{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:KK5H3F3X7V4UEE4SGFA2XYINN2","short_pith_number":"pith:KK5H3F3X","canonical_record":{"source":{"id":"2103.16332","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.AP","submitted_at":"2021-03-30T13:27:56Z","cross_cats_sorted":[],"title_canon_sha256":"f41a0c71e4af4392316c57fb711040001a1e7bb1195bc2fd81cd81bf75a8d1a0","abstract_canon_sha256":"8d582ddf03346e288b418cc326d6f026f49676c2b9fe074caec7df0cbb667970"},"schema_version":"1.0"},"canonical_sha256":"52ba7d9777fd794213923141abe10d6e8d1af2e57e363643caa1e5a6aadf4a26","source":{"kind":"arxiv","id":"2103.16332","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2103.16332","created_at":"2026-07-05T03:26:16Z"},{"alias_kind":"arxiv_version","alias_value":"2103.16332v3","created_at":"2026-07-05T03:26:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2103.16332","created_at":"2026-07-05T03:26:16Z"},{"alias_kind":"pith_short_12","alias_value":"KK5H3F3X7V4U","created_at":"2026-07-05T03:26:16Z"},{"alias_kind":"pith_short_16","alias_value":"KK5H3F3X7V4UEE4S","created_at":"2026-07-05T03:26:16Z"},{"alias_kind":"pith_short_8","alias_value":"KK5H3F3X","created_at":"2026-07-05T03:26:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:KK5H3F3X7V4UEE4SGFA2XYINN2","target":"record","payload":{"canonical_record":{"source":{"id":"2103.16332","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.AP","submitted_at":"2021-03-30T13:27:56Z","cross_cats_sorted":[],"title_canon_sha256":"f41a0c71e4af4392316c57fb711040001a1e7bb1195bc2fd81cd81bf75a8d1a0","abstract_canon_sha256":"8d582ddf03346e288b418cc326d6f026f49676c2b9fe074caec7df0cbb667970"},"schema_version":"1.0"},"canonical_sha256":"52ba7d9777fd794213923141abe10d6e8d1af2e57e363643caa1e5a6aadf4a26","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:26:16.027332Z","signature_b64":"Zlo/K5SzLhP/I9IHU929NZC0i8z5Cv0RJS7AI8jz7t5qO7AUr3La7QfdulLtyT6yeAPhHaNP72u6Toou4iV1BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"52ba7d9777fd794213923141abe10d6e8d1af2e57e363643caa1e5a6aadf4a26","last_reissued_at":"2026-07-05T03:26:16.026332Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:26:16.026332Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2103.16332","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:26:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QZ0QAHFtHCBZDD2AQ20rJEwKm2SY9GVK53c8jAyymoYNL3HuyvSkMzHRiXOjFIPtQzhjUxns6qVQqrDKFyNEAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T06:22:16.161762Z"},"content_sha256":"62002d3372d871e84fc385ca358ef731c975a249963e10cf036cbc802d2d7123","schema_version":"1.0","event_id":"sha256:62002d3372d871e84fc385ca358ef731c975a249963e10cf036cbc802d2d7123"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:KK5H3F3X7V4UEE4SGFA2XYINN2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Well-Posedness and Exponential Decay for the Navier-Stokes Equations of Viscous Compressible Heat-Conductive Fluids with Vacuum","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hao Xu, Jianwen Zhang, Suhua Lai","submitted_at":"2021-03-30T13:27:56Z","abstract_excerpt":"This paper is concerned with the Cauchy problem of Navier-Stokes equations for compressible viscous heat-conductive fluids with far-field vacuum at infinity in $\\R^3$. For less regular data and weaker compatibility condition than those proposed by Cho-Kim \\cite{CK2006}, we first prove the existence of local-in-time solutions belonging to a larger class of functions in which the uniqueness can be shown to hold. The local solution is in fact a classical one away from the initial time, provided the initial density is regular. We also establish the global well-posedness of classical solutions with"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.16332","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2103.16332/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T03:26:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tkcYwe37WEbxfVecBmZ/UiNpKPT+f40ngUDUYgLHzd5578sVziiAGb5H9YpmkbP8ZMwNu3pcgNn2Oq77ZhImBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T06:22:16.162777Z"},"content_sha256":"baa6c2cf689c83b39aac00d048cd0abad541abb343e13adacfd661b07a7056e8","schema_version":"1.0","event_id":"sha256:baa6c2cf689c83b39aac00d048cd0abad541abb343e13adacfd661b07a7056e8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KK5H3F3X7V4UEE4SGFA2XYINN2/bundle.json","state_url":"https://pith.science/pith/KK5H3F3X7V4UEE4SGFA2XYINN2