{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:UPJ2RRYV5QYLLX4F7UNYLCZM5F","short_pith_number":"pith:UPJ2RRYV","canonical_record":{"source":{"id":"1707.09162","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-28T09:17:52Z","cross_cats_sorted":[],"title_canon_sha256":"49d9a518ece5380dba2a5553fbed6e75b2c3c3809219f7c971179415217200aa","abstract_canon_sha256":"a0e26913a68b252c0beb36397a8b80e94262dd02bc84c55751dbda2387fd4183"},"schema_version":"1.0"},"canonical_sha256":"a3d3a8c715ec30b5df85fd1b858b2ce952f28a0a6c026b7f1b8e5288fbf7c677","source":{"kind":"arxiv","id":"1707.09162","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.09162","created_at":"2026-05-18T00:18:31Z"},{"alias_kind":"arxiv_version","alias_value":"1707.09162v2","created_at":"2026-05-18T00:18:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.09162","created_at":"2026-05-18T00:18:31Z"},{"alias_kind":"pith_short_12","alias_value":"UPJ2RRYV5QYL","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"UPJ2RRYV5QYLLX4F","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"UPJ2RRYV","created_at":"2026-05-18T12:31:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:UPJ2RRYV5QYLLX4F7UNYLCZM5F","target":"record","payload":{"canonical_record":{"source":{"id":"1707.09162","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-28T09:17:52Z","cross_cats_sorted":[],"title_canon_sha256":"49d9a518ece5380dba2a5553fbed6e75b2c3c3809219f7c971179415217200aa","abstract_canon_sha256":"a0e26913a68b252c0beb36397a8b80e94262dd02bc84c55751dbda2387fd4183"},"schema_version":"1.0"},"canonical_sha256":"a3d3a8c715ec30b5df85fd1b858b2ce952f28a0a6c026b7f1b8e5288fbf7c677","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:31.679109Z","signature_b64":"7eGl8POZFF8N/jw0irJv0X7SmMdLXd/fqXMA8xc5ApYEsfFwOB05766mFgWdW0xQgWmhJRyhwINq764OzA/KBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a3d3a8c715ec30b5df85fd1b858b2ce952f28a0a6c026b7f1b8e5288fbf7c677","last_reissued_at":"2026-05-18T00:18:31.678597Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:31.678597Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.09162","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":"2026-05-18T00:18:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OG8E4HULol7hduOLz8stQ/F7Aa8NQwKNPHS144aWF5m7L5E0v2z1vnGZwBaaazhxOjzH9M7/GtTCWBTVuHuzBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T02:19:19.679926Z"},"content_sha256":"ba2f4637caec1b7888e0ff640c9d83388e4aa25376685725c828e1f057f8cd9b","schema_version":"1.0","event_id":"sha256:ba2f4637caec1b7888e0ff640c9d83388e4aa25376685725c828e1f057f8cd9b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:UPJ2RRYV5QYLLX4F7UNYLCZM5F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fundamental solutions for second order parabolic systems with drift terms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hongjie Dong, Seick Kim","submitted_at":"2017-07-28T09:17:52Z","abstract_excerpt":"We construct fundamental solutions of second-order parabolic systems of divergence form with bounded and measurable leading coefficients and divergence free first-order coefficients in the class of $BMO^{-1}_x$, under the assumption that weak solutions of the system satisfy a certain local boundedness estimate. We also establish Gaussian upper bound for such fundamental solutions under the same conditions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.09162","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":"2026-05-18T00:18:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Sndktr/3xENXBuakOQ2ckIpX3tMUzHuHD8oLPHFw2qcPXsHdr0PzEnWSE/403KzRSWa1XzNRyjroxWGWrZXbDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T02:19:19.680278Z"},"content_sha256":"cba7b095c88cade24a7ce15256c29485346e1a443db799cf3aaaf8f51db2df58","schema_version":"1.0","event_id":"sha256:cba7b095c88cade24a7ce15256c29485346e1a443db799cf3aaaf8f51db2df58"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UPJ2RRYV5QYLLX4F7UNYLCZM5F/bundle.json","state_url":"https://pith