLL52","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":"d5e48f36931630e20814c46da439c26a0cbb366d75e1b26a3e03c88f9ac8472a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-08-07T17:51:51Z","title_canon_sha256":"d007d7625a576d47df5fa723ef3de6ea75be014b68c8ed024841f099e524d06d"},"schema_version":"1.0","source":{"id":"1808.02475","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.02475","created_at":"2026-05-18T00:08:36Z"},{"alias_kind":"arxiv_version","alias_value":"1808.02475v1","created_at":"2026-05-18T00:08:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.02475","created_at":"2026-05-18T00:08:36Z"},{"alias_kind":"pith_short_12","alias_value":"S634F3BXDEGD","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"S634F3BXDEGDVTEP","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"S634F3BX","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:7e350282998d189b6c50847b803ec0376f9f3b0c8464befc9d7eeb9a2c510a57","target":"graph","created_at":"2026-05-18T00:08:36Z","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":"Let $M$ be a complete Riemannian manifold and suppose $p\\in M$. For each unit vector $v \\in T_p M$, the $\\textit{Jacobi operator}$, $\\mathcal{J}_v: v^\\perp \\rightarrow v^\\perp$ is the symmetric endomorphism, $\\mathcal{J}_v(w) = R(w,v)v$. Then $p$ is an $\\textit{isotropic point}$ if there exists a constant $\\kappa_p \\in \\mathbf{R}$ such that $\\mathcal{J}_v = \\kappa_p \\textit{ Id}_{v^\\perp}$ for each unit vector $v \\in T_pM$. If all points are isotropic, then $M$ is said to be isotropic; it is a classical result of Schur that isotropic manifolds of dimension at least 3 have constant sectional cu","authors_text":"Benjamin Schmidt, Krishnan Shankar, Ralf Spatzier","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-08-07T17:51:51Z","title":"Almost Isotropic Kaehler Manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.02475","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":"sha256:464ee68d0796bc08cfb1c65e2f1aee3c68baba7c08b65c4e306c24c9406b6f7f","target":"record","created_at":"2026-05-18T00:08:36Z","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":"d5e48f36931630e20814c46da439c26a0cbb366d75e1b26a3e03c88f9ac8472a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-08-07T17:51:51Z","title_canon_sha256":"d007d7625a576d47df5fa723ef3de6ea75be014b68c8ed024841f099e524d06d"},"schema_version":"1.0","source":{"id":"1808.02475","kind":"arxiv","version":1}},"canonical_sha256":"97b7c2ec37190c3acc8f0ca5f4556beea851289284f6f61c4f1f7a86f697b3b7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"97b7c2ec37190c3acc8f0ca5f4556beea851289284f6f61c4f1f7a86f697b3b7","first_computed_at":"2026-05-18T00:08:36.962890Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:08:36.962890Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ip4SglmBl2otpHs6sX2EEPbNzC7WNeZ8grq/TIZHvcmRnZJq8xu2EqX8cDZDt6+bi8DxlIc9n3yzVRyoVNsoBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:08:36.963414Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.02475","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:464ee68d0796bc08cfb1c65e2f1aee3c68baba7c08b65c4e306c24c9406b6f7f","sha256:7e350282998d189b6c50847b803ec0376f9f3b0c8464befc9d7eeb9a2c510a57"],"state_sha256":"2d861eaab54ea4fd7cd4dba72fd5545fe57f5b790b7e6d0577ad2dbd925af70a"}