{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:JQHQUYPODKICJ2ZIO2HXJ5KD6D","short_pith_number":"pith:JQHQUYPO","canonical_record":{"source":{"id":"1504.06826","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-26T14:09:44Z","cross_cats_sorted":[],"title_canon_sha256":"c8573df05406f446302194fdd63dc0c6b0e88b4fb0122da7e8afc0d312eacfde","abstract_canon_sha256":"2bb799897e871ff03bff455a1b710fa224bf1599659e4c652a0d758d84a0860e"},"schema_version":"1.0"},"canonical_sha256":"4c0f0a61ee1a9024eb28768f74f543f0ff0ce93a96bb63dd1946f4c0472f49c6","source":{"kind":"arxiv","id":"1504.06826","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.06826","created_at":"2026-05-18T01:27:15Z"},{"alias_kind":"arxiv_version","alias_value":"1504.06826v2","created_at":"2026-05-18T01:27:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.06826","created_at":"2026-05-18T01:27:15Z"},{"alias_kind":"pith_short_12","alias_value":"JQHQUYPODKIC","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JQHQUYPODKICJ2ZI","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JQHQUYPO","created_at":"2026-05-18T12:29:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:JQHQUYPODKICJ2ZIO2HXJ5KD6D","target":"record","payload":{"canonical_record":{"source":{"id":"1504.06826","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-26T14:09:44Z","cross_cats_sorted":[],"title_canon_sha256":"c8573df05406f446302194fdd63dc0c6b0e88b4fb0122da7e8afc0d312eacfde","abstract_canon_sha256":"2bb799897e871ff03bff455a1b710fa224bf1599659e4c652a0d758d84a0860e"},"schema_version":"1.0"},"canonical_sha256":"4c0f0a61ee1a9024eb28768f74f543f0ff0ce93a96bb63dd1946f4c0472f49c6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:15.130865Z","signature_b64":"RfkShPhV001f66viPqBgKliCfjbrXnWslGAic9nQCj6ryqVnM/kdoGmqzbJ2zHK41j13X0YvU3ExBugBgWlJCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4c0f0a61ee1a9024eb28768f74f543f0ff0ce93a96bb63dd1946f4c0472f49c6","last_reissued_at":"2026-05-18T01:27:15.130213Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:15.130213Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.06826","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":"2026-05-18T01:27:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vOZItcZ1XN/ib91EJXeOtTWbK9OaAbicUTtTWBPqqlODn9QLN4nG+XT6WQb/Wa2OPyqk3LE6vq36joiLaRwBAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T22:25:53.495548Z"},"content_sha256":"a177f56fd2d4801dfc9bb91b6dd0c99c87b669dea3302e569211ecbe9c98c3fa","schema_version":"1.0","event_id":"sha256:a177f56fd2d4801dfc9bb91b6dd0c99c87b669dea3302e569211ecbe9c98c3fa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:JQHQUYPODKICJ2ZIO2HXJ5KD6D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global Existence of Weak Solutions to the Barotropic Compressible Navier-Stokes Flows with Degenerate Viscosities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jing Li, Zhouping Xin","submitted_at":"2015-04-26T14:09:44Z","abstract_excerpt":"This paper concerns the existence of global weak solutions to the barotropic compressible Navier-Stokes equations with degenerate viscosity coefficients. We construct suitable approximate system which has smooth solutions satisfying the energy inequality, the BD entropy one, and the Mellet-Vasseur type estimate. Then, after adapting the compactness results due to Mellet-Vasseur [Comm. Partial Differential Equations 32 (2007)], we obtain the global existence of weak solutions to the barotropic compressible Navier-Stokes equations with degenerate viscosity coefficients in two or three dimensiona"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.06826","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":"2026-05-18T01:27:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1nOsERZHPao8K9PAa/2XCtSNqaKRZZF0MR/pu8JpAoZgsTe7xJ9j9cpfLjABeE25UiDXANu2Nj25boRDjEomBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T22:25:53.496242Z"},"content_sha256":"3c399aed90912ce9eab69a4d18a91ab51e85788a2fc9050f01c554ed51b41d36","schema_version":"1.0","event_id":"sha256:3c399aed90912ce9eab69a4d18a91ab51e85788a2fc9050f01c554ed51b41d36"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JQHQUYPODKICJ2ZIO2HXJ5KD6D/bundle.json","state_url":