{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:2MRARZY4DSKOLUTVPGVY5CZPE2","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":"f6d0dbbf7451fc36e847eb4e7b52d81f0815a4e9e69478b11ac342515cb62676","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-06-12T08:32:12Z","title_canon_sha256":"6a632d634d1eaabc9a77c739a18178fe49b34212c53b2da2f5c03b99bf536703"},"schema_version":"1.0","source":{"id":"1506.03934","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.03934","created_at":"2026-05-18T00:13:13Z"},{"alias_kind":"arxiv_version","alias_value":"1506.03934v1","created_at":"2026-05-18T00:13:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.03934","created_at":"2026-05-18T00:13:13Z"},{"alias_kind":"pith_short_12","alias_value":"2MRARZY4DSKO","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"2MRARZY4DSKOLUTV","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"2MRARZY4","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:e2231db182d5f36139b32280f788cc6688e92a94bedb53fa11c9f753b6a6b777","target":"graph","created_at":"2026-05-18T00:13:13Z","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":"Quaternionic Monge-Amp\\`{e}re equations have recently been studied intensively using methods from pluripotential theory. We present an alternative approach by using the viscosity methods. We study the viscosity solutions to the Dirichlet problem for quaternionic Monge-Amp\\`{e}re equations $det(f)=F(q,f)$ with boundary value $f=g$ on $\\partial\\Omega$. Here $\\Omega$ is a bounded domain on the quaternionic space $\\mathbb{H}^n$, $g\\in C(\\partial\\Omega)$, and $F(q,t)$ is a continuous function on $\\Omega\\times\\mathbb{R}\\rightarrow\\mathbb{R}^+$ which is non-decreasing in the second variable. We prove","authors_text":"Dongrui Wan, Wei Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-06-12T08:32:12Z","title":"Viscosity solutions to quaternionic Monge-Amp\\`{e}re equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.03934","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":"sha256:0e686c35a8af428707e6033800a49ad29de47dc2a2d3ef899ffe279e7c171024","target":"record","created_at":"2026-05-18T00:13:13Z","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":"f6d0dbbf7451fc36e847eb4e7b52d81f0815a4e9e69478b11ac342515cb62676","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-06-12T08:32:12Z","title_canon_sha256":"6a632d634d1eaabc9a77c739a18178fe49b34212c53b2da2f5c03b99bf536703"},"schema_version":"1.0","source":{"id":"1506.03934","kind":"arxiv","version":1}},"canonical_sha256":"d32208e71c1c94e5d27579ab8e8b2f2692e1b03d861448c9149ac384548324db","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d32208e71c1c94e5d27579ab8e8b2f2692e1b03d861448c9149ac384548324db","first_computed_at":"2026-05-18T00:13:13.851933Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:13.851933Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"viWCsTVzlL8s4sgg14Ool62RZ793jVglG3QlZ/dQdajCeCaTNgXZsgySj/z4P4aYT6HmQkGdZZjNW+M/r86eDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:13.852777Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.03934","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0e686c35a8af428707e6033800a49ad29de47dc2a2d3ef899ffe279e7c171024","sha256:e2231db182d5f36139b32280f788cc6688e92a94bedb53fa11c9f753b6a6b777"],"state_sha256":"9b592cae7671b6cd50fbfc2bace84416c54f049cbe17f6b745f4f69818dadf8b"}