{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:6SRJQ5WI3JFKJIDJJMIFBVPWCR","short_pith_number":"pith:6SRJQ5WI","canonical_record":{"source":{"id":"1503.06894","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-24T02:29:46Z","cross_cats_sorted":[],"title_canon_sha256":"88b2dc44cd485f4d9fb29461e4953a99cabde77dc4208ac338c46f09b143913a","abstract_canon_sha256":"3036095f740e7a5f67dc928d85dab0d024f3e5fe1eb1b2a44db7beb5fee3c439"},"schema_version":"1.0"},"canonical_sha256":"f4a29876c8da4aa4a0694b1050d5f6144aa44fadbb2d2fe532af0cb8f0ee3448","source":{"kind":"arxiv","id":"1503.06894","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.06894","created_at":"2026-05-18T01:34:50Z"},{"alias_kind":"arxiv_version","alias_value":"1503.06894v4","created_at":"2026-05-18T01:34:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.06894","created_at":"2026-05-18T01:34:50Z"},{"alias_kind":"pith_short_12","alias_value":"6SRJQ5WI3JFK","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6SRJQ5WI3JFKJIDJ","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6SRJQ5WI","created_at":"2026-05-18T12:29:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:6SRJQ5WI3JFKJIDJJMIFBVPWCR","target":"record","payload":{"canonical_record":{"source":{"id":"1503.06894","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-24T02:29:46Z","cross_cats_sorted":[],"title_canon_sha256":"88b2dc44cd485f4d9fb29461e4953a99cabde77dc4208ac338c46f09b143913a","abstract_canon_sha256":"3036095f740e7a5f67dc928d85dab0d024f3e5fe1eb1b2a44db7beb5fee3c439"},"schema_version":"1.0"},"canonical_sha256":"f4a29876c8da4aa4a0694b1050d5f6144aa44fadbb2d2fe532af0cb8f0ee3448","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:50.246146Z","signature_b64":"SSkizDkiUZAklGDMBKjcBfMRH+gSTviCnF1Oi5wvQepadladAVPMSO6S2yODe5RCBhDU1RkW69UXJNg/NWnSCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f4a29876c8da4aa4a0694b1050d5f6144aa44fadbb2d2fe532af0cb8f0ee3448","last_reissued_at":"2026-05-18T01:34:50.245644Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:50.245644Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.06894","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:34:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nFXa6HGoDU6oOKgff6ZJ5OKvnFycTSK0CIeMp5rY/1nNeQzSTSpkRnzhrCaTU3UdODEbCcId9wZjHdFyTKn/CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T12:59:16.812900Z"},"content_sha256":"c95e467a6d2533db273f14f4c5be5ea52e3980d51b882a71fae3175c00d9ce25","schema_version":"1.0","event_id":"sha256:c95e467a6d2533db273f14f4c5be5ea52e3980d51b882a71fae3175c00d9ce25"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:6SRJQ5WI3JFKJIDJJMIFBVPWCR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global weak solutions to compressible quantum Navier-Stokes equations with damping","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alexis F. Vasseur, Cheng Yu","submitted_at":"2015-03-24T02:29:46Z","abstract_excerpt":"The global-in-time existence of weak solutions to the barotropic compressible quantum Navier-Stokes equations with damping is proved for large data in three dimensional space. The model consists of the compressible Navier-Stokes equations with degenerate viscosity, and a nonlinear third-order differential operator, with the quantum Bohm potential, and the damping terms. The global weak solutions to such system is shown by using the Faedo-Galerkin method and the compactness argument. This system is also a very important approximated system to the compressible Navier-Stokes equations. It will he"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06894","kind":"arxiv","version":4},"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":"2026-05-18T01:34:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7kO7IIYXDX1AlI44uUGrlfUQvDCPOgsvmIpSq2wLSETh3/aBLZhIysi0+4LacE580CLSiXR37SYY1xsq1gNkDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T12:59:16.813282Z"},"content_sha256":"e3f1c88a53ea18d3148c9f05d41b4a3503dfa1dd4854e5291f4a435eef140ac5","schema_version":"1.0","event_id":"sha256:e3f1c88a53ea18d3148c9f05d41b4a3503dfa1dd4854e5291f4a435eef140ac5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6SRJQ5WI3JFKJIDJJMIFBVPWCR/bundle.json","state_url":"https://