{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:D2Y3XPPBMPEHBKXLR7TTN3MODB","short_pith_number":"pith:D2Y3XPPB","canonical_record":{"source":{"id":"1001.2618","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-01-15T16:00:21Z","cross_cats_sorted":[],"title_canon_sha256":"0793451f5a45db5fdf3827f3af919c8c61e8fb5b65a26edf8ad5cb370b7fc98f","abstract_canon_sha256":"6815984db9d7c24d4a278ffb725114adf6edaaec8b6aeb005b72bcb954dc19bc"},"schema_version":"1.0"},"canonical_sha256":"1eb1bbbde163c870aaeb8fe736ed8e184430833abf0678df27ee36b9bbb27911","source":{"kind":"arxiv","id":"1001.2618","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.2618","created_at":"2026-05-18T04:41:25Z"},{"alias_kind":"arxiv_version","alias_value":"1001.2618v2","created_at":"2026-05-18T04:41:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.2618","created_at":"2026-05-18T04:41:25Z"},{"alias_kind":"pith_short_12","alias_value":"D2Y3XPPBMPEH","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"D2Y3XPPBMPEHBKXL","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"D2Y3XPPB","created_at":"2026-05-18T12:26:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:D2Y3XPPBMPEHBKXLR7TTN3MODB","target":"record","payload":{"canonical_record":{"source":{"id":"1001.2618","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-01-15T16:00:21Z","cross_cats_sorted":[],"title_canon_sha256":"0793451f5a45db5fdf3827f3af919c8c61e8fb5b65a26edf8ad5cb370b7fc98f","abstract_canon_sha256":"6815984db9d7c24d4a278ffb725114adf6edaaec8b6aeb005b72bcb954dc19bc"},"schema_version":"1.0"},"canonical_sha256":"1eb1bbbde163c870aaeb8fe736ed8e184430833abf0678df27ee36b9bbb27911","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:41:25.090877Z","signature_b64":"osz4+rtN8G1KIMuS0IIiAIk2wmp/QqQrMAbsONXV8g9VhyTT+dyUgVLdekQwEAwRKBUCecH0rLPYJTtpfLvrBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1eb1bbbde163c870aaeb8fe736ed8e184430833abf0678df27ee36b9bbb27911","last_reissued_at":"2026-05-18T04:41:25.090412Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:41:25.090412Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1001.2618","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":"2026-05-18T04:41:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Nd4rr0yV3oZltETp9KUySzzbcxU+23/Td2An4/8ypgLiNXqmVYmlTp3VXO36gM/D695wKVRILA4UwM+K8s3uAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T16:56:54.061305Z"},"content_sha256":"425bf224db5b11a55a13c9379b3b8ffe10c29cf7a5ff30bb03a312e38c8ddd37","schema_version":"1.0","event_id":"sha256:425bf224db5b11a55a13c9379b3b8ffe10c29cf7a5ff30bb03a312e38c8ddd37"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:D2Y3XPPBMPEHBKXLR7TTN3MODB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global pointwise estimates for Green's matrix of second order elliptic systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Kyungkeun Kang, Seick Kim","submitted_at":"2010-01-15T16:00:21Z","abstract_excerpt":"We establish global pointwise bounds for the Green's matrix for divergence form, second order elliptic systems in a domain under the assumption that weak solutions of the system vanishing on a portion of the boundary satisfy a certain local boundedness estimate. Moreover, we prove that such a local boundedness estimate for weak solutions of the system is equivalent to the usual global pointwise bound for the Green's matrix. In the scalar case, such an estimate is a consequence of De Giorgi-Moser-Nash theory and holds for equations with bounded measurable coefficients in arbitrary domains. In t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.2618","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":"2026-05-18T04:41:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"foGuftEGE63kykTxhH3eoKWSVezdOgVUPDmUNmz2YD5nJ1NFfyCk8nCWIDOvxQJsPlbBmPxlJ7U34pVpRDnTBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T16:56:54.061783Z"},"content_sha256":"f5ab0a5b77b2bcc6faea2a5579c79360a90b04efb68e6ea06f327e606a08418c","schema_version":"1.0","event_id":"sha256:f5ab0a5b77b2bcc6faea2a5579c79360a90b04efb68e6ea06f327e606a08418c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D2Y3XPPBMPEHBKXLR7TTN3MODB/bundle.json","state_url":"https://