{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:7JSDFI66XCHDCG3ZK3ND5HXEEZ","short_pith_number":"pith:7JSDFI66","canonical_record":{"source":{"id":"2412.17017","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-12-22T13:39:37Z","cross_cats_sorted":[],"title_canon_sha256":"31257a83f0a82a22a7a69c5e5dfc9593fffedf68080a7863c6bd62093ebef31b","abstract_canon_sha256":"4441d6a73870d334847025d4cb2fbb2d51295bd241faf9624b34cbf43587e111"},"schema_version":"1.0"},"canonical_sha256":"fa6432a3deb88e311b7956da3e9ee4265d3f575482940a34ee42d1d4a10f3391","source":{"kind":"arxiv","id":"2412.17017","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.17017","created_at":"2026-07-05T09:53:16Z"},{"alias_kind":"arxiv_version","alias_value":"2412.17017v1","created_at":"2026-07-05T09:53:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.17017","created_at":"2026-07-05T09:53:16Z"},{"alias_kind":"pith_short_12","alias_value":"7JSDFI66XCHD","created_at":"2026-07-05T09:53:16Z"},{"alias_kind":"pith_short_16","alias_value":"7JSDFI66XCHDCG3Z","created_at":"2026-07-05T09:53:16Z"},{"alias_kind":"pith_short_8","alias_value":"7JSDFI66","created_at":"2026-07-05T09:53:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:7JSDFI66XCHDCG3ZK3ND5HXEEZ","target":"record","payload":{"canonical_record":{"source":{"id":"2412.17017","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-12-22T13:39:37Z","cross_cats_sorted":[],"title_canon_sha256":"31257a83f0a82a22a7a69c5e5dfc9593fffedf68080a7863c6bd62093ebef31b","abstract_canon_sha256":"4441d6a73870d334847025d4cb2fbb2d51295bd241faf9624b34cbf43587e111"},"schema_version":"1.0"},"canonical_sha256":"fa6432a3deb88e311b7956da3e9ee4265d3f575482940a34ee42d1d4a10f3391","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:53:16.623909Z","signature_b64":"Gp2xLrzzSfP7XL5JX3sfSJTKTmkLkEbgmNEYHfkA/h4yD568TtCdUgVKcbUarg/LS/pvuzMdE+EXkKMQU7WiDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fa6432a3deb88e311b7956da3e9ee4265d3f575482940a34ee42d1d4a10f3391","last_reissued_at":"2026-07-05T09:53:16.623474Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:53:16.623474Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2412.17017","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":"2026-07-05T09:53:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"reFDaMiCw6YYEjhnQWvhNHsyMZM0k9FSp7d/IKJe5VbhesQsxnHiVpQDxaQC70Gqh+Fj2IzipF6zSB3zhfZ0DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T20:18:55.131422Z"},"content_sha256":"9d0c91b51cf711be23aca2202450f2e5955b0f6d7b6ad06252b18b8218611efc","schema_version":"1.0","event_id":"sha256:9d0c91b51cf711be23aca2202450f2e5955b0f6d7b6ad06252b18b8218611efc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:7JSDFI66XCHDCG3ZK3ND5HXEEZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global well-posedness and optimal decay rates of classical solutions to the compressible Navier-Stokes-Fourier-P$_1$ approximation model in radiation hydrodynamics","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fucai Li, Jinkai Ni, Peng Jiang","submitted_at":"2024-12-22T13:39:37Z","abstract_excerpt":"In this paper, the compressible Navier-Stokes-Fourier-$P_1$ (NSF-$P_1$) approximation model in radiation hydrodynamics is investigated in the whole space $\\mathbb{R}^3$. This model consists of the compressible NSF equations of fluid coupled with the transport equations of the radiation field propagation. Assuming that the initial data are a small perturbation near the equilibrium state, we establish the global well-posedness of classical solutions for this model by performing the Fourier analysis techniques and employing the delicate energy estimates in frequency spaces. Here, we develop a new"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.17017","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.17017/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":"2026-07-05T09:53:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3sKF+FANa2ucOE5q/1jDwk3ncrFdq89WFvo6UCYeK5bhA2rNjiCdb5G/KPynSlYRPLvFi4fLsdOl/lHeWC9SCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T20:18:55.131981Z"},"content_sha256":"05fb753efdaf3d92ebcb3140f37766a450344630a96847fdd731abb80aa314bc","schema_version":"1.0","event_id":"sha256:05fb753efdaf3d92ebcb3140f37766a450344630a96847fdd731abb80aa314bc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7JSDFI66XCHDCG3ZK3ND5HXEEZ/bundle.json","state_url":"https://