.science/pith/UPJ2RRYV5QYLLX4F7UNYLCZM5F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UPJ2RRYV5QYLLX4F7UNYLCZM5F/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":"2026-06-03T02:19:19Z","links":{"resolver":"https://pith.science/pith/UPJ2RRYV5QYLLX4F7UNYLCZM5F","bundle":"https://pith.science/pith/UPJ2RRYV5QYLLX4F7UNYLCZM5F/bundle.json","state":"https://pith.science/pith/UPJ2RRYV5QYLLX4F7UNYLCZM5F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UPJ2RRYV5QYLLX4F7UNYLCZM5F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:UPJ2RRYV5QYLLX4F7UNYLCZM5F","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":"a0e26913a68b252c0beb36397a8b80e94262dd02bc84c55751dbda2387fd4183","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-28T09:17:52Z","title_canon_sha256":"49d9a518ece5380dba2a5553fbed6e75b2c3c3809219f7c971179415217200aa"},"schema_version":"1.0","source":{"id":"1707.09162","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.09162","created_at":"2026-05-18T00:18:31Z"},{"alias_kind":"arxiv_version","alias_value":"1707.09162v2","created_at":"2026-05-18T00:18:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.09162","created_at":"2026-05-18T00:18:31Z"},{"alias_kind":"pith_short_12","alias_value":"UPJ2RRYV5QYL","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"UPJ2RRYV5QYLLX4F","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"UPJ2RRYV","created_at":"2026-05-18T12:31:46Z"}],"graph_snapshots":[{"event_id":"sha256:cba7b095c88cade24a7ce15256c29485346e1a443db799cf3aaaf8f51db2df58","target":"graph","created_at":"2026-05-18T00:18:31Z","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 construct fundamental solutions of second-order parabolic systems of divergence form with bounded and measurable leading coefficients and divergence free first-order coefficients in the class of $BMO^{-1}_x$, under the assumption that weak solutions of the system satisfy a certain local boundedness estimate. We also establish Gaussian upper bound for such fundamental solutions under the same conditions.","authors_text":"Hongjie Dong, Seick Kim","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-28T09:17:52Z","title":"Fundamental solutions for second order parabolic systems with drift terms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.09162","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:ba2f4637caec1b7888e0ff640c9d83388e4aa25376685725c828e1f057f8cd9b","target":"record","created_at":"2026-05-18T00:18:31Z","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":"a0e26913a68b252c0beb36397a8b80e94262dd02bc84c55751dbda2387fd4183","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-28T09:17:52Z","title_canon_sha256":"49d9a518ece5380dba2a5553fbed6e75b2c3c3809219f7c971179415217200aa"},"schema_version":"1.0","source":{"id":"1707.09162","kind":"arxiv","version":2}},"canonical_sha256":"a3d3a8c715ec30b5df85fd1b858b2ce952f28a0a6c026b7f1b8e5288fbf7c677","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a3d3a8c715ec30b5df85fd1b858b2ce952f28a0a6c026b7f1b8e5288fbf7c677","first_computed_at":"2026-05-18T00:18:31.678597Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:31.678597Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7eGl8POZFF8N/jw0irJv0X7SmMdLXd/fqXMA8xc5ApYEsfFwOB05766mFgWdW0xQgWmhJRyhwINq764OzA/KBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:31.679109Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.09162","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba2f4637caec1b7888e0ff640c9d83388e4aa25376685725c828e1f057f8cd9b","sha256:cba7b095c88cade24a7ce15256c29485346e1a443db799cf3aaaf8f51db2df58"],"state_sha256":"709bc16167e23548fb0b124380d537454ccf8f30bf6be09202894c18ced19d89"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9m3linxZOii+hTdu5dWDJxhADcTWJZIyM/OqgcMaQ09LIr1ukyWyxZ3DspdR4tM8KmGec1fiboH/CpMBw7A2CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T02:19:19.682189Z","bundle_sha256":"1f31fe132af9cb03fcbf4295b03c063d6ec46e9fd43725e0803494b921a89442"}}