{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:TTFFU7BO35BT4UOE26M4ZLSXSB","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":"278d250411cb597716efff71713b8c9989ac722677fad871e1c4771731e5b21e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2007-07-26T10:43:21Z","title_canon_sha256":"172b37f51ffacfe0a841091b06d26dd8cd698d8668bbcbafdb9b58707475d06c"},"schema_version":"1.0","source":{"id":"0707.3894","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0707.3894","created_at":"2026-05-18T04:24:52Z"},{"alias_kind":"arxiv_version","alias_value":"0707.3894v4","created_at":"2026-05-18T04:24:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0707.3894","created_at":"2026-05-18T04:24:52Z"},{"alias_kind":"pith_short_12","alias_value":"TTFFU7BO35BT","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"TTFFU7BO35BT4UOE","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"TTFFU7BO","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:68ac7a4c4cbd3cb678b0651903f519c0586c78741b1096f24b299e442d27fd50","target":"graph","created_at":"2026-05-18T04:24:52Z","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":"We prove that if $(M^n,g)$, $n \\ge 4$, is a compact, orientable, locally irreducible Riemannian manifold with nonnegative isotropic curvature, then one of the following possibilities hold:\n  (i) $M$ admits a metric with positive isotropic curvature\n  (ii) $(M,g)$ is isometric to a locally symmetric space\n  (iii) $(M,g)$ is K\\\"ahler and biholomorphic to $\\C P^\\frac {n}{2}$.\n  (iv) $(M,g)$ is quaternionic-K\\\"ahler.\n  This is implied by the following result:\n  Let $(M^{2n},g)$ be a compact, locally irreducible K\\\"ahler manifold with nonnegative isotropic curvature. Then either $M$ is biholomorphi","authors_text":"Harish Seshadri","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2007-07-26T10:43:21Z","title":"Manifolds with nonnegative isotropic curvature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0707.3894","kind":"arxiv","version":4},"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":"sha256:21d63427bf0b4047996f7c9bcc59190433d3198730e1b1573646418ce08af522","target":"record","created_at":"2026-05-18T04:24:52Z","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":"278d250411cb597716efff71713b8c9989ac722677fad871e1c4771731e5b21e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2007-07-26T10:43:21Z","title_canon_sha256":"172b37f51ffacfe0a841091b06d26dd8cd698d8668bbcbafdb9b58707475d06c"},"schema_version":"1.0","source":{"id":"0707.3894","kind":"arxiv","version":4}},"canonical_sha256":"9cca5a7c2edf433e51c4d799ccae57904d7e802554cc0eec9f2dedb33380f7ba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9cca5a7c2edf433e51c4d799ccae57904d7e802554cc0eec9f2dedb33380f7ba","first_computed_at":"2026-05-18T04:24:52.084872Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:24:52.084872Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Z5tAd3rS+wRfuXBqnyw/olnyUlIo8ie67X2RClJdsu7hvQ+xp6gv+bIidhnxD4/nXqc7P1F1fNnSCO0LVaKlBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:24:52.085348Z","signed_message":"canonical_sha256_bytes"},"source_id":"0707.3894","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:21d63427bf0b4047996f7c9bcc59190433d3198730e1b1573646418ce08af522","sha256:68ac7a4c4cbd3cb678b0651903f519c0586c78741b1096f24b299e442d27fd50"],"state_sha256":"5321c351f4277130ed3964d8d56d16819b8c0cc5b6b42a9d8f0a4a387e84b0a1"}