{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:JOJ6CBQS5UU5IGLCNLARND2VXX","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":"0b457a76c169a3643e69dcd316f86438ed3696ceb2c64403b1183004f6acbb47","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-06-23T08:03:21Z","title_canon_sha256":"70a68497f74c88e177f3a04260d94b1837949fa157bd392e167baa9a864f7049"},"schema_version":"1.0","source":{"id":"1406.5825","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.5825","created_at":"2026-05-18T02:49:10Z"},{"alias_kind":"arxiv_version","alias_value":"1406.5825v1","created_at":"2026-05-18T02:49:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.5825","created_at":"2026-05-18T02:49:10Z"},{"alias_kind":"pith_short_12","alias_value":"JOJ6CBQS5UU5","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"JOJ6CBQS5UU5IGLC","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"JOJ6CBQS","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:fbf2708e0cabe338ccb779921f2d891e57e064ed14f1fe966e791732a54068d9","target":"graph","created_at":"2026-05-18T02:49:10Z","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 present a somewhat new proof to the $C^{2,\\alpha}$-aprori estimate for the uniform elliptic Monge-Ampere equations, in both the real and complex settings. Our estimates do not need to differentiate the equation, and only depends on the $C^{\\alpha^{\\prime}}-$norm of the right hand side of the equation, $0<\\alpha<\\alpha^{\\prime}$.","authors_text":"Xiuxiong Chen, Yuanqi Wang","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-06-23T08:03:21Z","title":"$C^{2,\\alpha}$-estimate for Monge-Ampere equations with H\\\"older-continuous right hand side"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5825","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:fa3e8995f0def32162b74dc7130b3b757eaef59b9a21b52825ae0ba193911b36","target":"record","created_at":"2026-05-18T02:49:10Z","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":"0b457a76c169a3643e69dcd316f86438ed3696ceb2c64403b1183004f6acbb47","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-06-23T08:03:21Z","title_canon_sha256":"70a68497f74c88e177f3a04260d94b1837949fa157bd392e167baa9a864f7049"},"schema_version":"1.0","source":{"id":"1406.5825","kind":"arxiv","version":1}},"canonical_sha256":"4b93e10612ed29d419626ac1168f55bde6b82dd347dc17fbe5e182c1e6389ab5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b93e10612ed29d419626ac1168f55bde6b82dd347dc17fbe5e182c1e6389ab5","first_computed_at":"2026-05-18T02:49:10.653895Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:49:10.653895Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mQHUycxpIA1fZxR6I7Uo+BUaQSQqbyxJN6w3SYHyxc1OhfldUAjKx18gu5I0vyuN44mg2JRLn5EGBUXuQVisCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:49:10.654447Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.5825","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fa3e8995f0def32162b74dc7130b3b757eaef59b9a21b52825ae0ba193911b36","sha256:fbf2708e0cabe338ccb779921f2d891e57e064ed14f1fe966e791732a54068d9"],"state_sha256":"008a186da497dc48f151bb4b68331b67d39f921bd5861793894d3b0093457132"}