{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:KYIO6L5574X6MVKWENRD2JDAL3","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":"5b4c5e1b80b838d3331dca8d0da140870024d6393d7e8b42417f3a1707e9a72d","cross_cats_sorted":["math.CV","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-07-01T06:44:44Z","title_canon_sha256":"cf555043ff950a557c32cd57b1751c613c65d492d09e2892f7cf5f807d423fd4"},"schema_version":"1.0","source":{"id":"1007.0076","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.0076","created_at":"2026-05-18T02:56:58Z"},{"alias_kind":"arxiv_version","alias_value":"1007.0076v1","created_at":"2026-05-18T02:56:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.0076","created_at":"2026-05-18T02:56:58Z"},{"alias_kind":"pith_short_12","alias_value":"KYIO6L5574X6","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"KYIO6L5574X6MVKW","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"KYIO6L55","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:66d9fd4d300adc3b8561d4249a1af04a74bcf388a4160c15095907768518d4ce","target":"graph","created_at":"2026-05-18T02:56:58Z","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 develop an alternative approach to Degenerate complex Monge-Amp\\`ere equations on compact K\\\"ahler manifolds based on the concept of viscosity solutions and compare systematically viscosity concepts with pluripotential theoretic ones. We generalize to the K\\\"ahler case a theorem due to Dinew and Zhang in the projective case to the effect that their pluripotential solutions constructed previously by the authors are continuous.","authors_text":"Ahmed Zeriahi (IMT), Philippe Eyssidieux (IF), Vincent Guedj (LATP)","cross_cats":["math.CV","math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-07-01T06:44:44Z","title":"Viscosity solutions to degenerate Complex Monge-Amp\\`ere equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.0076","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":"sha256:3140d77e6ec3778fbe17d0fee59a8a129d2896cd862e5942025a1ff5292903e7","target":"record","created_at":"2026-05-18T02:56:58Z","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":"5b4c5e1b80b838d3331dca8d0da140870024d6393d7e8b42417f3a1707e9a72d","cross_cats_sorted":["math.CV","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-07-01T06:44:44Z","title_canon_sha256":"cf555043ff950a557c32cd57b1751c613c65d492d09e2892f7cf5f807d423fd4"},"schema_version":"1.0","source":{"id":"1007.0076","kind":"arxiv","version":1}},"canonical_sha256":"5610ef2fbdff2fe6555623623d24605edd6e6c88cadaa39cf21907973c5250a5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5610ef2fbdff2fe6555623623d24605edd6e6c88cadaa39cf21907973c5250a5","first_computed_at":"2026-05-18T02:56:58.699942Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:56:58.699942Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Bvhkhnmxh+fRj8VHHqsFVijm6qOJSqu136NK+FURyd47tv8XNtvbJYMqDg1j2OVpbVT+XdjEYGHTdIM/To0yBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:56:58.700401Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.0076","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3140d77e6ec3778fbe17d0fee59a8a129d2896cd862e5942025a1ff5292903e7","sha256:66d9fd4d300adc3b8561d4249a1af04a74bcf388a4160c15095907768518d4ce"],"state_sha256":"ac356f7261090a0b39dca580a98d3cc0a1322ed6f2b97fa5a7f9a5da48971d13"}