{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:ZHV27XB5UAEXAU7B6FQSOXULWY","short_pith_number":"pith:ZHV27XB5","canonical_record":{"source":{"id":"1808.07264","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-08-22T08:10:31Z","cross_cats_sorted":[],"title_canon_sha256":"506d673557476c17174ad1b7dd7e06f6ffc72d9b96673c5f21284c2a6ec37956","abstract_canon_sha256":"120392ff2f923cefa5d162fa46b5371a8c726071dfdb914391e2746c65e3d06a"},"schema_version":"1.0"},"canonical_sha256":"c9ebafdc3da0097053e1f161275e8bb621673a374b11a114197594eda34d4053","source":{"kind":"arxiv","id":"1808.07264","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.07264","created_at":"2026-05-18T00:07:29Z"},{"alias_kind":"arxiv_version","alias_value":"1808.07264v1","created_at":"2026-05-18T00:07:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.07264","created_at":"2026-05-18T00:07:29Z"},{"alias_kind":"pith_short_12","alias_value":"ZHV27XB5UAEX","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"ZHV27XB5UAEXAU7B","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"ZHV27XB5","created_at":"2026-05-18T12:33:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:ZHV27XB5UAEXAU7B6FQSOXULWY","target":"record","payload":{"canonical_record":{"source":{"id":"1808.07264","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-08-22T08:10:31Z","cross_cats_sorted":[],"title_canon_sha256":"506d673557476c17174ad1b7dd7e06f6ffc72d9b96673c5f21284c2a6ec37956","abstract_canon_sha256":"120392ff2f923cefa5d162fa46b5371a8c726071dfdb914391e2746c65e3d06a"},"schema_version":"1.0"},"canonical_sha256":"c9ebafdc3da0097053e1f161275e8bb621673a374b11a114197594eda34d4053","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:29.386164Z","signature_b64":"GlZbSeAIC+BuhA5iL+SfdCdT/PRTN5bZFjDo+E8PTiFfnTE/I6XLEKpQeek/Dl3mCbTFkyOaecfLzdfnbl24Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c9ebafdc3da0097053e1f161275e8bb621673a374b11a114197594eda34d4053","last_reissued_at":"2026-05-18T00:07:29.385471Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:29.385471Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1808.07264","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:07:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SGOvt0dItbyB/41bmpB2YWwbP6EYk0rB7YzynI+HxrKNubFHzWbrOn0SfhoFCI6k2ZIKao2pqnAH1AIyLrWfCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T14:44:33.279354Z"},"content_sha256":"5c7442f55f7e0c1e2248c8db99115515041884405e908afd80975b50411b89a1","schema_version":"1.0","event_id":"sha256:5c7442f55f7e0c1e2248c8db99115515041884405e908afd80975b50411b89a1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:ZHV27XB5UAEXAU7B6FQSOXULWY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Complex Monge-Amp\\`ere equation in strictly pseudoconvex domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Hoang Hiep Pham, Hoang-Son Do, Thai Duong Do","submitted_at":"2018-08-22T08:10:31Z","abstract_excerpt":"We study the complex Monge-Amp\\`ere equation $(dd^c u)^n=\\mu$ in a strictly pseudoconvex domain $\\Omega$ with the boundary condition $u=\\varphi$, where $\\varphi\\in C(\\partial\\Omega)$. We provide a non-trivial sufficient condition for continuity of the solution $u$ outside \"small sets\"."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.07264","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:07:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zwhythAsuXsJHGsWI3xvRG7e/7tiq8ROZY37AlDRLTYR5AjeHPxvwlLnKcWlQYEvpc4Qz1GmJFpEwdPtB3bZBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T14:44:33.279705Z"},"content_sha256":"8557fba7553e1686d9eaa88cdc0bb3db3240c26cf5e4b4710a59f74faed9ed66","schema_version":"1.0","event_id":"sha256:8557fba7553e1686d9eaa88cdc0bb3db3240c26cf5e4b4710a59f74faed9ed66"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZHV27XB5UAEXAU7B6FQSOXULWY/bundle.json","state_url":"https://pith.science