{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1999:JVGMLZEBITODJP3LPQIOKGANSF","short_pith_number":"pith:JVGMLZEB","canonical_record":{"source":{"id":"math/9910118","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"1999-10-22T12:59:32Z","cross_cats_sorted":[],"title_canon_sha256":"a38f276fde2bfa0589f288c9590c6559434fba6a6b1e00b7d15935d2ee0c401e","abstract_canon_sha256":"01943877d8256286b1dcd9f7ca680b0bc7f8e401368bbde8ac3aca5afe2e222e"},"schema_version":"1.0"},"canonical_sha256":"4d4cc5e48144dc34bf6b7c10e5180d914b6e2cac38966b9a6f1d9518408ea1c2","source":{"kind":"arxiv","id":"math/9910118","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9910118","created_at":"2026-05-18T03:07:11Z"},{"alias_kind":"arxiv_version","alias_value":"math/9910118v3","created_at":"2026-05-18T03:07:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9910118","created_at":"2026-05-18T03:07:11Z"},{"alias_kind":"pith_short_12","alias_value":"JVGMLZEBITOD","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"JVGMLZEBITODJP3L","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"JVGMLZEB","created_at":"2026-05-18T12:25:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1999:JVGMLZEBITODJP3LPQIOKGANSF","target":"record","payload":{"canonical_record":{"source":{"id":"math/9910118","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"1999-10-22T12:59:32Z","cross_cats_sorted":[],"title_canon_sha256":"a38f276fde2bfa0589f288c9590c6559434fba6a6b1e00b7d15935d2ee0c401e","abstract_canon_sha256":"01943877d8256286b1dcd9f7ca680b0bc7f8e401368bbde8ac3aca5afe2e222e"},"schema_version":"1.0"},"canonical_sha256":"4d4cc5e48144dc34bf6b7c10e5180d914b6e2cac38966b9a6f1d9518408ea1c2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:07:11.300442Z","signature_b64":"qWGlWcixcZQiZH5iTqkZnPo72WGqlt47Evx6oj0/6fQDihNPULwgpx2xuDTMQBKu80IuY6wNQcYEy/WT8xJOBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4d4cc5e48144dc34bf6b7c10e5180d914b6e2cac38966b9a6f1d9518408ea1c2","last_reissued_at":"2026-05-18T03:07:11.299995Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:07:11.299995Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/9910118","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:07:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0tU+hsZA4/eCQ3kv8FIcoK0E4xsJEmgTH2dplxlxTtqx16qD+WdXvPtgN7WYVvKeZ/6Bx529M6OHBHgxvmxFCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T05:04:55.935095Z"},"content_sha256":"530d0753e9226acc1da61ec5085b2ff632b7455c4aa8050678d428f6f7ebdbd8","schema_version":"1.0","event_id":"sha256:530d0753e9226acc1da61ec5085b2ff632b7455c4aa8050678d428f6f7ebdbd8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1999:JVGMLZEBITODJP3LPQIOKGANSF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Semi-continuity of complex singularity exponents and K\\\"ahler-Einstein metrics on Fano orbifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"J\\'anos Koll\\'ar, Jean-Pierre Demailly","submitted_at":"1999-10-22T12:59:32Z","abstract_excerpt":"We introduce complex singularity exponents of plurisubharmonic functions and prove a general semi-continuity result for them. This concept contains as a special case several similar concepts which have been considered e.g. by Arnold and Varchenko, mostly for the study of hypersurface singularities. The plurisubharmonic version is somehow based on a reduction to the algebraic case, but it also takes into account more quantitative informations of great interest for complex analysis and complex differential geometry. We give as an application a new derivation of criteria for the existence of K\\\"a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9910118","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:07:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OO1MHBvlzghVbsH6tT/B1PcAlVptuu2TryVZP3KXupuVkwRxMFEv44Ucq1T1gKQDKeQnMIrEOljSH6XWcig/Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T05:04:55.935781Z"},"content_sha256":"1f882128cdc149e62937c3c1e815b5203c8ac4d2220a1120de05fd3590863ab0","schema_version":"1.0","event_id":"sha256:1f882128cdc149e62937c3c1e815b5203c8ac4d2220a1120de05fd3590863ab0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JVGMLZEBITODJP3LPQIOKGANSF/bundle.json","state_url":"https://pith