{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:VXIDDEDKNMCOHOEY4YNYZYNJSO","short_pith_number":"pith:VXIDDEDK","canonical_record":{"source":{"id":"1207.7346","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-07-31T19:15:48Z","cross_cats_sorted":["math.CV","math.DG"],"title_canon_sha256":"1a79257258330c4200e6b7ec2c46e4c599d41845b4d81b31ec2af5fdf8a3ac30","abstract_canon_sha256":"630961af259349d3707180f92596f26fbfe50f7b93f92b8b9ff52ee1eef7f150"},"schema_version":"1.0"},"canonical_sha256":"add031906a6b04e3b898e61b8ce1a9939e58f3306778edda528a18150aac65c6","source":{"kind":"arxiv","id":"1207.7346","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.7346","created_at":"2026-05-18T00:05:15Z"},{"alias_kind":"arxiv_version","alias_value":"1207.7346v4","created_at":"2026-05-18T00:05:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.7346","created_at":"2026-05-18T00:05:15Z"},{"alias_kind":"pith_short_12","alias_value":"VXIDDEDKNMCO","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VXIDDEDKNMCOHOEY","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VXIDDEDK","created_at":"2026-05-18T12:27:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:VXIDDEDKNMCOHOEY4YNYZYNJSO","target":"record","payload":{"canonical_record":{"source":{"id":"1207.7346","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-07-31T19:15:48Z","cross_cats_sorted":["math.CV","math.DG"],"title_canon_sha256":"1a79257258330c4200e6b7ec2c46e4c599d41845b4d81b31ec2af5fdf8a3ac30","abstract_canon_sha256":"630961af259349d3707180f92596f26fbfe50f7b93f92b8b9ff52ee1eef7f150"},"schema_version":"1.0"},"canonical_sha256":"add031906a6b04e3b898e61b8ce1a9939e58f3306778edda528a18150aac65c6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:15.023410Z","signature_b64":"T9w2LmS6p5c7h/3D2wikbng1sVlTDAgx4cDuidfrIaag81B7uREVW7kuliidXZioBZ/tm4Iys0Ct/xYBDnFSAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"add031906a6b04e3b898e61b8ce1a9939e58f3306778edda528a18150aac65c6","last_reissued_at":"2026-05-18T00:05:15.022851Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:15.022851Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.7346","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:05:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IzOzfHIP9odhBYo+ZpQTOswlbecGzhy+FfPE8pj0hi8ezBMjLegSXwExucl0/MGYAUvY3RtzDIlvIc4eBU3TCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T18:38:26.323903Z"},"content_sha256":"8a29c3b767531d548af85c3dc30b5df3419c74f824ae8322fcedacef7290f69b","schema_version":"1.0","event_id":"sha256:8a29c3b767531d548af85c3dc30b5df3419c74f824ae8322fcedacef7290f69b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:VXIDDEDKNMCOHOEY4YNYZYNJSO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Positivity criteria for log canonical divisors and hyperbolicity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.DG"],"primary_cat":"math.AG","authors_text":"De-Qi Zhang, Steven S. Y. Lu","submitted_at":"2012-07-31T19:15:48Z","abstract_excerpt":"Let X be a complex projective variety and D a reduced divisor on X. Under a natural minimal condition on the singularities of the pair (X, D), which includes the case of smooth X with simple normal crossing D, we ask for geometric criteria guaranteeing various positivity conditions for the log-canonical divisor K_X+D. By adjunction and running the log minimal model program, natural to our setting, we obtain a geometric criterion for K_X+D to be numerically effective as well as a geometric version of the cone theorem, generalizing to the context of log pairs these results of Mori. A criterion f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.7346","kind":"arxiv","version":4},"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":"2026-05-18T00:05:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M8kzt2lEmYVXbEwVn+EedKA7Qw5sO+OmnGGGPgRWb0P27Y0aD2ZA0CLP13SfhR2NfpxBl8zGSaX+NXflax82CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T18:38:26.324266Z"},"content_sha256":"0ba7dc8ee002cb4fc91382da00a5d7ce2a315d38d2435626082e20b589366b9e","schema_version":"1.0","event_id":"sha256:0ba7dc8ee002cb4fc91382da00a5d7ce2a315d38d2435626082e20b589366b9e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VXIDDEDKNMCOHOEY4YNYZYNJSO/bundle.json","state_url":"https