/pith/ZHV27XB5UAEXAU7B6FQSOXULWY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZHV27XB5UAEXAU7B6FQSOXULWY/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-23T14:44:33Z","links":{"resolver":"https://pith.science/pith/ZHV27XB5UAEXAU7B6FQSOXULWY","bundle":"https://pith.science/pith/ZHV27XB5UAEXAU7B6FQSOXULWY/bundle.json","state":"https://pith.science/pith/ZHV27XB5UAEXAU7B6FQSOXULWY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZHV27XB5UAEXAU7B6FQSOXULWY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ZHV27XB5UAEXAU7B6FQSOXULWY","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":"120392ff2f923cefa5d162fa46b5371a8c726071dfdb914391e2746c65e3d06a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-08-22T08:10:31Z","title_canon_sha256":"506d673557476c17174ad1b7dd7e06f6ffc72d9b96673c5f21284c2a6ec37956"},"schema_version":"1.0","source":{"id":"1808.07264","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.07264","created_at":"2026-05-18T00:07:29Z"},{"alias_kind":"arxiv_version","alias_value":"1808.07264v1","created_at":"2026-05-18T00:07:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.07264","created_at":"2026-05-18T00:07:29Z"},{"alias_kind":"pith_short_12","alias_value":"ZHV27XB5UAEX","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"ZHV27XB5UAEXAU7B","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"ZHV27XB5","created_at":"2026-05-18T12:33:07Z"}],"graph_snapshots":[{"event_id":"sha256:8557fba7553e1686d9eaa88cdc0bb3db3240c26cf5e4b4710a59f74faed9ed66","target":"graph","created_at":"2026-05-18T00:07:29Z","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 complex Monge-Amp\\`ere equation $(dd^c u)^n=\\mu$ in a strictly pseudoconvex domain $\\Omega$ with the boundary condition $u=\\varphi$, where $\\varphi\\in C(\\partial\\Omega)$. We provide a non-trivial sufficient condition for continuity of the solution $u$ outside \"small sets\".","authors_text":"Hoang Hiep Pham, Hoang-Son Do, Thai Duong Do","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-08-22T08:10:31Z","title":"Complex Monge-Amp\\`ere equation in strictly pseudoconvex domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.07264","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":"sha256:5c7442f55f7e0c1e2248c8db99115515041884405e908afd80975b50411b89a1","target":"record","created_at":"2026-05-18T00:07:29Z","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":"120392ff2f923cefa5d162fa46b5371a8c726071dfdb914391e2746c65e3d06a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-08-22T08:10:31Z","title_canon_sha256":"506d673557476c17174ad1b7dd7e06f6ffc72d9b96673c5f21284c2a6ec37956"},"schema_version":"1.0","source":{"id":"1808.07264","kind":"arxiv","version":1}},"canonical_sha256":"c9ebafdc3da0097053e1f161275e8bb621673a374b11a114197594eda34d4053","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c9ebafdc3da0097053e1f161275e8bb621673a374b11a114197594eda34d4053","first_computed_at":"2026-05-18T00:07:29.385471Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:29.385471Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GlZbSeAIC+BuhA5iL+SfdCdT/PRTN5bZFjDo+E8PTiFfnTE/I6XLEKpQeek/Dl3mCbTFkyOaecfLzdfnbl24Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:29.386164Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.07264","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5c7442f55f7e0c1e2248c8db99115515041884405e908afd80975b50411b89a1","sha256:8557fba7553e1686d9eaa88cdc0bb3db3240c26cf5e4b4710a59f74faed9ed66"],"state_sha256":"949c6ad8ace97614ae49925ce2d55a666105a5c0eb17604c21c0c3a71e1ad1d6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AnVk2PT9veSuXsm8hxHy564ZFayhxWo4AvwkHYHlLK3gqpO0/+x49TsIT1k41xL6Rq6hynipUSSy46i0TSDDCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T14:44:33.281617Z","bundle_sha256":"4561f5dd9e3796237666b479d1a20699d3119beca174c959a28906e502d1d169"}}