{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:FEZ5DC5EF6NGGPMFCKOTMZU6TE","short_pith_number":"pith:FEZ5DC5E","canonical_record":{"source":{"id":"1305.7511","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-05-31T19:24:38Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"478056b86dd4671947cb902aac70c8b348706914955d86fb04ee0266c0c066cc","abstract_canon_sha256":"95ecfd90ed32b2d21e9af2346a9b9fde399e966f6a3f9fcd10a8f86ed12422fc"},"schema_version":"1.0"},"canonical_sha256":"2933d18ba42f9a633d85129d36669e99293b332273b5fa1a27b0e70e8869a727","source":{"kind":"arxiv","id":"1305.7511","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.7511","created_at":"2026-05-18T00:52:17Z"},{"alias_kind":"arxiv_version","alias_value":"1305.7511v3","created_at":"2026-05-18T00:52:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.7511","created_at":"2026-05-18T00:52:17Z"},{"alias_kind":"pith_short_12","alias_value":"FEZ5DC5EF6NG","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"FEZ5DC5EF6NGGPMF","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"FEZ5DC5E","created_at":"2026-05-18T12:27:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:FEZ5DC5EF6NGGPMFCKOTMZU6TE","target":"record","payload":{"canonical_record":{"source":{"id":"1305.7511","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-05-31T19:24:38Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"478056b86dd4671947cb902aac70c8b348706914955d86fb04ee0266c0c066cc","abstract_canon_sha256":"95ecfd90ed32b2d21e9af2346a9b9fde399e966f6a3f9fcd10a8f86ed12422fc"},"schema_version":"1.0"},"canonical_sha256":"2933d18ba42f9a633d85129d36669e99293b332273b5fa1a27b0e70e8869a727","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:17.949730Z","signature_b64":"66B47Lvbed99T7qoF4XPaCxKIzKf2sAOz2JOAIlCnxAZzAtKeqnJZacallMMqdNG+bGXlLLTccM3xiOwn8SSCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2933d18ba42f9a633d85129d36669e99293b332273b5fa1a27b0e70e8869a727","last_reissued_at":"2026-05-18T00:52:17.949084Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:17.949084Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1305.7511","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":"2026-05-18T00:52:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0uVeTalAklbRmLAm3wemprrSP/ARhNC2JS3w1xcFtgC4ki6VxYW7hys00WzGTgNVNgeges8mjaZDs9gvNfsFAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T20:32:25.488505Z"},"content_sha256":"901e832a05a57378c75dc2e4eeab452ae9da26cebaa501f2217679ed95e66e02","schema_version":"1.0","event_id":"sha256:901e832a05a57378c75dc2e4eeab452ae9da26cebaa501f2217679ed95e66e02"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:FEZ5DC5EF6NGGPMFCKOTMZU6TE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Monge-Amp\\`ere equation for (n-1)-plurisubharmonic functions on a compact K\\\"ahler manifold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DG","authors_text":"Ben Weinkove, Valentino Tosatti","submitted_at":"2013-05-31T19:24:38Z","abstract_excerpt":"A C^2 function on C^n is called (n-1)-plurisubharmonic in the sense of Harvey-Lawson if the sum of any n-1 eigenvalues of its complex Hessian is nonnegative. We show that the associated Monge-Ampere equation can be solved on any compact Kahler manifold. As a consequence we prove the existence of solutions to an equation of Fu-Wang-Wu, giving Calabi-Yau theorems for balanced, Gauduchon and strongly Gauduchon metrics on compact Kahler manifolds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.7511","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":"2026-05-18T00:52:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9fotbTIjguXkNDETkLzMcCMzeo3mEi0XQyBMk4kalJ1Qdr3c2lJO8qQjEWPaWBBDJMgv44cEdFa37cDpn65pCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T20:32:25.488843Z"},"content_sha256":"204f31504551afd78af96cddd5c1dd5e8f8d02a2302c44977be4f8d2d728f47d","schema_version":"1.0","event_id":"sha256:204f31504551afd78af96cddd5c1dd5e8f8d02a2302c44977be4f8d2d728f47d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FEZ5DC5EF6NGGPMFCKOTMZU6TE/bundle.json","state