{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:MY5OJN4V7JCQLJEIE6PEJKLTDH","short_pith_number":"pith:MY5OJN4V","canonical_record":{"source":{"id":"1801.00556","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-02T05:55:20Z","cross_cats_sorted":[],"title_canon_sha256":"a923c5fa4c248a0b1a771032072e8c1f92eb2e3e89e862687352fac4dae4d17a","abstract_canon_sha256":"b3fd61d84d66b97c899811b3a18276e51532c0a1d81f7a35d434f2598d3c6b3a"},"schema_version":"1.0"},"canonical_sha256":"663ae4b795fa4505a488279e44a97319ed5c6853a9df0e4c9d67ea6807a4a5ac","source":{"kind":"arxiv","id":"1801.00556","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.00556","created_at":"2026-05-18T00:22:15Z"},{"alias_kind":"arxiv_version","alias_value":"1801.00556v1","created_at":"2026-05-18T00:22:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.00556","created_at":"2026-05-18T00:22:15Z"},{"alias_kind":"pith_short_12","alias_value":"MY5OJN4V7JCQ","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"MY5OJN4V7JCQLJEI","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"MY5OJN4V","created_at":"2026-05-18T12:32:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:MY5OJN4V7JCQLJEIE6PEJKLTDH","target":"record","payload":{"canonical_record":{"source":{"id":"1801.00556","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-02T05:55:20Z","cross_cats_sorted":[],"title_canon_sha256":"a923c5fa4c248a0b1a771032072e8c1f92eb2e3e89e862687352fac4dae4d17a","abstract_canon_sha256":"b3fd61d84d66b97c899811b3a18276e51532c0a1d81f7a35d434f2598d3c6b3a"},"schema_version":"1.0"},"canonical_sha256":"663ae4b795fa4505a488279e44a97319ed5c6853a9df0e4c9d67ea6807a4a5ac","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:15.697969Z","signature_b64":"82hxMvNgeOgmcG2fXv7qU+FOZVxDqk/Y+wxq2iQEv6zo4GDpROqWdvwFwEiwLTQ4L3Zhw7VTmvUzNFhjd7DeCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"663ae4b795fa4505a488279e44a97319ed5c6853a9df0e4c9d67ea6807a4a5ac","last_reissued_at":"2026-05-18T00:22:15.697376Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:15.697376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.00556","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":"2026-05-18T00:22:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QvX6whVlOFghSVKAhsctKvrl0u+ryoEP6+Axo/8sZEsGSwf94iNDF9nPkhyGx2nAZIk6wyrdaB8h/pGbtdrOBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T16:55:45.530543Z"},"content_sha256":"38ab050a77df1dc3cfd515d0e3c7ba1f903e6a519987ac101191649ff902a3d3","schema_version":"1.0","event_id":"sha256:38ab050a77df1dc3cfd515d0e3c7ba1f903e6a519987ac101191649ff902a3d3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:MY5OJN4V7JCQLJEIE6PEJKLTDH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Uniqueness of solutions for Keller-Segel system of porous medium type coupled to fluid equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hantaek Bae, Kyungkeun Kang, Seick Kim","submitted_at":"2018-01-02T05:55:20Z","abstract_excerpt":"We prove the uniqueness of H\\\"older continuous weak solutions via duality argument and vanishing viscosity method for the Keller-Segel system of porous medium type equations coupled to the Stokes system in dimensions three. An important step is the estimate of the Green function of parabolic equations with lower order terms of variable coefficients, which seems to be of independent interest."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.00556","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":"2026-05-18T00:22:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W+yt9WEfMky5v4DTE6L0EWH0I/PmCo8rZJZHp9UKVkG2KhC6XBJxKuy+K9y2qjkm8hglUE1e0Gu9eF5pd1rZCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T16:55:45.530935Z"},"content_sha256":"3dd3cb0d40d62c41df3a6d843f61f4c0f24cd84140efc8ecfc71c1cc52a2c565","schema_version":"1.0","event_id":"sha256:3dd3cb0d40d62c41df3a6d843f61f4c0f24cd84140efc8ecfc71c1cc52a2c565"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MY5OJN4V7JCQLJEIE6PEJKLTDH/bundle.json","state_url":"