pith.science/pith/7JSDFI66XCHDCG3ZK3ND5HXEEZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7JSDFI66XCHDCG3ZK3ND5HXEEZ/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":"2026-08-06T20:18:55Z","links":{"resolver":"https://pith.science/pith/7JSDFI66XCHDCG3ZK3ND5HXEEZ","bundle":"https://pith.science/pith/7JSDFI66XCHDCG3ZK3ND5HXEEZ/bundle.json","state":"https://pith.science/pith/7JSDFI66XCHDCG3ZK3ND5HXEEZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7JSDFI66XCHDCG3ZK3ND5HXEEZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:7JSDFI66XCHDCG3ZK3ND5HXEEZ","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":"4441d6a73870d334847025d4cb2fbb2d51295bd241faf9624b34cbf43587e111","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-12-22T13:39:37Z","title_canon_sha256":"31257a83f0a82a22a7a69c5e5dfc9593fffedf68080a7863c6bd62093ebef31b"},"schema_version":"1.0","source":{"id":"2412.17017","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.17017","created_at":"2026-07-05T09:53:16Z"},{"alias_kind":"arxiv_version","alias_value":"2412.17017v1","created_at":"2026-07-05T09:53:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.17017","created_at":"2026-07-05T09:53:16Z"},{"alias_kind":"pith_short_12","alias_value":"7JSDFI66XCHD","created_at":"2026-07-05T09:53:16Z"},{"alias_kind":"pith_short_16","alias_value":"7JSDFI66XCHDCG3Z","created_at":"2026-07-05T09:53:16Z"},{"alias_kind":"pith_short_8","alias_value":"7JSDFI66","created_at":"2026-07-05T09:53:16Z"}],"graph_snapshots":[{"event_id":"sha256:05fb753efdaf3d92ebcb3140f37766a450344630a96847fdd731abb80aa314bc","target":"graph","created_at":"2026-07-05T09:53:16Z","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/2412.17017/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, the compressible Navier-Stokes-Fourier-$P_1$ (NSF-$P_1$) approximation model in radiation hydrodynamics is investigated in the whole space $\\mathbb{R}^3$. This model consists of the compressible NSF equations of fluid coupled with the transport equations of the radiation field propagation. Assuming that the initial data are a small perturbation near the equilibrium state, we establish the global well-posedness of classical solutions for this model by performing the Fourier analysis techniques and employing the delicate energy estimates in frequency spaces. Here, we develop a new","authors_text":"Fucai Li, Jinkai Ni, Peng Jiang","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-12-22T13:39:37Z","title":"Global well-posedness and optimal decay rates of classical solutions to the compressible Navier-Stokes-Fourier-P$_1$ approximation model in radiation hydrodynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.17017","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":"sha256:9d0c91b51cf711be23aca2202450f2e5955b0f6d7b6ad06252b18b8218611efc","target":"record","created_at":"2026-07-05T09:53:16Z","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":"4441d6a73870d334847025d4cb2fbb2d51295bd241faf9624b34cbf43587e111","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-12-22T13:39:37Z","title_canon_sha256":"31257a83f0a82a22a7a69c5e5dfc9593fffedf68080a7863c6bd62093ebef31b"},"schema_version":"1.0","source":{"id":"2412.17017","kind":"arxiv","version":1}},"canonical_sha256":"fa6432a3deb88e311b7956da3e9ee4265d3f575482940a34ee42d1d4a10f3391","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fa6432a3deb88e311b7956da3e9ee4265d3f575482940a34ee42d1d4a10f3391","first_computed_at":"2026-07-05T09:53:16.623474Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:53:16.623474Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Gp2xLrzzSfP7XL5JX3sfSJTKTmkLkEbgmNEYHfkA/h4yD568TtCdUgVKcbUarg/LS/pvuzMdE+EXkKMQU7WiDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:53:16.623909Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.17017","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d0c91b51cf711be23aca2202450f2e5955b0f6d7b6ad06252b18b8218611efc","sha256:05fb753efdaf3d92ebcb3140f37766a450344630a96847fdd731abb80aa314bc"],"state_sha256":"0b091ad780f8e45c76e4dc29beba13f06c6fbb7ed56fdc7ef5770288bc931b98"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gzW/4+lqof8yx/sStabVfytDnTv3GIbsYai1d7WB7b6iZ6NXDDYQOryeapVCOIGG9dF/mVR8LnqYfDRA4gCRBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T20:18:55.135798Z","bundle_sha256":"9cdd0924acb7c99c712a33717e54d5701dba8009f3c37c8392d136b5cf3f7a66"}}