pith.science/pith/6SRJQ5WI3JFKJIDJJMIFBVPWCR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6SRJQ5WI3JFKJIDJJMIFBVPWCR/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":"2026-06-01T12:59:16Z","links":{"resolver":"https://pith.science/pith/6SRJQ5WI3JFKJIDJJMIFBVPWCR","bundle":"https://pith.science/pith/6SRJQ5WI3JFKJIDJJMIFBVPWCR/bundle.json","state":"https://pith.science/pith/6SRJQ5WI3JFKJIDJJMIFBVPWCR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6SRJQ5WI3JFKJIDJJMIFBVPWCR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:6SRJQ5WI3JFKJIDJJMIFBVPWCR","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":"3036095f740e7a5f67dc928d85dab0d024f3e5fe1eb1b2a44db7beb5fee3c439","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-24T02:29:46Z","title_canon_sha256":"88b2dc44cd485f4d9fb29461e4953a99cabde77dc4208ac338c46f09b143913a"},"schema_version":"1.0","source":{"id":"1503.06894","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.06894","created_at":"2026-05-18T01:34:50Z"},{"alias_kind":"arxiv_version","alias_value":"1503.06894v4","created_at":"2026-05-18T01:34:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.06894","created_at":"2026-05-18T01:34:50Z"},{"alias_kind":"pith_short_12","alias_value":"6SRJQ5WI3JFK","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6SRJQ5WI3JFKJIDJ","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6SRJQ5WI","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:e3f1c88a53ea18d3148c9f05d41b4a3503dfa1dd4854e5291f4a435eef140ac5","target":"graph","created_at":"2026-05-18T01:34:50Z","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":"The global-in-time existence of weak solutions to the barotropic compressible quantum Navier-Stokes equations with damping is proved for large data in three dimensional space. The model consists of the compressible Navier-Stokes equations with degenerate viscosity, and a nonlinear third-order differential operator, with the quantum Bohm potential, and the damping terms. The global weak solutions to such system is shown by using the Faedo-Galerkin method and the compactness argument. This system is also a very important approximated system to the compressible Navier-Stokes equations. It will he","authors_text":"Alexis F. Vasseur, Cheng Yu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-24T02:29:46Z","title":"Global weak solutions to compressible quantum Navier-Stokes equations with damping"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06894","kind":"arxiv","version":4},"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:c95e467a6d2533db273f14f4c5be5ea52e3980d51b882a71fae3175c00d9ce25","target":"record","created_at":"2026-05-18T01:34:50Z","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":"3036095f740e7a5f67dc928d85dab0d024f3e5fe1eb1b2a44db7beb5fee3c439","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-24T02:29:46Z","title_canon_sha256":"88b2dc44cd485f4d9fb29461e4953a99cabde77dc4208ac338c46f09b143913a"},"schema_version":"1.0","source":{"id":"1503.06894","kind":"arxiv","version":4}},"canonical_sha256":"f4a29876c8da4aa4a0694b1050d5f6144aa44fadbb2d2fe532af0cb8f0ee3448","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f4a29876c8da4aa4a0694b1050d5f6144aa44fadbb2d2fe532af0cb8f0ee3448","first_computed_at":"2026-05-18T01:34:50.245644Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:50.245644Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SSkizDkiUZAklGDMBKjcBfMRH+gSTviCnF1Oi5wvQepadladAVPMSO6S2yODe5RCBhDU1RkW69UXJNg/NWnSCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:50.246146Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.06894","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c95e467a6d2533db273f14f4c5be5ea52e3980d51b882a71fae3175c00d9ce25","sha256:e3f1c88a53ea18d3148c9f05d41b4a3503dfa1dd4854e5291f4a435eef140ac5"],"state_sha256":"370dd897bda4b6146c3c59cf9546fc1b3946f35f75efa5ffd28ad0a56b3ee004"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yTv/enPphK1pYtzeP/Dx4WrEWWL17wxrAejxw7DekaSD4X6FvJyD4hyjUrHrDMClXreVTycq6xTnHuisVtV8CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T12:59:16.815334Z","bundle_sha256":"57dd2e1b6ff096bfff5aa7291ad29523ddf60d2b615ad4937c50def1cccaf5fb"}}