_url":"https://pith.science/pith/FEZ5DC5EF6NGGPMFCKOTMZU6TE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FEZ5DC5EF6NGGPMFCKOTMZU6TE/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":"2026-05-22T20:32:25Z","links":{"resolver":"https://pith.science/pith/FEZ5DC5EF6NGGPMFCKOTMZU6TE","bundle":"https://pith.science/pith/FEZ5DC5EF6NGGPMFCKOTMZU6TE/bundle.json","state":"https://pith.science/pith/FEZ5DC5EF6NGGPMFCKOTMZU6TE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FEZ5DC5EF6NGGPMFCKOTMZU6TE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:FEZ5DC5EF6NGGPMFCKOTMZU6TE","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":"95ecfd90ed32b2d21e9af2346a9b9fde399e966f6a3f9fcd10a8f86ed12422fc","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-05-31T19:24:38Z","title_canon_sha256":"478056b86dd4671947cb902aac70c8b348706914955d86fb04ee0266c0c066cc"},"schema_version":"1.0","source":{"id":"1305.7511","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.7511","created_at":"2026-05-18T00:52:17Z"},{"alias_kind":"arxiv_version","alias_value":"1305.7511v3","created_at":"2026-05-18T00:52:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.7511","created_at":"2026-05-18T00:52:17Z"},{"alias_kind":"pith_short_12","alias_value":"FEZ5DC5EF6NG","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"FEZ5DC5EF6NGGPMF","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"FEZ5DC5E","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:204f31504551afd78af96cddd5c1dd5e8f8d02a2302c44977be4f8d2d728f47d","target":"graph","created_at":"2026-05-18T00:52:17Z","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":"A C^2 function on C^n is called (n-1)-plurisubharmonic in the sense of Harvey-Lawson if the sum of any n-1 eigenvalues of its complex Hessian is nonnegative. We show that the associated Monge-Ampere equation can be solved on any compact Kahler manifold. As a consequence we prove the existence of solutions to an equation of Fu-Wang-Wu, giving Calabi-Yau theorems for balanced, Gauduchon and strongly Gauduchon metrics on compact Kahler manifolds.","authors_text":"Ben Weinkove, Valentino Tosatti","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-05-31T19:24:38Z","title":"The Monge-Amp\\`ere equation for (n-1)-plurisubharmonic functions on a compact K\\\"ahler manifold"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.7511","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":"sha256:901e832a05a57378c75dc2e4eeab452ae9da26cebaa501f2217679ed95e66e02","target":"record","created_at":"2026-05-18T00:52:17Z","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":"95ecfd90ed32b2d21e9af2346a9b9fde399e966f6a3f9fcd10a8f86ed12422fc","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-05-31T19:24:38Z","title_canon_sha256":"478056b86dd4671947cb902aac70c8b348706914955d86fb04ee0266c0c066cc"},"schema_version":"1.0","source":{"id":"1305.7511","kind":"arxiv","version":3}},"canonical_sha256":"2933d18ba42f9a633d85129d36669e99293b332273b5fa1a27b0e70e8869a727","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2933d18ba42f9a633d85129d36669e99293b332273b5fa1a27b0e70e8869a727","first_computed_at":"2026-05-18T00:52:17.949084Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:17.949084Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"66B47Lvbed99T7qoF4XPaCxKIzKf2sAOz2JOAIlCnxAZzAtKeqnJZacallMMqdNG+bGXlLLTccM3xiOwn8SSCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:17.949730Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.7511","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:901e832a05a57378c75dc2e4eeab452ae9da26cebaa501f2217679ed95e66e02","sha256:204f31504551afd78af96cddd5c1dd5e8f8d02a2302c44977be4f8d2d728f47d"],"state_sha256":"56c94973e2608d448586c6f05e8f80b07de52cbcaa42c14acfc6da146b8c3f7b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bHfrzA1F2fLTRVZ7jV7QVhdsFGEwxE+QiaVHj6nGgvtz0CD/NmFeZPl5Imnd931qKk4n5gATCztqnCafR0fnDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T20:32:25.490881Z","bundle_sha256":"c45d674b7fc3a8a189e60feb5f1521ba9bbc213e898b947c238489fcb524bdf6"}}