{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:BLLWX75JKTMUX5LVDV2I5EM4D3","short_pith_number":"pith:BLLWX75J","canonical_record":{"source":{"id":"1906.10235","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-06-24T21:13:45Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"a0012c34a5f96eb6d404d20111e78afcc30c8848acc88c960a54d1be01182193","abstract_canon_sha256":"5de02f5f8c12e4d3715805f417a84f9685f33ca6282f74e57dbb6f18808e99e4"},"schema_version":"1.0"},"canonical_sha256":"0ad76bffa954d94bf5751d748e919c1ec8dc1102fe0b0f94955a94f0a1441840","source":{"kind":"arxiv","id":"1906.10235","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.10235","created_at":"2026-05-17T23:42:31Z"},{"alias_kind":"arxiv_version","alias_value":"1906.10235v1","created_at":"2026-05-17T23:42:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.10235","created_at":"2026-05-17T23:42:31Z"},{"alias_kind":"pith_short_12","alias_value":"BLLWX75JKTMU","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"BLLWX75JKTMUX5LV","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"BLLWX75J","created_at":"2026-05-18T12:33:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:BLLWX75JKTMUX5LVDV2I5EM4D3","target":"record","payload":{"canonical_record":{"source":{"id":"1906.10235","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-06-24T21:13:45Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"a0012c34a5f96eb6d404d20111e78afcc30c8848acc88c960a54d1be01182193","abstract_canon_sha256":"5de02f5f8c12e4d3715805f417a84f9685f33ca6282f74e57dbb6f18808e99e4"},"schema_version":"1.0"},"canonical_sha256":"0ad76bffa954d94bf5751d748e919c1ec8dc1102fe0b0f94955a94f0a1441840","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:31.916087Z","signature_b64":"oEvFPt0QyeHRZ+zj9dYjuHA4boQp6pVTcH3WGygDbA6+DeDeA0EFLfK3wtPcJ2rqDsxyMxsR7bkudwEanhmUBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ad76bffa954d94bf5751d748e919c1ec8dc1102fe0b0f94955a94f0a1441840","last_reissued_at":"2026-05-17T23:42:31.915419Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:31.915419Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1906.10235","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:42:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pkwl5XUQicDoPH8xuW3qGPtKh2cXq6aIWX/20XgQKJlBW2FATF5B/9v6Ank7Isl6lQ9rwPdqLXSRBZuEwjxCAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T18:27:49.061745Z"},"content_sha256":"ab2967e57fa850492a55a37fb49c5949c482b2daf7699c9396765f4ceb4f7013","schema_version":"1.0","event_id":"sha256:ab2967e57fa850492a55a37fb49c5949c482b2daf7699c9396765f4ceb4f7013"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:BLLWX75JKTMUX5LVDV2I5EM4D3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Parabolic complex Monge-Ampere equations on compact Kahler manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AP","authors_text":"Sebastien Picard, Xiangwen Zhang","submitted_at":"2019-06-24T21:13:45Z","abstract_excerpt":"We study the long-time existence and convergence of general parabolic complex Monge-Ampere type equations whose second order operator is not necessarily convex or concave in the Hessian matrix of the unknown solution."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.10235","kind":"arxiv","version":1},"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":"2026-05-17T23:42:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ag7uKxmAAEPTQLpLLuoqUy9lnE9/Ljmrb4/gNFHxb04AZkMdYOMrvqKRJokPbTKVMkn5+VrQ4aCSArnt6+aJBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T18:27:49.062235Z"},"content_sha256":"709e22b8cdc10636658b0b112d2afca5bf9a755c82768d97785c28b7fcef8f2a","schema_version":"1.0","event_id":"sha256:709e22b8cdc10636658b0b112d2afca5bf9a755c82768d97785c28b7fcef8f2a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BLLWX75JKTMUX5LVDV2I5EM4D3/bundle.json","