https://pith.science/pith/MY5OJN4V7JCQLJEIE6PEJKLTDH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MY5OJN4V7JCQLJEIE6PEJKLTDH/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":"2026-05-26T16:55:45Z","links":{"resolver":"https://pith.science/pith/MY5OJN4V7JCQLJEIE6PEJKLTDH","bundle":"https://pith.science/pith/MY5OJN4V7JCQLJEIE6PEJKLTDH/bundle.json","state":"https://pith.science/pith/MY5OJN4V7JCQLJEIE6PEJKLTDH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MY5OJN4V7JCQLJEIE6PEJKLTDH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:MY5OJN4V7JCQLJEIE6PEJKLTDH","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":"b3fd61d84d66b97c899811b3a18276e51532c0a1d81f7a35d434f2598d3c6b3a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-02T05:55:20Z","title_canon_sha256":"a923c5fa4c248a0b1a771032072e8c1f92eb2e3e89e862687352fac4dae4d17a"},"schema_version":"1.0","source":{"id":"1801.00556","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.00556","created_at":"2026-05-18T00:22:15Z"},{"alias_kind":"arxiv_version","alias_value":"1801.00556v1","created_at":"2026-05-18T00:22:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.00556","created_at":"2026-05-18T00:22:15Z"},{"alias_kind":"pith_short_12","alias_value":"MY5OJN4V7JCQ","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"MY5OJN4V7JCQLJEI","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"MY5OJN4V","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:3dd3cb0d40d62c41df3a6d843f61f4c0f24cd84140efc8ecfc71c1cc52a2c565","target":"graph","created_at":"2026-05-18T00:22:15Z","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 prove the uniqueness of H\\\"older continuous weak solutions via duality argument and vanishing viscosity method for the Keller-Segel system of porous medium type equations coupled to the Stokes system in dimensions three. An important step is the estimate of the Green function of parabolic equations with lower order terms of variable coefficients, which seems to be of independent interest.","authors_text":"Hantaek Bae, Kyungkeun Kang, Seick Kim","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-02T05:55:20Z","title":"Uniqueness of solutions for Keller-Segel system of porous medium type coupled to fluid equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.00556","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":"sha256:38ab050a77df1dc3cfd515d0e3c7ba1f903e6a519987ac101191649ff902a3d3","target":"record","created_at":"2026-05-18T00:22:15Z","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":"b3fd61d84d66b97c899811b3a18276e51532c0a1d81f7a35d434f2598d3c6b3a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-02T05:55:20Z","title_canon_sha256":"a923c5fa4c248a0b1a771032072e8c1f92eb2e3e89e862687352fac4dae4d17a"},"schema_version":"1.0","source":{"id":"1801.00556","kind":"arxiv","version":1}},"canonical_sha256":"663ae4b795fa4505a488279e44a97319ed5c6853a9df0e4c9d67ea6807a4a5ac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"663ae4b795fa4505a488279e44a97319ed5c6853a9df0e4c9d67ea6807a4a5ac","first_computed_at":"2026-05-18T00:22:15.697376Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:15.697376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"82hxMvNgeOgmcG2fXv7qU+FOZVxDqk/Y+wxq2iQEv6zo4GDpROqWdvwFwEiwLTQ4L3Zhw7VTmvUzNFhjd7DeCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:15.697969Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.00556","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:38ab050a77df1dc3cfd515d0e3c7ba1f903e6a519987ac101191649ff902a3d3","sha256:3dd3cb0d40d62c41df3a6d843f61f4c0f24cd84140efc8ecfc71c1cc52a2c565"],"state_sha256":"be626e344a39f40d70ab0297f7235eb41054575ce012dda6d6888aed07e33aad"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Obur3qUYU/cyCWeyCrMNSS0Noraz4+D/i695gsxjQ0L4Bqeq/n5cK3OhRRTfDy5wOnQzMOsUgbOJF6UNT7J0CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T16:55:45.533439Z","bundle_sha256":"335f10b3f13369c13bd1e41e314f2e3864cff2c361fc06e443bd9a345f720dfe"}}