{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:UEEWCZBJJN7C2AT5OFBARQJWLL","short_pith_number":"pith:UEEWCZBJ","canonical_record":{"source":{"id":"1706.07392","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-06-22T16:45:20Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"61dc9084b11e8f0e4658415b94fe22fb36f52c23ca252cbc1c235cea1b987237","abstract_canon_sha256":"08115a27ceb1da636aebbbf715e5712f1eda6845263d2bb52c94568fe2c2cd03"},"schema_version":"1.0"},"canonical_sha256":"a1096164294b7e2d027d714208c1365ad8790ca90102b36fdc6c3b72a978802c","source":{"kind":"arxiv","id":"1706.07392","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.07392","created_at":"2026-05-18T00:37:57Z"},{"alias_kind":"arxiv_version","alias_value":"1706.07392v2","created_at":"2026-05-18T00:37:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.07392","created_at":"2026-05-18T00:37:57Z"},{"alias_kind":"pith_short_12","alias_value":"UEEWCZBJJN7C","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"UEEWCZBJJN7C2AT5","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"UEEWCZBJ","created_at":"2026-05-18T12:31:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:UEEWCZBJJN7C2AT5OFBARQJWLL","target":"record","payload":{"canonical_record":{"source":{"id":"1706.07392","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-06-22T16:45:20Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"61dc9084b11e8f0e4658415b94fe22fb36f52c23ca252cbc1c235cea1b987237","abstract_canon_sha256":"08115a27ceb1da636aebbbf715e5712f1eda6845263d2bb52c94568fe2c2cd03"},"schema_version":"1.0"},"canonical_sha256":"a1096164294b7e2d027d714208c1365ad8790ca90102b36fdc6c3b72a978802c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:37:57.416540Z","signature_b64":"rZQ/OHqIPMj/UcALLDZ/FnxGv+MpFFdF9wW8RYl/AbkgCde+6JFTW7ht43tJL17Bvl+S17xGF/i1EG5xsKmtBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a1096164294b7e2d027d714208c1365ad8790ca90102b36fdc6c3b72a978802c","last_reissued_at":"2026-05-18T00:37:57.415853Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:37:57.415853Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.07392","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:37:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xy5YiwA8unzbOwPmbMQSIccsMz9Oc9M7FpcahFiJKHSfRkm4UQfZaaBZnDAQYLT+KJl8eg+dzi9BH1Kt8h1oCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T20:31:26.160037Z"},"content_sha256":"26d6b41a781169ade2c114a6f18acf741f12b1c27d9d9063df5d0d0bd8c1d539","schema_version":"1.0","event_id":"sha256:26d6b41a781169ade2c114a6f18acf741f12b1c27d9d9063df5d0d0bd8c1d539"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:UEEWCZBJJN7C2AT5OFBARQJWLL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An analytic proof of the Krylov estimates for the complex Monge-Ampere equation and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CV","authors_text":"Slawomir Dinew, Szymon Plis","submitted_at":"2017-06-22T16:45:20Z","abstract_excerpt":"We provide an analytic proof of a theorem of Krylov dealing with global $C^{1,1}$ estimates to solutons of degenerate complex Monge-Amp\\`ere equations. As an application we show optimal regularity for various extremal functions with nonconstant boundary values."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.07392","kind":"arxiv","version":2},"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":"2026-05-18T00:37:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eauPORb9HyX/fTKZe8vuWhUNbuoplxUVNYlgOtllTA9M4gkHZskSl8XwyajE7AnKCadDJpws2ldT2ucdF8JUBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T20:31:26.160577Z"},"content_sha256":"3e1a2259e56747dc824d97bccb00ecb4b5b4cd750ee39e1b643ed3365349e347","schema_version":"1.0","event_id":"sha256:3e1a2259e56747dc824d97bccb00ecb4b5b4cd750ee39e1b643ed3365349e347"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UEEWCZBJJN7C2AT5OFBARQJWLL/bundle.json","state_url