pith.science/pith/D2Y3XPPBMPEHBKXLR7TTN3MODB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D2Y3XPPBMPEHBKXLR7TTN3MODB/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":"2026-05-26T16:56:54Z","links":{"resolver":"https://pith.science/pith/D2Y3XPPBMPEHBKXLR7TTN3MODB","bundle":"https://pith.science/pith/D2Y3XPPBMPEHBKXLR7TTN3MODB/bundle.json","state":"https://pith.science/pith/D2Y3XPPBMPEHBKXLR7TTN3MODB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D2Y3XPPBMPEHBKXLR7TTN3MODB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:D2Y3XPPBMPEHBKXLR7TTN3MODB","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":"6815984db9d7c24d4a278ffb725114adf6edaaec8b6aeb005b72bcb954dc19bc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-01-15T16:00:21Z","title_canon_sha256":"0793451f5a45db5fdf3827f3af919c8c61e8fb5b65a26edf8ad5cb370b7fc98f"},"schema_version":"1.0","source":{"id":"1001.2618","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.2618","created_at":"2026-05-18T04:41:25Z"},{"alias_kind":"arxiv_version","alias_value":"1001.2618v2","created_at":"2026-05-18T04:41:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.2618","created_at":"2026-05-18T04:41:25Z"},{"alias_kind":"pith_short_12","alias_value":"D2Y3XPPBMPEH","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"D2Y3XPPBMPEHBKXL","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"D2Y3XPPB","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:f5ab0a5b77b2bcc6faea2a5579c79360a90b04efb68e6ea06f327e606a08418c","target":"graph","created_at":"2026-05-18T04:41:25Z","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 establish global pointwise bounds for the Green's matrix for divergence form, second order elliptic systems in a domain under the assumption that weak solutions of the system vanishing on a portion of the boundary satisfy a certain local boundedness estimate. Moreover, we prove that such a local boundedness estimate for weak solutions of the system is equivalent to the usual global pointwise bound for the Green's matrix. In the scalar case, such an estimate is a consequence of De Giorgi-Moser-Nash theory and holds for equations with bounded measurable coefficients in arbitrary domains. In t","authors_text":"Kyungkeun Kang, Seick Kim","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-01-15T16:00:21Z","title":"Global pointwise estimates for Green's matrix of second order elliptic systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.2618","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":"sha256:425bf224db5b11a55a13c9379b3b8ffe10c29cf7a5ff30bb03a312e38c8ddd37","target":"record","created_at":"2026-05-18T04:41:25Z","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":"6815984db9d7c24d4a278ffb725114adf6edaaec8b6aeb005b72bcb954dc19bc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-01-15T16:00:21Z","title_canon_sha256":"0793451f5a45db5fdf3827f3af919c8c61e8fb5b65a26edf8ad5cb370b7fc98f"},"schema_version":"1.0","source":{"id":"1001.2618","kind":"arxiv","version":2}},"canonical_sha256":"1eb1bbbde163c870aaeb8fe736ed8e184430833abf0678df27ee36b9bbb27911","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1eb1bbbde163c870aaeb8fe736ed8e184430833abf0678df27ee36b9bbb27911","first_computed_at":"2026-05-18T04:41:25.090412Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:41:25.090412Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"osz4+rtN8G1KIMuS0IIiAIk2wmp/QqQrMAbsONXV8g9VhyTT+dyUgVLdekQwEAwRKBUCecH0rLPYJTtpfLvrBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:41:25.090877Z","signed_message":"canonical_sha256_bytes"},"source_id":"1001.2618","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:425bf224db5b11a55a13c9379b3b8ffe10c29cf7a5ff30bb03a312e38c8ddd37","sha256:f5ab0a5b77b2bcc6faea2a5579c79360a90b04efb68e6ea06f327e606a08418c"],"state_sha256":"a88f7e2b42f5da3f5d7a279d1d41c8aca868b645a428f44fddec381c7883ab78"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U7hxIL56hy4J+SXBJUbgZOVQqN3e6fH8hfBXLe2kt1z1A/8ctwqaLkhXT4YczDViN2kyUs82VQFCOyGNG5+NCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T16:56:54.065047Z","bundle_sha256":"a1125940d86f53103fb6b58dfc18f81e8b78fcf5907529d4708a5082e933f9e1"}}