{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:EXNMRCHQJ23JF222MPJTGNPOLZ","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":"49d7bacbf80d99ce2c08386a08b72fbb817834d07804b4697ed06003637c449d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-07-09T02:41:01Z","title_canon_sha256":"37b495b68f137a2dabf23a7abae4e3f3ee533edc9e7a41ecbaad32582e04bddb"},"schema_version":"1.0","source":{"id":"1007.1498","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.1498","created_at":"2026-05-18T04:39:38Z"},{"alias_kind":"arxiv_version","alias_value":"1007.1498v2","created_at":"2026-05-18T04:39:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.1498","created_at":"2026-05-18T04:39:38Z"},{"alias_kind":"pith_short_12","alias_value":"EXNMRCHQJ23J","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"EXNMRCHQJ23JF222","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"EXNMRCHQ","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:79d235d9f9b083ecf1d6bd4334302701d1f693c5f0ba4a79d0b799277b884a11","target":"graph","created_at":"2026-05-18T04:39:38Z","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":"In this work, we will verify some comparison results on Kahler manifolds. They are complex Hessian comparison for the distance function from a closed complex submanifold of a Kahler manifold with holomorphic bisectional curvature bounded below by a constant, eigenvalue comparison and volume comparison in terms of scalar curvature. This work is motivated by comparison results of Li and Wang .","authors_text":"Chengjie Yu, Luen-fai Tam","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-07-09T02:41:01Z","title":"Some comparison theorems for Kahler manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.1498","kind":"arxiv","version":2},"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":"sha256:1d5fe5285f761994e2306906e680e6be2d6b3bd3022e8cd89d14515dbb98c6cb","target":"record","created_at":"2026-05-18T04:39:38Z","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":"49d7bacbf80d99ce2c08386a08b72fbb817834d07804b4697ed06003637c449d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-07-09T02:41:01Z","title_canon_sha256":"37b495b68f137a2dabf23a7abae4e3f3ee533edc9e7a41ecbaad32582e04bddb"},"schema_version":"1.0","source":{"id":"1007.1498","kind":"arxiv","version":2}},"canonical_sha256":"25dac888f04eb692eb5a63d33335ee5e6d1fc4f901ab3e812bb22327dca9f78c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"25dac888f04eb692eb5a63d33335ee5e6d1fc4f901ab3e812bb22327dca9f78c","first_computed_at":"2026-05-18T04:39:38.705972Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:39:38.705972Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"X0BFIWsL7uFynLBI5Rp5nCpwhrwptM7Ib1vHYTbPSwnp5r7mkb2W6mEiGaTL4m62SC3Qg0rNIRlGBUeLnbrRCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:39:38.706448Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.1498","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1d5fe5285f761994e2306906e680e6be2d6b3bd3022e8cd89d14515dbb98c6cb","sha256:79d235d9f9b083ecf1d6bd4334302701d1f693c5f0ba4a79d0b799277b884a11"],"state_sha256":"9efba53b660fcb304304b3b5d598dacaf0e7a5bcdca6c3536e9dacc3b7ff1f13"}