{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:DHBVTPI7NJHGTVCTKKZQGFFY6N","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":"58ebf5df357420554f9ecda2fe1b582d435bb57b9626a88e21676576dc1596da","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2022-09-01T06:14:49Z","title_canon_sha256":"2027a54ad6003a32ebb290433f9ccc35e7be14e88b3080a3de9a4feec10601bb"},"schema_version":"1.0","source":{"id":"2209.00248","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.00248","created_at":"2026-07-05T05:21:02Z"},{"alias_kind":"arxiv_version","alias_value":"2209.00248v2","created_at":"2026-07-05T05:21:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.00248","created_at":"2026-07-05T05:21:02Z"},{"alias_kind":"pith_short_12","alias_value":"DHBVTPI7NJHG","created_at":"2026-07-05T05:21:02Z"},{"alias_kind":"pith_short_16","alias_value":"DHBVTPI7NJHGTVCT","created_at":"2026-07-05T05:21:02Z"},{"alias_kind":"pith_short_8","alias_value":"DHBVTPI7","created_at":"2026-07-05T05:21:02Z"}],"graph_snapshots":[{"event_id":"sha256:6bdb6484d2a2b6e7a31591b3fd3c247436e7de5edeb426933be0bb4a75b4ed4f","target":"graph","created_at":"2026-07-05T05:21:02Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2209.00248/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove several quantitative stability estimates for solutions of complex Monge-Ampere equations when both the cohomology class and the prescribed singularity vary. In a broad sense, our results fit well into the study of degeneration of families of Kaehler-Einstein metrics. The key mechanism in our method is the pluripotential theory in the space of potentials of finite lower energy.","authors_text":"Duc-Viet Vu, Hoang-Son Do","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2022-09-01T06:14:49Z","title":"Quantitative stability for the complex Monge-Ampere equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.00248","kind":"arxiv","version":2},"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":"sha256:269818ea828593e311dfdc30a2154df208a65491438eebe31b26d0284fdb9d4a","target":"record","created_at":"2026-07-05T05:21:02Z","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":"58ebf5df357420554f9ecda2fe1b582d435bb57b9626a88e21676576dc1596da","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2022-09-01T06:14:49Z","title_canon_sha256":"2027a54ad6003a32ebb290433f9ccc35e7be14e88b3080a3de9a4feec10601bb"},"schema_version":"1.0","source":{"id":"2209.00248","kind":"arxiv","version":2}},"canonical_sha256":"19c359bd1f6a4e69d45352b30314b8f376abb42b5b2fb3ef3e298f1d0852120c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"19c359bd1f6a4e69d45352b30314b8f376abb42b5b2fb3ef3e298f1d0852120c","first_computed_at":"2026-07-05T05:21:02.804627Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:21:02.804627Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"su3c6JsrfD3RgxI5sRZ4MtN3Q+M5OW/1gssokFgzaPMg8bKMk2UxxpzDziIuPxodoee0zm2oe7HPr5aPAGTqCw==","signature_status":"signed_v1","signed_at":"2026-07-05T05:21:02.805082Z","signed_message":"canonical_sha256_bytes"},"source_id":"2209.00248","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:269818ea828593e311dfdc30a2154df208a65491438eebe31b26d0284fdb9d4a","sha256:6bdb6484d2a2b6e7a31591b3fd3c247436e7de5edeb426933be0bb4a75b4ed4f"],"state_sha256":"8b0c9fec06f9a782b065fb0b4fceba1f860f26b6575c527fb8394b012677a2c7"}