{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:VVNWWTVXELIXX3WBKZSYM2U4P5","short_pith_number":"pith:VVNWWTVX","canonical_record":{"source":{"id":"2205.01375","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-05-03T08:48:10Z","cross_cats_sorted":[],"title_canon_sha256":"f2a15871645c099d57b99feb0f3c486800b3045e93d25a6a811a922f97ad1c2d","abstract_canon_sha256":"a3fd43e8c6a72d5d554f96df11044a399438d3d6537ee50ebd6dae4da1742153"},"schema_version":"1.0"},"canonical_sha256":"ad5b6b4eb722d17beec15665866a9c7f55550282e612e83b69e2378d81614684","source":{"kind":"arxiv","id":"2205.01375","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2205.01375","created_at":"2026-07-05T04:20:04Z"},{"alias_kind":"arxiv_version","alias_value":"2205.01375v1","created_at":"2026-07-05T04:20:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2205.01375","created_at":"2026-07-05T04:20:04Z"},{"alias_kind":"pith_short_12","alias_value":"VVNWWTVXELIX","created_at":"2026-07-05T04:20:04Z"},{"alias_kind":"pith_short_16","alias_value":"VVNWWTVXELIXX3WB","created_at":"2026-07-05T04:20:04Z"},{"alias_kind":"pith_short_8","alias_value":"VVNWWTVX","created_at":"2026-07-05T04:20:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:VVNWWTVXELIXX3WBKZSYM2U4P5","target":"record","payload":{"canonical_record":{"source":{"id":"2205.01375","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-05-03T08:48:10Z","cross_cats_sorted":[],"title_canon_sha256":"f2a15871645c099d57b99feb0f3c486800b3045e93d25a6a811a922f97ad1c2d","abstract_canon_sha256":"a3fd43e8c6a72d5d554f96df11044a399438d3d6537ee50ebd6dae4da1742153"},"schema_version":"1.0"},"canonical_sha256":"ad5b6b4eb722d17beec15665866a9c7f55550282e612e83b69e2378d81614684","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:20:04.007527Z","signature_b64":"pCQjcDs9TYK/SttPp1LEvLNW9jKVuU+lk7xw+MrOSwjZQzj/6P+SRE+7qmuIzWXlXtk6xznQ44RmyHVqS5BVBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ad5b6b4eb722d17beec15665866a9c7f55550282e612e83b69e2378d81614684","last_reissued_at":"2026-07-05T04:20:04.007121Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:20:04.007121Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2205.01375","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":"2026-07-05T04:20:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Re0sZaqAlIEUb3m5B4+PZvpEN/ye3+OzaGdNdnBUEZy9kWn6UEmAF3rw4Pl1YCrTNjrOK1MbgCuQfHT6KTkVDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T22:30:36.362459Z"},"content_sha256":"8ab08c8f4388e1cd05ba69b35d8d6d583492719c381f0e92f3c6f33aee57cf0e","schema_version":"1.0","event_id":"sha256:8ab08c8f4388e1cd05ba69b35d8d6d583492719c381f0e92f3c6f33aee57cf0e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:VVNWWTVXELIXX3WBKZSYM2U4P5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Large time behavior of solutions to a diffusion approximation radiation hydrodynamics model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Feng Xie, Wenjun Wang, Xiongfeng Yang","submitted_at":"2022-05-03T08:48:10Z","abstract_excerpt":"This paper concerns with the large time behavior of solutions to a diffusion approximation radiation hydrodynamics model when the initial data is a small perturbation around an equilibrium state. The global-in-time well-posedness of solutions is achieved in Sobolev spaces depending on the Littlewood-Paley decomposition technique together with certain elaborate energy estimates in frequency space. Moreover, the optimal decay rate of the solution is also yielded provided the initial data also satisfy an additional $L^1$ condition. Meanwhile, the similar results of the diffusion approximation sys"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.01375","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/2205.01375/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":"2026-07-05T04:20:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UtP/dL1Z4cOH4gsWlGtthbrzRZ8DsD67mYFCdTpuQz5cGzamBHW9iybq/Qi6F1tJQTJpOVOLoNHM4sLcYRk+AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T22:30:36.362952Z"},"content_sha256":"89cca306e83ade97655e856302868d169fc10c25d3c61a2d442f4a87745b99c5","schema_version":"1.0","event_id":"sha256:89cca306e83ade97655e856302868d169fc10c25d3c61a2d442f4a87745b99c5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VVNWWTVXELIXX3WBKZSYM2U4P5/bundle.json","state_url":"https://pith.science