{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:HXON235BMJHSYSPQO4KL7EWNXR","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":"eae196b1a8996721e59d1174b9954b7e6f8312a0cde0f8e082584b9398ce0420","cross_cats_sorted":["math.AG","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-09-30T03:18:38Z","title_canon_sha256":"420f3003292b91a6416cbd661d79093560db88f521de6277ea8445b902b8fdab"},"schema_version":"1.0","source":{"id":"1409.8374","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.8374","created_at":"2026-05-18T02:41:25Z"},{"alias_kind":"arxiv_version","alias_value":"1409.8374v1","created_at":"2026-05-18T02:41:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.8374","created_at":"2026-05-18T02:41:25Z"},{"alias_kind":"pith_short_12","alias_value":"HXON235BMJHS","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HXON235BMJHSYSPQ","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HXON235B","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:7f643024bfe55b68198966fa06851eac4f54caec432cec69664d39c33d9781f3","target":"graph","created_at":"2026-05-18T02:41:25Z","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 by Kawamata that the canonical bundle of a projective manifold is semi-ample if it is big and nef. We give an analytic proof using the Ricci flow, degeneration of Riemannian manifolds and $L^2$-theory. Combined with our earlier results, we construct unique singular Kahler-Einstein metrics with a global Riemannian structure on canonical models. Our approach can be viewed as the Kodaira embedding theorem on singular metric spaces with canonical Kahler metrics.","authors_text":"Jian Song","cross_cats":["math.AG","math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-09-30T03:18:38Z","title":"Riemannian geometry of Kahler-Einstein currents II: an analytic proof of Kawamata's base point free theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.8374","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:b16e7bea887fc17efe3f1d9d8c0a89dd4afd57e3e3ca19a402218e90f562b101","target":"record","created_at":"2026-05-18T02:41:25Z","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":"eae196b1a8996721e59d1174b9954b7e6f8312a0cde0f8e082584b9398ce0420","cross_cats_sorted":["math.AG","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-09-30T03:18:38Z","title_canon_sha256":"420f3003292b91a6416cbd661d79093560db88f521de6277ea8445b902b8fdab"},"schema_version":"1.0","source":{"id":"1409.8374","kind":"arxiv","version":1}},"canonical_sha256":"3ddcdd6fa1624f2c49f07714bf92cdbc7ad9af58e11f128e072f4ab11f1688b5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3ddcdd6fa1624f2c49f07714bf92cdbc7ad9af58e11f128e072f4ab11f1688b5","first_computed_at":"2026-05-18T02:41:25.463695Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:25.463695Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EjkDNeGWNsMiKsG1O9NG+7MmtYCEDB42ufUSOf2kFpTsV58sHri32a3nvAqSUt1WVWxOo+0dvwgLzQ2yxzZZAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:25.464434Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.8374","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b16e7bea887fc17efe3f1d9d8c0a89dd4afd57e3e3ca19a402218e90f562b101","sha256:7f643024bfe55b68198966fa06851eac4f54caec432cec69664d39c33d9781f3"],"state_sha256":"25fe838758363541576215064732b68b05947cbc11c16c5070d1c10795b2fb43"}