://pith.science/pith/VXIDDEDKNMCOHOEY4YNYZYNJSO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VXIDDEDKNMCOHOEY4YNYZYNJSO/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":"2026-06-02T18:38:26Z","links":{"resolver":"https://pith.science/pith/VXIDDEDKNMCOHOEY4YNYZYNJSO","bundle":"https://pith.science/pith/VXIDDEDKNMCOHOEY4YNYZYNJSO/bundle.json","state":"https://pith.science/pith/VXIDDEDKNMCOHOEY4YNYZYNJSO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VXIDDEDKNMCOHOEY4YNYZYNJSO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:VXIDDEDKNMCOHOEY4YNYZYNJSO","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":"630961af259349d3707180f92596f26fbfe50f7b93f92b8b9ff52ee1eef7f150","cross_cats_sorted":["math.CV","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-07-31T19:15:48Z","title_canon_sha256":"1a79257258330c4200e6b7ec2c46e4c599d41845b4d81b31ec2af5fdf8a3ac30"},"schema_version":"1.0","source":{"id":"1207.7346","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.7346","created_at":"2026-05-18T00:05:15Z"},{"alias_kind":"arxiv_version","alias_value":"1207.7346v4","created_at":"2026-05-18T00:05:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.7346","created_at":"2026-05-18T00:05:15Z"},{"alias_kind":"pith_short_12","alias_value":"VXIDDEDKNMCO","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VXIDDEDKNMCOHOEY","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VXIDDEDK","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:0ba7dc8ee002cb4fc91382da00a5d7ce2a315d38d2435626082e20b589366b9e","target":"graph","created_at":"2026-05-18T00:05:15Z","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 X be a complex projective variety and D a reduced divisor on X. Under a natural minimal condition on the singularities of the pair (X, D), which includes the case of smooth X with simple normal crossing D, we ask for geometric criteria guaranteeing various positivity conditions for the log-canonical divisor K_X+D. By adjunction and running the log minimal model program, natural to our setting, we obtain a geometric criterion for K_X+D to be numerically effective as well as a geometric version of the cone theorem, generalizing to the context of log pairs these results of Mori. A criterion f","authors_text":"De-Qi Zhang, Steven S. Y. Lu","cross_cats":["math.CV","math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-07-31T19:15:48Z","title":"Positivity criteria for log canonical divisors and hyperbolicity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.7346","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":"sha256:8a29c3b767531d548af85c3dc30b5df3419c74f824ae8322fcedacef7290f69b","target":"record","created_at":"2026-05-18T00:05:15Z","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":"630961af259349d3707180f92596f26fbfe50f7b93f92b8b9ff52ee1eef7f150","cross_cats_sorted":["math.CV","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-07-31T19:15:48Z","title_canon_sha256":"1a79257258330c4200e6b7ec2c46e4c599d41845b4d81b31ec2af5fdf8a3ac30"},"schema_version":"1.0","source":{"id":"1207.7346","kind":"arxiv","version":4}},"canonical_sha256":"add031906a6b04e3b898e61b8ce1a9939e58f3306778edda528a18150aac65c6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"add031906a6b04e3b898e61b8ce1a9939e58f3306778edda528a18150aac65c6","first_computed_at":"2026-05-18T00:05:15.022851Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:15.022851Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"T9w2LmS6p5c7h/3D2wikbng1sVlTDAgx4cDuidfrIaag81B7uREVW7kuliidXZioBZ/tm4Iys0Ct/xYBDnFSAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:15.023410Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.7346","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a29c3b767531d548af85c3dc30b5df3419c74f824ae8322fcedacef7290f69b","sha256:0ba7dc8ee002cb4fc91382da00a5d7ce2a315d38d2435626082e20b589366b9e"],"state_sha256":"888d9632380bfe4655387b004340e4dabc8f644e7251ebb1250d129a3ff98317"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HNZUT/c/DlH/uRehHcfb8NggFol0AxUjV/gjtTKNDgwIbHl5Ni7pYiAFNORys3PwjDeBbC39pJhK7AjizcQoBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T18:38:26.326183Z","bundle_sha256":"5a5c3a9a29a21cee39376a3a9a95fd1c9e58a8ddbe59e4ba78b7a5a914ae5ddc"}}