"https://pith.science/pith/JQHQUYPODKICJ2ZIO2HXJ5KD6D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JQHQUYPODKICJ2ZIO2HXJ5KD6D/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":"2026-05-25T22:25:53Z","links":{"resolver":"https://pith.science/pith/JQHQUYPODKICJ2ZIO2HXJ5KD6D","bundle":"https://pith.science/pith/JQHQUYPODKICJ2ZIO2HXJ5KD6D/bundle.json","state":"https://pith.science/pith/JQHQUYPODKICJ2ZIO2HXJ5KD6D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JQHQUYPODKICJ2ZIO2HXJ5KD6D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:JQHQUYPODKICJ2ZIO2HXJ5KD6D","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":"2bb799897e871ff03bff455a1b710fa224bf1599659e4c652a0d758d84a0860e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-26T14:09:44Z","title_canon_sha256":"c8573df05406f446302194fdd63dc0c6b0e88b4fb0122da7e8afc0d312eacfde"},"schema_version":"1.0","source":{"id":"1504.06826","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.06826","created_at":"2026-05-18T01:27:15Z"},{"alias_kind":"arxiv_version","alias_value":"1504.06826v2","created_at":"2026-05-18T01:27:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.06826","created_at":"2026-05-18T01:27:15Z"},{"alias_kind":"pith_short_12","alias_value":"JQHQUYPODKIC","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JQHQUYPODKICJ2ZI","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JQHQUYPO","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:3c399aed90912ce9eab69a4d18a91ab51e85788a2fc9050f01c554ed51b41d36","target":"graph","created_at":"2026-05-18T01:27:15Z","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":"This paper concerns the existence of global weak solutions to the barotropic compressible Navier-Stokes equations with degenerate viscosity coefficients. We construct suitable approximate system which has smooth solutions satisfying the energy inequality, the BD entropy one, and the Mellet-Vasseur type estimate. Then, after adapting the compactness results due to Mellet-Vasseur [Comm. Partial Differential Equations 32 (2007)], we obtain the global existence of weak solutions to the barotropic compressible Navier-Stokes equations with degenerate viscosity coefficients in two or three dimensiona","authors_text":"Jing Li, Zhouping Xin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-26T14:09:44Z","title":"Global Existence of Weak Solutions to the Barotropic Compressible Navier-Stokes Flows with Degenerate Viscosities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.06826","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:a177f56fd2d4801dfc9bb91b6dd0c99c87b669dea3302e569211ecbe9c98c3fa","target":"record","created_at":"2026-05-18T01:27:15Z","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":"2bb799897e871ff03bff455a1b710fa224bf1599659e4c652a0d758d84a0860e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-26T14:09:44Z","title_canon_sha256":"c8573df05406f446302194fdd63dc0c6b0e88b4fb0122da7e8afc0d312eacfde"},"schema_version":"1.0","source":{"id":"1504.06826","kind":"arxiv","version":2}},"canonical_sha256":"4c0f0a61ee1a9024eb28768f74f543f0ff0ce93a96bb63dd1946f4c0472f49c6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4c0f0a61ee1a9024eb28768f74f543f0ff0ce93a96bb63dd1946f4c0472f49c6","first_computed_at":"2026-05-18T01:27:15.130213Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:27:15.130213Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RfkShPhV001f66viPqBgKliCfjbrXnWslGAic9nQCj6ryqVnM/kdoGmqzbJ2zHK41j13X0YvU3ExBugBgWlJCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:27:15.130865Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.06826","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a177f56fd2d4801dfc9bb91b6dd0c99c87b669dea3302e569211ecbe9c98c3fa","sha256:3c399aed90912ce9eab69a4d18a91ab51e85788a2fc9050f01c554ed51b41d36"],"state_sha256":"ae9c1d8195ec8c141704c1da3ea7948cff1811bc033e7cf613915c7cd05fa81f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o3It3SYl4iqdRPn+ftbxAh+GIGu4cASWZqf8b4klOi7BNr98slGgHw+CXSlawunFz28/csDHotDt54Y8+U6KCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T22:25:53.500168Z","bundle_sha256":"46c12337586765a398ab0dbb7f03f922e8038bcd31536834e70e0c6e96a15c42"}}