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KK5H3F3X7V4UEE4SGFA2XYINN2/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":"2026-08-06T06:22:16Z","links":{"resolver":"https://pith.science/pith/KK5H3F3X7V4UEE4SGFA2XYINN2","bundle":"https://pith.science/pith/KK5H3F3X7V4UEE4SGFA2XYINN2/bundle.json","state":"https://pith.science/pith/KK5H3F3X7V4UEE4SGFA2XYINN2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KK5H3F3X7V4UEE4SGFA2XYINN2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:KK5H3F3X7V4UEE4SGFA2XYINN2","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":"8d582ddf03346e288b418cc326d6f026f49676c2b9fe074caec7df0cbb667970","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.AP","submitted_at":"2021-03-30T13:27:56Z","title_canon_sha256":"f41a0c71e4af4392316c57fb711040001a1e7bb1195bc2fd81cd81bf75a8d1a0"},"schema_version":"1.0","source":{"id":"2103.16332","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2103.16332","created_at":"2026-07-05T03:26:16Z"},{"alias_kind":"arxiv_version","alias_value":"2103.16332v3","created_at":"2026-07-05T03:26:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2103.16332","created_at":"2026-07-05T03:26:16Z"},{"alias_kind":"pith_short_12","alias_value":"KK5H3F3X7V4U","created_at":"2026-07-05T03:26:16Z"},{"alias_kind":"pith_short_16","alias_value":"KK5H3F3X7V4UEE4S","created_at":"2026-07-05T03:26:16Z"},{"alias_kind":"pith_short_8","alias_value":"KK5H3F3X","created_at":"2026-07-05T03:26:16Z"}],"graph_snapshots":[{"event_id":"sha256:baa6c2cf689c83b39aac00d048cd0abad541abb343e13adacfd661b07a7056e8","target":"graph","created_at":"2026-07-05T03:26:16Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2103.16332/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper is concerned with the Cauchy problem of Navier-Stokes equations for compressible viscous heat-conductive fluids with far-field vacuum at infinity in $\\R^3$. For less regular data and weaker compatibility condition than those proposed by Cho-Kim \\cite{CK2006}, we first prove the existence of local-in-time solutions belonging to a larger class of functions in which the uniqueness can be shown to hold. The local solution is in fact a classical one away from the initial time, provided the initial density is regular. We also establish the global well-posedness of classical solutions with","authors_text":"Hao Xu, Jianwen Zhang, Suhua Lai","cross_cats":[],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.AP","submitted_at":"2021-03-30T13:27:56Z","title":"Well-Posedness and Exponential Decay for the Navier-Stokes Equations of Viscous Compressible Heat-Conductive Fluids with Vacuum"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.16332","kind":"arxiv","version":3},"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":"sha256:62002d3372d871e84fc385ca358ef731c975a249963e10cf036cbc802d2d7123","target":"record","created_at":"2026-07-05T03:26:16Z","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":"8d582ddf03346e288b418cc326d6f026f49676c2b9fe074caec7df0cbb667970","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.AP","submitted_at":"2021-03-30T13:27:56Z","title_canon_sha256":"f41a0c71e4af4392316c57fb711040001a1e7bb1195bc2fd81cd81bf75a8d1a0"},"schema_version":"1.0","source":{"id":"2103.16332","kind":"arxiv","version":3}},"canonical_sha256":"52ba7d9777fd794213923141abe10d6e8d1af2e57e363643caa1e5a6aadf4a26","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"52ba7d9777fd794213923141abe10d6e8d1af2e57e363643caa1e5a6aadf4a26","first_computed_at":"2026-07-05T03:26:16.026332Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:26:16.026332Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Zlo/K5SzLhP/I9IHU929NZC0i8z5Cv0RJS7AI8jz7t5qO7AUr3La7QfdulLtyT6yeAPhHaNP72u6Toou4iV1BQ==","signature_status":"signed_v1","signed_at":"2026-07-05T03:26:16.027332Z","signed_message":"canonical_sha256_bytes"},"source_id":"2103.16332","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:62002d3372d871e84fc385ca358ef731c975a249963e10cf036cbc802d2d7123","sha256:baa6c2cf689c83b39aac00d048cd0abad541abb343e13adacfd661b07a7056e8"],"state_sha256":"16e964ef5172a9c254ad444077ca302a44d00517dade661969060f5fefe85008"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5AzdI1x2ong/M/MmprbvzIkKUguYNoWmsy4W8oFpuRpHDMIVF1tWTSRgaaouJcC2/vjBcIcZL+4q4cM0jo3wCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T06:22:16.168284Z","bundle_sha256":"041b2bcbfb6ecbb8faa5910af3d432bee0fc7bcc98c52fcc2f7eeea602d7547c"}}