{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:DHBVTPI7NJHGTVCTKKZQGFFY6N","short_pith_number":"pith:DHBVTPI7","canonical_record":{"source":{"id":"2209.00248","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2022-09-01T06:14:49Z","cross_cats_sorted":[],"title_canon_sha256":"2027a54ad6003a32ebb290433f9ccc35e7be14e88b3080a3de9a4feec10601bb","abstract_canon_sha256":"58ebf5df357420554f9ecda2fe1b582d435bb57b9626a88e21676576dc1596da"},"schema_version":"1.0"},"canonical_sha256":"19c359bd1f6a4e69d45352b30314b8f376abb42b5b2fb3ef3e298f1d0852120c","source":{"kind":"arxiv","id":"2209.00248","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:DHBVTPI7NJHGTVCTKKZQGFFY6N","target":"record","payload":{"canonical_record":{"source":{"id":"2209.00248","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2022-09-01T06:14:49Z","cross_cats_sorted":[],"title_canon_sha256":"2027a54ad6003a32ebb290433f9ccc35e7be14e88b3080a3de9a4feec10601bb","abstract_canon_sha256":"58ebf5df357420554f9ecda2fe1b582d435bb57b9626a88e21676576dc1596da"},"schema_version":"1.0"},"canonical_sha256":"19c359bd1f6a4e69d45352b30314b8f376abb42b5b2fb3ef3e298f1d0852120c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:21:02.805082Z","signature_b64":"su3c6JsrfD3RgxI5sRZ4MtN3Q+M5OW/1gssokFgzaPMg8bKMk2UxxpzDziIuPxodoee0zm2oe7HPr5aPAGTqCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"19c359bd1f6a4e69d45352b30314b8f376abb42b5b2fb3ef3e298f1d0852120c","last_reissued_at":"2026-07-05T05:21:02.804627Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:21:02.804627Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2209.00248","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:21:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ETl9/n1AfbA2lLhpKlC2Gtam0lpQX2LGFDgprFVy2pYKS5OGYgntNyLSIK/uYy9MG4q017078SX+zu8L1PseBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T23:26:07.846010Z"},"content_sha256":"269818ea828593e311dfdc30a2154df208a65491438eebe31b26d0284fdb9d4a","schema_version":"1.0","event_id":"sha256:269818ea828593e311dfdc30a2154df208a65491438eebe31b26d0284fdb9d4a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:DHBVTPI7NJHGTVCTKKZQGFFY6N","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantitative stability for the complex Monge-Ampere equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Duc-Viet Vu, Hoang-Son Do","submitted_at":"2022-09-01T06:14:49Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.00248","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2209.00248/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T05:21:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b4iNoF2uhrImA518EsTtzT19XMwUoGJl9MD08ramNouoPxyMOgB/Vd3gVoWZuSz3l3ZBW+AUPlRgM8IIXximBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T23:26:07.846519Z"},"content_sha256":"6bdb6484d2a2b6e7a31591b3fd3c247436e7de5edeb426933be0bb4a75b4ed4f","schema_version":"1.0","event_id":"sha256:6bdb6484d2a2b6e7a31591b3fd3c247436e7de5edeb426933be0bb4a75b4ed4f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DHBVTPI7NJHGTVCTKKZQGFFY6N/bundle.json","state_url":"https://pith.science/pith/DHBVTPI7NJHGTVCTKKZQGFFY6N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DHBVTPI7NJHGTVCTKKZQGFFY6N/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":"2026-08-13T23:26:07Z","links":{"resolver":"https://pith.science/pith/DHBVTPI7NJHGTVCTKKZQGFFY6N","bundle":"https://pith.science/pith/DHBVTPI7NJHGTVCTKKZQGFFY6N/bundle.json","state":"https://pith.science/pith/DHBVTPI7NJHGTVCTKKZQGFFY6N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DHBVTPI7NJHGTVCTKKZQGFFY6N/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YgzS8jHwT7sOuGsf73UYz6gF1RrU3xOWNnypxtrYXUUsI/XlJ/SkeCD9GI5GxwLS3rufX1Lg5fHgkOTAvfNTAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T23:26:07.852632Z","bundle_sha256":"c562b1f4b7537b155dbac449fde6c841f9125af2c534d5746cade6e0ea51d7bb"}}