{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:3OHY4NJE3Y7WBSRW6T4TCVFKNA","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":"aa7a2cbc38d097d1e568c1a831973ca447ed3f1dbfd5f4758332816fde4defe7","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-12-06T19:57:10Z","title_canon_sha256":"db4947d1cc05d29890ffe20afd8c45c3db2d3be6268ccfb3b90d7dff1ff7ca17"},"schema_version":"1.0","source":{"id":"1112.1388","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.1388","created_at":"2026-05-18T02:57:54Z"},{"alias_kind":"arxiv_version","alias_value":"1112.1388v1","created_at":"2026-05-18T02:57:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.1388","created_at":"2026-05-18T02:57:54Z"},{"alias_kind":"pith_short_12","alias_value":"3OHY4NJE3Y7W","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"3OHY4NJE3Y7WBSRW","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"3OHY4NJE","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:7d1545a29d14e679e650a9361ec2320b7e8da48398f79419b92496636c1eba3b","target":"graph","created_at":"2026-05-18T02:57:54Z","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":"Let $(X,\\omega)$ be a compact K\\\"ahler manifold. We obtain uniform H\\\"older regularity for solutions to the complex Monge-Amp\\`ere equation on $X$ with $L^p$ right hand side, $p>1$. The same regularity is furthermore proved on the ample locus in any big cohomology class. We also study the range $\\MAH(X,\\omega)$ of the complex Monge-Amp\\`ere operator acting on $\\omega$-plurisubharmonic H\\\"older continuous functions. We show that this set is convex, by sharpening Ko{\\l}odziej's result that measures with $L^p$-density belong to $\\MAH(X,\\omega)$ and proving that $\\MAH(X,\\omega)$ has the \"$L^p$-pro","authors_text":"Ahmed Zeriahi (IMT), Hoang Hiep Pham (IF), Jean-Pierre Demailly (IF), Slawomir Dinew (IMT), Slawomir Kolodziej (IMT), Vincent Guedj (IMT)","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-12-06T19:57:10Z","title":"H\\\"older continuous solutions to Monge-Amp\\`ere equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1388","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":"sha256:2017e261430f6a9629fc0509e2819fa4e43457236bd4d45dbab20e829f69d3d3","target":"record","created_at":"2026-05-18T02:57:54Z","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":"aa7a2cbc38d097d1e568c1a831973ca447ed3f1dbfd5f4758332816fde4defe7","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-12-06T19:57:10Z","title_canon_sha256":"db4947d1cc05d29890ffe20afd8c45c3db2d3be6268ccfb3b90d7dff1ff7ca17"},"schema_version":"1.0","source":{"id":"1112.1388","kind":"arxiv","version":1}},"canonical_sha256":"db8f8e3524de3f60ca36f4f93154aa6809bf37e48487a6df1c9523eccecc4708","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"db8f8e3524de3f60ca36f4f93154aa6809bf37e48487a6df1c9523eccecc4708","first_computed_at":"2026-05-18T02:57:54.027120Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:57:54.027120Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o2H69/qxqs52UYilBy5qalxoSeu/TiiSX5xDT7vSUxWAhxHNrC+m8h5XGsIeNl9q76r28nGBcS6a04BYFLh+BA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:57:54.027601Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.1388","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2017e261430f6a9629fc0509e2819fa4e43457236bd4d45dbab20e829f69d3d3","sha256:7d1545a29d14e679e650a9361ec2320b7e8da48398f79419b92496636c1eba3b"],"state_sha256":"30e98734de9ab79adb3def969166ea4f7b760691a8ac2ccd1e043ee0a457b73b"}