state_url":"https://pith.science/pith/BLLWX75JKTMUX5LVDV2I5EM4D3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BLLWX75JKTMUX5LVDV2I5EM4D3/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":"2026-05-25T18:27:49Z","links":{"resolver":"https://pith.science/pith/BLLWX75JKTMUX5LVDV2I5EM4D3","bundle":"https://pith.science/pith/BLLWX75JKTMUX5LVDV2I5EM4D3/bundle.json","state":"https://pith.science/pith/BLLWX75JKTMUX5LVDV2I5EM4D3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BLLWX75JKTMUX5LVDV2I5EM4D3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:BLLWX75JKTMUX5LVDV2I5EM4D3","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":"5de02f5f8c12e4d3715805f417a84f9685f33ca6282f74e57dbb6f18808e99e4","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-06-24T21:13:45Z","title_canon_sha256":"a0012c34a5f96eb6d404d20111e78afcc30c8848acc88c960a54d1be01182193"},"schema_version":"1.0","source":{"id":"1906.10235","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.10235","created_at":"2026-05-17T23:42:31Z"},{"alias_kind":"arxiv_version","alias_value":"1906.10235v1","created_at":"2026-05-17T23:42:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.10235","created_at":"2026-05-17T23:42:31Z"},{"alias_kind":"pith_short_12","alias_value":"BLLWX75JKTMU","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"BLLWX75JKTMUX5LV","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"BLLWX75J","created_at":"2026-05-18T12:33:12Z"}],"graph_snapshots":[{"event_id":"sha256:709e22b8cdc10636658b0b112d2afca5bf9a755c82768d97785c28b7fcef8f2a","target":"graph","created_at":"2026-05-17T23:42:31Z","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 study the long-time existence and convergence of general parabolic complex Monge-Ampere type equations whose second order operator is not necessarily convex or concave in the Hessian matrix of the unknown solution.","authors_text":"Sebastien Picard, Xiangwen Zhang","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-06-24T21:13:45Z","title":"Parabolic complex Monge-Ampere equations on compact Kahler manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.10235","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:ab2967e57fa850492a55a37fb49c5949c482b2daf7699c9396765f4ceb4f7013","target":"record","created_at":"2026-05-17T23:42:31Z","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":"5de02f5f8c12e4d3715805f417a84f9685f33ca6282f74e57dbb6f18808e99e4","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-06-24T21:13:45Z","title_canon_sha256":"a0012c34a5f96eb6d404d20111e78afcc30c8848acc88c960a54d1be01182193"},"schema_version":"1.0","source":{"id":"1906.10235","kind":"arxiv","version":1}},"canonical_sha256":"0ad76bffa954d94bf5751d748e919c1ec8dc1102fe0b0f94955a94f0a1441840","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0ad76bffa954d94bf5751d748e919c1ec8dc1102fe0b0f94955a94f0a1441840","first_computed_at":"2026-05-17T23:42:31.915419Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:31.915419Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oEvFPt0QyeHRZ+zj9dYjuHA4boQp6pVTcH3WGygDbA6+DeDeA0EFLfK3wtPcJ2rqDsxyMxsR7bkudwEanhmUBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:31.916087Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.10235","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ab2967e57fa850492a55a37fb49c5949c482b2daf7699c9396765f4ceb4f7013","sha256:709e22b8cdc10636658b0b112d2afca5bf9a755c82768d97785c28b7fcef8f2a"],"state_sha256":"a324489babc282bfa0200a07666c922ab393a1e183c3941053cd71fedcb3840b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yjlY5XCjm34ihd1kbnso5J1Xhk23+swhN0pxLh2TqJgj76m/S5NPKK9mwmoohcqJhDfmuR6GGUkZoTs15YHeDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T18:27:49.065679Z","bundle_sha256":"c53b152e29f2169423d458f93410cb10b607cd159cb4900bdf80dfe50f8779a8"}}