{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:DYRUWWBOE7JA6AN7G5JDIPEOCI","short_pith_number":"pith:DYRUWWBO","canonical_record":{"source":{"id":"2103.04071","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-03-06T08:41:43Z","cross_cats_sorted":[],"title_canon_sha256":"66b38498198b11233f12da646812715bc11f425b38fc14ecd3aa2383a8864c63","abstract_canon_sha256":"08ee1ddb214390daf6068ecaf58b098012bfb47be1fdfd3b422c402b1076f4f2"},"schema_version":"1.0"},"canonical_sha256":"1e234b582e27d20f01bf3752343c8e123926997492703baadcdf949b7bd5c7e3","source":{"kind":"arxiv","id":"2103.04071","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2103.04071","created_at":"2026-07-05T03:07:47Z"},{"alias_kind":"arxiv_version","alias_value":"2103.04071v2","created_at":"2026-07-05T03:07:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2103.04071","created_at":"2026-07-05T03:07:47Z"},{"alias_kind":"pith_short_12","alias_value":"DYRUWWBOE7JA","created_at":"2026-07-05T03:07:47Z"},{"alias_kind":"pith_short_16","alias_value":"DYRUWWBOE7JA6AN7","created_at":"2026-07-05T03:07:47Z"},{"alias_kind":"pith_short_8","alias_value":"DYRUWWBO","created_at":"2026-07-05T03:07:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:DYRUWWBOE7JA6AN7G5JDIPEOCI","target":"record","payload":{"canonical_record":{"source":{"id":"2103.04071","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-03-06T08:41:43Z","cross_cats_sorted":[],"title_canon_sha256":"66b38498198b11233f12da646812715bc11f425b38fc14ecd3aa2383a8864c63","abstract_canon_sha256":"08ee1ddb214390daf6068ecaf58b098012bfb47be1fdfd3b422c402b1076f4f2"},"schema_version":"1.0"},"canonical_sha256":"1e234b582e27d20f01bf3752343c8e123926997492703baadcdf949b7bd5c7e3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:07:47.331868Z","signature_b64":"40HBIg5pHLA93hqex15OecgpxaL7WgnMi5encs/KRND1EksIai/zfSTHXzA0qIm8/r6r/RCiuGGqNu1PazTBAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1e234b582e27d20f01bf3752343c8e123926997492703baadcdf949b7bd5c7e3","last_reissued_at":"2026-07-05T03:07:47.331326Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:07:47.331326Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2103.04071","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":"2026-07-05T03:07:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iqLGXu+Atfy6Cnab8JrMIYxcMJtaiiZtwQZP7zVO/YtKoXf7V71nJF2wdyYX96sWa5xxgf8fMMC0NIdQEUtpCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T10:10:41.997160Z"},"content_sha256":"465252b62d600c1f2b911c8dbe164f7b18224628ed567f2557b5c60d14b78894","schema_version":"1.0","event_id":"sha256:465252b62d600c1f2b911c8dbe164f7b18224628ed567f2557b5c60d14b78894"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:DYRUWWBOE7JA6AN7G5JDIPEOCI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Estimates for Green's functions of elliptic equations in non-divergence form with continuous coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Seick Kim, Sungjin Lee","submitted_at":"2021-03-06T08:41:43Z","abstract_excerpt":"We present a new method for the existence and pointwise estimates of a Green's function of non-divergence form elliptic operator with Dini mean oscillation coefficients. We also present a sharp comparison with the corresponding Green's function for constant coefficients equations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.04071","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2103.04071/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T03:07:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tInq/t7EROFFeLbPt5LYJJ732zuOxVhu0XWd+Inzg1zWm+lm6pylhRT1gnEFBK+0aCCcEOb7MtHKQcc/s5xfBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T10:10:41.997648Z"},"content_sha256":"1609d093bc4f1cc2033be21c3921af9eaebd4197d147db0906c2a0a150eac5d0","schema_version":"1.0","event_id":"sha256:1609d093bc4f1cc2033be21c3921af9eaebd4197d147db0906c2a0a150eac5d0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DYRUWWBOE7JA6AN7G5JDIPEOCI/bundle.json","state_url":"https://pith.science/pith/DYRUWWBOE7JA6AN7G5JDIPEOCI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DYRUWWBOE7JA6AN7G5JDIPEOCI/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":"2026-08-13T10:10:41Z","links":{"resolver":"https://pith.science/pith/DYRUWWBOE7JA6AN7G5JDIPEOCI","bundle":"https://pith.science/pith/DYRUWWBOE7JA6AN7G5JDIPEOCI/bundle.json","state":"https://pith.science/pith/DYRUWWBOE7JA6AN7G5JDIPEOCI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DYRUWWBOE7JA6AN7G5JDIPEOCI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:DYRUWWBOE7JA6AN7G5JDIPEOCI","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":"08ee1ddb214390daf6068ecaf58b098012bfb47be1fdfd3b422c402b1076f4f2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-03-06T08:41:43Z","title_canon_sha256":"66b38498198b11233f12da646812715bc11f425b38fc14ecd3aa2383a8864c63"},"schema_version":"1.0","source":{"id":"2103.04071","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2103.04071","created_at":"2026-07-05T03:07:47Z"},{"alias_kind":"arxiv_version","alias_value":"2103.04071v2","created_at":"2026-07-05T03:07:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2103.04071","created_at":"2026-07-05T03:07:47Z"},{"alias_kind":"pith_short_12","alias_value":"DYRUWWBOE7JA","created_at":"2026-07-05T03:07:47Z"},{"alias_kind":"pith_short_16","alias_value":"DYRUWWBOE7JA6AN7","created_at":"2026-07-05T03:07:47Z"},{"alias_kind":"pith_short_8","alias_value":"DYRUWWBO","created_at":"2026-07-05T03:07:47Z"}],"graph_snapshots":[{"event_id":"sha256:1609d093bc4f1cc2033be21c3921af9eaebd4197d147db0906c2a0a150eac5d0","target":"graph","created_at":"2026-07-05T03:07:47Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2103.04071/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a new method for the existence and pointwise estimates of a Green's function of non-divergence form elliptic operator with Dini mean oscillation coefficients. We also present a sharp comparison with the corresponding Green's function for constant coefficients equations.","authors_text":"Seick Kim, Sungjin Lee","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-03-06T08:41:43Z","title":"Estimates for Green's functions of elliptic equations in non-divergence form with continuous coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.04071","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":"sha256:465252b62d600c1f2b911c8dbe164f7b18224628ed567f2557b5c60d14b78894","target":"record","created_at":"2026-07-05T03:07:47Z","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":"08ee1ddb214390daf6068ecaf58b098012bfb47be1fdfd3b422c402b1076f4f2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-03-06T08:41:43Z","title_canon_sha256":"66b38498198b11233f12da646812715bc11f425b38fc14ecd3aa2383a8864c63"},"schema_version":"1.0","source":{"id":"2103.04071","kind":"arxiv","version":2}},"canonical_sha256":"1e234b582e27d20f01bf3752343c8e123926997492703baadcdf949b7bd5c7e3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1e234b582e27d20f01bf3752343c8e123926997492703baadcdf949b7bd5c7e3","first_computed_at":"2026-07-05T03:07:47.331326Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:07:47.331326Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"40HBIg5pHLA93hqex15OecgpxaL7WgnMi5encs/KRND1EksIai/zfSTHXzA0qIm8/r6r/RCiuGGqNu1PazTBAw==","signature_status":"signed_v1","signed_at":"2026-07-05T03:07:47.331868Z","signed_message":"canonical_sha256_bytes"},"source_id":"2103.04071","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:465252b62d600c1f2b911c8dbe164f7b18224628ed567f2557b5c60d14b78894","sha256:1609d093bc4f1cc2033be21c3921af9eaebd4197d147db0906c2a0a150eac5d0"],"state_sha256":"98f0231e196247087a3ea332bb38ed7adab1b6098f56b3fea23821dfe6598c21"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5ck9w38WFsKTUHpxo8ydQjRVmmDBKpqWbByOUPP8X4/Yj7Bfpi6jpEDzN7SlN8O9I8gI+kNuG86cs8HHDal6AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T10:10:42.001101Z","bundle_sha256":"6116bde52aea529456ba9e98d7c00df6f799e33ba6401bc4b1a378bedb2a2ccc"}}