{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:OSFQJWUE3RXAY7HAJHNB2BEKF6","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":"e73a65cac16af5fe08584ff78176d8894f5bbc448837e409ff8c5c31c7754c78","cross_cats_sorted":["math.CV","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-10-24T08:27:08Z","title_canon_sha256":"180ef98d5a5df75f3b715f1e81a83a47dba3fa07a4e097a862508cb9a97ad8a4"},"schema_version":"1.0","source":{"id":"2410.18532","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.18532","created_at":"2026-07-05T09:29:16Z"},{"alias_kind":"arxiv_version","alias_value":"2410.18532v2","created_at":"2026-07-05T09:29:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.18532","created_at":"2026-07-05T09:29:16Z"},{"alias_kind":"pith_short_12","alias_value":"OSFQJWUE3RXA","created_at":"2026-07-05T09:29:16Z"},{"alias_kind":"pith_short_16","alias_value":"OSFQJWUE3RXAY7HA","created_at":"2026-07-05T09:29:16Z"},{"alias_kind":"pith_short_8","alias_value":"OSFQJWUE","created_at":"2026-07-05T09:29:16Z"}],"graph_snapshots":[{"event_id":"sha256:996728322e2f43d55dae6d6c1935f9fe637a2799758bdaa570db25da34338399","target":"graph","created_at":"2026-07-05T09:29:16Z","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/2410.18532/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We generalize previous diameter estimates and local non-vanishing of volumes for Kaehler metrics to the case of big cohomology classes. In our proof, among other things, we will prove a uniform diameter estimate for a family of smooth Kaehler metrics only involving an integrability condition. We also have to use fine stability properties of complex Monge-Ampere equations with prescribed singularities.","authors_text":"Duc-Bao Nguyen, Duc-Viet Vu","cross_cats":["math.CV","math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-10-24T08:27:08Z","title":"Uniform diameter estimates for Kaehler metrics in big cohomology classes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.18532","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":"sha256:6589dc64d718e232959f127aa94c45ad4cb9b267983821e1052ef292b26ba174","target":"record","created_at":"2026-07-05T09:29:16Z","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":"e73a65cac16af5fe08584ff78176d8894f5bbc448837e409ff8c5c31c7754c78","cross_cats_sorted":["math.CV","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-10-24T08:27:08Z","title_canon_sha256":"180ef98d5a5df75f3b715f1e81a83a47dba3fa07a4e097a862508cb9a97ad8a4"},"schema_version":"1.0","source":{"id":"2410.18532","kind":"arxiv","version":2}},"canonical_sha256":"748b04da84dc6e0c7ce049da1d048a2f89639a0f798ff52922b17d7fdb6fcb23","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"748b04da84dc6e0c7ce049da1d048a2f89639a0f798ff52922b17d7fdb6fcb23","first_computed_at":"2026-07-05T09:29:16.208036Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:29:16.208036Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KTAAT3Z4/BYUqUeaQyOqBu2PAiPJ+TG1BmxSz+nzfRYnIu7Uc9+6k8Xcc6F7BHVa0Timh5q30FaDXdxt++usCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:29:16.208518Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.18532","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6589dc64d718e232959f127aa94c45ad4cb9b267983821e1052ef292b26ba174","sha256:996728322e2f43d55dae6d6c1935f9fe637a2799758bdaa570db25da34338399"],"state_sha256":"239d35608b3c48728f8777110f21777c1b7a7319ce40252f2db7689593e87c77"}