.science/pith/JVGMLZEBITODJP3LPQIOKGANSF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JVGMLZEBITODJP3LPQIOKGANSF/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-27T05:04:55Z","links":{"resolver":"https://pith.science/pith/JVGMLZEBITODJP3LPQIOKGANSF","bundle":"https://pith.science/pith/JVGMLZEBITODJP3LPQIOKGANSF/bundle.json","state":"https://pith.science/pith/JVGMLZEBITODJP3LPQIOKGANSF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JVGMLZEBITODJP3LPQIOKGANSF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1999:JVGMLZEBITODJP3LPQIOKGANSF","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":"01943877d8256286b1dcd9f7ca680b0bc7f8e401368bbde8ac3aca5afe2e222e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"1999-10-22T12:59:32Z","title_canon_sha256":"a38f276fde2bfa0589f288c9590c6559434fba6a6b1e00b7d15935d2ee0c401e"},"schema_version":"1.0","source":{"id":"math/9910118","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9910118","created_at":"2026-05-18T03:07:11Z"},{"alias_kind":"arxiv_version","alias_value":"math/9910118v3","created_at":"2026-05-18T03:07:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9910118","created_at":"2026-05-18T03:07:11Z"},{"alias_kind":"pith_short_12","alias_value":"JVGMLZEBITOD","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"JVGMLZEBITODJP3L","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"JVGMLZEB","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:1f882128cdc149e62937c3c1e815b5203c8ac4d2220a1120de05fd3590863ab0","target":"graph","created_at":"2026-05-18T03:07:11Z","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 introduce complex singularity exponents of plurisubharmonic functions and prove a general semi-continuity result for them. This concept contains as a special case several similar concepts which have been considered e.g. by Arnold and Varchenko, mostly for the study of hypersurface singularities. The plurisubharmonic version is somehow based on a reduction to the algebraic case, but it also takes into account more quantitative informations of great interest for complex analysis and complex differential geometry. We give as an application a new derivation of criteria for the existence of K\\\"a","authors_text":"J\\'anos Koll\\'ar, Jean-Pierre Demailly","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"1999-10-22T12:59:32Z","title":"Semi-continuity of complex singularity exponents and K\\\"ahler-Einstein metrics on Fano orbifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9910118","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":"sha256:530d0753e9226acc1da61ec5085b2ff632b7455c4aa8050678d428f6f7ebdbd8","target":"record","created_at":"2026-05-18T03:07:11Z","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":"01943877d8256286b1dcd9f7ca680b0bc7f8e401368bbde8ac3aca5afe2e222e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"1999-10-22T12:59:32Z","title_canon_sha256":"a38f276fde2bfa0589f288c9590c6559434fba6a6b1e00b7d15935d2ee0c401e"},"schema_version":"1.0","source":{"id":"math/9910118","kind":"arxiv","version":3}},"canonical_sha256":"4d4cc5e48144dc34bf6b7c10e5180d914b6e2cac38966b9a6f1d9518408ea1c2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4d4cc5e48144dc34bf6b7c10e5180d914b6e2cac38966b9a6f1d9518408ea1c2","first_computed_at":"2026-05-18T03:07:11.299995Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:07:11.299995Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qWGlWcixcZQiZH5iTqkZnPo72WGqlt47Evx6oj0/6fQDihNPULwgpx2xuDTMQBKu80IuY6wNQcYEy/WT8xJOBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:07:11.300442Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9910118","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:530d0753e9226acc1da61ec5085b2ff632b7455c4aa8050678d428f6f7ebdbd8","sha256:1f882128cdc149e62937c3c1e815b5203c8ac4d2220a1120de05fd3590863ab0"],"state_sha256":"be7bc87fad55045ce94e11d9108fb7589ad2f31c2c7cf5b1af30dc9be3b7fd52"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1pD/PvYbVmHcKXuXQG3XrC6+lOfwZfXRiMl19JMKe5FqQHAvPDbFndLTYWjY1p518k7RT+VfHQYfVfOvHyXHCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T05:04:55.938954Z","bundle_sha256":"80086eed9bfc53e57cf9840d85616d8691b5b62f6b7eb0f248723171d5eabc98"}}