{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:UNXONIOJ5VJ4MNGRLUNG2MJWA3","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":"19031d25fff4f5bab3519ab1e3cbdb9eafde6ce96b941869a7782803e138fcc5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-11-09T01:00:17Z","title_canon_sha256":"0d84981418557cf1ef8c607e9210ce235a7c96a52f4ece82caf58ebadbf8567a"},"schema_version":"1.0","source":{"id":"1611.02786","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.02786","created_at":"2026-05-18T00:05:00Z"},{"alias_kind":"arxiv_version","alias_value":"1611.02786v2","created_at":"2026-05-18T00:05:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.02786","created_at":"2026-05-18T00:05:00Z"},{"alias_kind":"pith_short_12","alias_value":"UNXONIOJ5VJ4","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"UNXONIOJ5VJ4MNGR","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"UNXONIOJ","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:0db28d4b6ae6d1f58f5aad120e30933f1896e670019a4dc8df7ac869a9c3b672","target":"graph","created_at":"2026-05-18T00:05:00Z","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 study the Oliker-Prussner method exploiting its geometric nature. We derive discrete stability and continuous dependence estimates in the max-norm by using a discrete Alexandroff estimate and the Brunn-Minkowski inequality. We show that the method is exact for all convex quadratic polynomials provided the underlying set of nodes is translation invariant within the domain; nodes still conform to the domain boundary. This gives a suitable notion of operator consistency which, combined with stability, leads to pointwise rates of convergence for classical and non-classical solutions of the Mong","authors_text":"Ricardo H. Nochetto, Wujun Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-11-09T01:00:17Z","title":"Pointwise rates of convergence for the Oliker-Prussner method for the Monge-Amp\\`{e}re equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.02786","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":"sha256:14dc1a3087973fa4017194e72860e4c53232a3464c94344d00b22909be3eb080","target":"record","created_at":"2026-05-18T00:05:00Z","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":"19031d25fff4f5bab3519ab1e3cbdb9eafde6ce96b941869a7782803e138fcc5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-11-09T01:00:17Z","title_canon_sha256":"0d84981418557cf1ef8c607e9210ce235a7c96a52f4ece82caf58ebadbf8567a"},"schema_version":"1.0","source":{"id":"1611.02786","kind":"arxiv","version":2}},"canonical_sha256":"a36ee6a1c9ed53c634d15d1a6d313606c335cd85f30dedef03d84b269efde8c0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a36ee6a1c9ed53c634d15d1a6d313606c335cd85f30dedef03d84b269efde8c0","first_computed_at":"2026-05-18T00:05:00.767166Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:00.767166Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eGk7G+JKx+IvlmnuDVrtmH37hUeE4NBtveMkmIIP/46DsKEpJZIlz2eRAKmWtagmzkL55Jo8iIGZUtVNvHbBDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:00.767599Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.02786","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:14dc1a3087973fa4017194e72860e4c53232a3464c94344d00b22909be3eb080","sha256:0db28d4b6ae6d1f58f5aad120e30933f1896e670019a4dc8df7ac869a9c3b672"],"state_sha256":"686cf6b8577bf95fe98f8973df20a547501db0c1802c184ec994c3923d842da8"}