":"https://pith.science/pith/UEEWCZBJJN7C2AT5OFBARQJWLL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UEEWCZBJJN7C2AT5OFBARQJWLL/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":"2026-05-29T20:31:26Z","links":{"resolver":"https://pith.science/pith/UEEWCZBJJN7C2AT5OFBARQJWLL","bundle":"https://pith.science/pith/UEEWCZBJJN7C2AT5OFBARQJWLL/bundle.json","state":"https://pith.science/pith/UEEWCZBJJN7C2AT5OFBARQJWLL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UEEWCZBJJN7C2AT5OFBARQJWLL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:UEEWCZBJJN7C2AT5OFBARQJWLL","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":"08115a27ceb1da636aebbbf715e5712f1eda6845263d2bb52c94568fe2c2cd03","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-06-22T16:45:20Z","title_canon_sha256":"61dc9084b11e8f0e4658415b94fe22fb36f52c23ca252cbc1c235cea1b987237"},"schema_version":"1.0","source":{"id":"1706.07392","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.07392","created_at":"2026-05-18T00:37:57Z"},{"alias_kind":"arxiv_version","alias_value":"1706.07392v2","created_at":"2026-05-18T00:37:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.07392","created_at":"2026-05-18T00:37:57Z"},{"alias_kind":"pith_short_12","alias_value":"UEEWCZBJJN7C","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"UEEWCZBJJN7C2AT5","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"UEEWCZBJ","created_at":"2026-05-18T12:31:46Z"}],"graph_snapshots":[{"event_id":"sha256:3e1a2259e56747dc824d97bccb00ecb4b5b4cd750ee39e1b643ed3365349e347","target":"graph","created_at":"2026-05-18T00:37:57Z","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 provide an analytic proof of a theorem of Krylov dealing with global $C^{1,1}$ estimates to solutons of degenerate complex Monge-Amp\\`ere equations. As an application we show optimal regularity for various extremal functions with nonconstant boundary values.","authors_text":"Slawomir Dinew, Szymon Plis","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-06-22T16:45:20Z","title":"An analytic proof of the Krylov estimates for the complex Monge-Ampere equation and applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.07392","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":"sha256:26d6b41a781169ade2c114a6f18acf741f12b1c27d9d9063df5d0d0bd8c1d539","target":"record","created_at":"2026-05-18T00:37:57Z","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":"08115a27ceb1da636aebbbf715e5712f1eda6845263d2bb52c94568fe2c2cd03","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-06-22T16:45:20Z","title_canon_sha256":"61dc9084b11e8f0e4658415b94fe22fb36f52c23ca252cbc1c235cea1b987237"},"schema_version":"1.0","source":{"id":"1706.07392","kind":"arxiv","version":2}},"canonical_sha256":"a1096164294b7e2d027d714208c1365ad8790ca90102b36fdc6c3b72a978802c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a1096164294b7e2d027d714208c1365ad8790ca90102b36fdc6c3b72a978802c","first_computed_at":"2026-05-18T00:37:57.415853Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:37:57.415853Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rZQ/OHqIPMj/UcALLDZ/FnxGv+MpFFdF9wW8RYl/AbkgCde+6JFTW7ht43tJL17Bvl+S17xGF/i1EG5xsKmtBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:37:57.416540Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.07392","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:26d6b41a781169ade2c114a6f18acf741f12b1c27d9d9063df5d0d0bd8c1d539","sha256:3e1a2259e56747dc824d97bccb00ecb4b5b4cd750ee39e1b643ed3365349e347"],"state_sha256":"5d904794ecfd04605915731f1c92e28a9261ffe7044c7ad6af633e093f343d8f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ck7pX6C5pgIK/eaQ0DOj+79/DrJChhaYNrJQg6AKUM2QJXgYuhhNCMowQVBGAO1x/Eraf7kakSco2WZx8ooWCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T20:31:26.164427Z","bundle_sha256":"062a906c02cb6756cebe775bcbe3a2405550333fef755e34c61422e83eee7792"}}