/pith/VVNWWTVXELIXX3WBKZSYM2U4P5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VVNWWTVXELIXX3WBKZSYM2U4P5/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":"2026-08-20T22:30:36Z","links":{"resolver":"https://pith.science/pith/VVNWWTVXELIXX3WBKZSYM2U4P5","bundle":"https://pith.science/pith/VVNWWTVXELIXX3WBKZSYM2U4P5/bundle.json","state":"https://pith.science/pith/VVNWWTVXELIXX3WBKZSYM2U4P5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VVNWWTVXELIXX3WBKZSYM2U4P5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:VVNWWTVXELIXX3WBKZSYM2U4P5","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":"a3fd43e8c6a72d5d554f96df11044a399438d3d6537ee50ebd6dae4da1742153","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-05-03T08:48:10Z","title_canon_sha256":"f2a15871645c099d57b99feb0f3c486800b3045e93d25a6a811a922f97ad1c2d"},"schema_version":"1.0","source":{"id":"2205.01375","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2205.01375","created_at":"2026-07-05T04:20:04Z"},{"alias_kind":"arxiv_version","alias_value":"2205.01375v1","created_at":"2026-07-05T04:20:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2205.01375","created_at":"2026-07-05T04:20:04Z"},{"alias_kind":"pith_short_12","alias_value":"VVNWWTVXELIX","created_at":"2026-07-05T04:20:04Z"},{"alias_kind":"pith_short_16","alias_value":"VVNWWTVXELIXX3WB","created_at":"2026-07-05T04:20:04Z"},{"alias_kind":"pith_short_8","alias_value":"VVNWWTVX","created_at":"2026-07-05T04:20:04Z"}],"graph_snapshots":[{"event_id":"sha256:89cca306e83ade97655e856302868d169fc10c25d3c61a2d442f4a87745b99c5","target":"graph","created_at":"2026-07-05T04:20:04Z","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/2205.01375/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper concerns with the large time behavior of solutions to a diffusion approximation radiation hydrodynamics model when the initial data is a small perturbation around an equilibrium state. The global-in-time well-posedness of solutions is achieved in Sobolev spaces depending on the Littlewood-Paley decomposition technique together with certain elaborate energy estimates in frequency space. Moreover, the optimal decay rate of the solution is also yielded provided the initial data also satisfy an additional $L^1$ condition. Meanwhile, the similar results of the diffusion approximation sys","authors_text":"Feng Xie, Wenjun Wang, Xiongfeng Yang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-05-03T08:48:10Z","title":"Large time behavior of solutions to a diffusion approximation radiation hydrodynamics model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.01375","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":"sha256:8ab08c8f4388e1cd05ba69b35d8d6d583492719c381f0e92f3c6f33aee57cf0e","target":"record","created_at":"2026-07-05T04:20:04Z","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":"a3fd43e8c6a72d5d554f96df11044a399438d3d6537ee50ebd6dae4da1742153","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-05-03T08:48:10Z","title_canon_sha256":"f2a15871645c099d57b99feb0f3c486800b3045e93d25a6a811a922f97ad1c2d"},"schema_version":"1.0","source":{"id":"2205.01375","kind":"arxiv","version":1}},"canonical_sha256":"ad5b6b4eb722d17beec15665866a9c7f55550282e612e83b69e2378d81614684","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ad5b6b4eb722d17beec15665866a9c7f55550282e612e83b69e2378d81614684","first_computed_at":"2026-07-05T04:20:04.007121Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:20:04.007121Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pCQjcDs9TYK/SttPp1LEvLNW9jKVuU+lk7xw+MrOSwjZQzj/6P+SRE+7qmuIzWXlXtk6xznQ44RmyHVqS5BVBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:20:04.007527Z","signed_message":"canonical_sha256_bytes"},"source_id":"2205.01375","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8ab08c8f4388e1cd05ba69b35d8d6d583492719c381f0e92f3c6f33aee57cf0e","sha256:89cca306e83ade97655e856302868d169fc10c25d3c61a2d442f4a87745b99c5"],"state_sha256":"3992e1dabf85ccb6fc9d895cf1f852f963e13882978667c6eb02239a4715aa61"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YHwMdx90N6v70/S+Q0nRIlR2/VSHAtYwTGWbPDhABNnTsPZcJSpQs3BIGpdWmkrzeXS5roI+cLCDwqO9S5scBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-20T22:30:36.366644Z","bundle_sha256":"0b67c10dc30d206de89d804d52906397edcec6373cc4a18dae4624e2281fb540"}}