{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:DFSYCDTWVXKDASGEBF5FMUWZ5W","short_pith_number":"pith:DFSYCDTW","canonical_record":{"source":{"id":"2608.00465","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-08-01T06:12:26Z","cross_cats_sorted":[],"title_canon_sha256":"9e04e0847a4f4d57211eb8fb9f9bcbbf09e624064c420c26b3e7c86ad0a92ae2","abstract_canon_sha256":"fcb4dfa6cf22c1e8ee6c12e3635ccc81eb0e17640c42fbbecd05692f81c40256"},"schema_version":"1.0"},"canonical_sha256":"1965810e76add43048c4097a5652d9edb22abd870cdb961a216dcebc2b4bd45d","source":{"kind":"arxiv","id":"2608.00465","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.00465","created_at":"2026-08-04T00:36:44Z"},{"alias_kind":"arxiv_version","alias_value":"2608.00465v1","created_at":"2026-08-04T00:36:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.00465","created_at":"2026-08-04T00:36:44Z"},{"alias_kind":"pith_short_12","alias_value":"DFSYCDTWVXKD","created_at":"2026-08-04T00:36:44Z"},{"alias_kind":"pith_short_16","alias_value":"DFSYCDTWVXKDASGE","created_at":"2026-08-04T00:36:44Z"},{"alias_kind":"pith_short_8","alias_value":"DFSYCDTW","created_at":"2026-08-04T00:36:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:DFSYCDTWVXKDASGEBF5FMUWZ5W","target":"record","payload":{"canonical_record":{"source":{"id":"2608.00465","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-08-01T06:12:26Z","cross_cats_sorted":[],"title_canon_sha256":"9e04e0847a4f4d57211eb8fb9f9bcbbf09e624064c420c26b3e7c86ad0a92ae2","abstract_canon_sha256":"fcb4dfa6cf22c1e8ee6c12e3635ccc81eb0e17640c42fbbecd05692f81c40256"},"schema_version":"1.0"},"canonical_sha256":"1965810e76add43048c4097a5652d9edb22abd870cdb961a216dcebc2b4bd45d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-04T00:36:44.184616Z","signature_b64":"prEG5i1IC4bZ0sp/RyTdUUhhgRwH3IX+f047GD9hTyfDQ6ZyRbZwcRedvXp6t5VBknMd2WbwOf0dcoD86OzZCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1965810e76add43048c4097a5652d9edb22abd870cdb961a216dcebc2b4bd45d","last_reissued_at":"2026-08-04T00:36:44.183164Z","signature_status":"signed_v1","first_computed_at":"2026-08-04T00:36:44.183164Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2608.00465","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":"2026-08-04T00:36:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sSuhYOFOL76FuLRr6bP0gfe1MRzp40VrY39gNFnNXoPq2aenrJAMYdPgliaRxZS3o37/EWVf2d8EWZ7ZzRJ/CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T09:09:53.288736Z"},"content_sha256":"72a847b473663bd590172c3e7e3140665886b1e7e7fbfb5b27fa19943d12ea3f","schema_version":"1.0","event_id":"sha256:72a847b473663bd590172c3e7e3140665886b1e7e7fbfb5b27fa19943d12ea3f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:DFSYCDTWVXKDASGEBF5FMUWZ5W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Compressible Navier--Stokes equations with a potential force: global well-posedness and optimal time-decay rates for arbitrarily large $L^2$ initial data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jinkai Ni, Luqi Wang, Zhipeng Zhang","submitted_at":"2026-08-01T06:12:26Z","abstract_excerpt":"We study the Cauchy problem for the three-dimensional barotropic compressible Navier--Stokes equations with a time-independent potential force near a spatially nonconstant stationary state. The potential is controlled in unweighted homogeneous Besov spaces; in particular, no polynomial spatial-weight condition involving $(1+|x|)^j\\nabla^j\\phi$ is imposed. For initial data relative to the stationary state that are sufficiently small in $\\dot H^{\\frac12-\\delta}\\cap\\dot H^3$, we establish the existence and uniqueness of a global strong solution in $H^3$, while allowing the initial $L^2$ norm to b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.00465","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/2608.00465/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":"2026-08-04T00:36:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VpnAKeNj6tTF7IMWSfJl0v0xyUy9BEtrJzgyAWberCJkkDJ8/Cj7/Ktmwp6jGXe5g4TMBAQSzfIEjJ9OzSpkBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T09:09:53.289596Z"},"content_sha256":"45fa72aeadb6b395d2ee98361eb797efe037d89abe9017d28be932cb7a582516","schema_version":"1.0","event_id":"sha256:45fa72aeadb6b395d2ee98361eb797efe037d89abe9017d28be932cb7a582516"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DFSYCDTWVXKDASGEBF5FMUWZ5W/bundle.json","state_url":"https://pith.science/pith/DFSYCDTWVXKDASGEBF5FMUWZ5W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DFSYCDTWVXKDASGEBF5FMUWZ5W/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":"2026-08-04T09:09:53Z","links":{"resolver":"https://pith.science/pith/DFSYCDTWVXKDASGEBF5FMUWZ5W","bundle":"https://pith.science/pith/DFSYCDTWVXKDASGEBF5FMUWZ5W/bundle.json","state":"https://pith.science/pith/DFSYCDTWVXKDASGEBF5FMUWZ5W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DFSYCDTWVXKDASGEBF5FMUWZ5W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:DFSYCDTWVXKDASGEBF5FMUWZ5W","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":"fcb4dfa6cf22c1e8ee6c12e3635ccc81eb0e17640c42fbbecd05692f81c40256","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-08-01T06:12:26Z","title_canon_sha256":"9e04e0847a4f4d57211eb8fb9f9bcbbf09e624064c420c26b3e7c86ad0a92ae2"},"schema_version":"1.0","source":{"id":"2608.00465","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.00465","created_at":"2026-08-04T00:36:44Z"},{"alias_kind":"arxiv_version","alias_value":"2608.00465v1","created_at":"2026-08-04T00:36:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.00465","created_at":"2026-08-04T00:36:44Z"},{"alias_kind":"pith_short_12","alias_value":"DFSYCDTWVXKD","created_at":"2026-08-04T00:36:44Z"},{"alias_kind":"pith_short_16","alias_value":"DFSYCDTWVXKDASGE","created_at":"2026-08-04T00:36:44Z"},{"alias_kind":"pith_short_8","alias_value":"DFSYCDTW","created_at":"2026-08-04T00:36:44Z"}],"graph_snapshots":[{"event_id":"sha256:45fa72aeadb6b395d2ee98361eb797efe037d89abe9017d28be932cb7a582516","target":"graph","created_at":"2026-08-04T00:36:44Z","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/2608.00465/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the Cauchy problem for the three-dimensional barotropic compressible Navier--Stokes equations with a time-independent potential force near a spatially nonconstant stationary state. The potential is controlled in unweighted homogeneous Besov spaces; in particular, no polynomial spatial-weight condition involving $(1+|x|)^j\\nabla^j\\phi$ is imposed. For initial data relative to the stationary state that are sufficiently small in $\\dot H^{\\frac12-\\delta}\\cap\\dot H^3$, we establish the existence and uniqueness of a global strong solution in $H^3$, while allowing the initial $L^2$ norm to b","authors_text":"Jinkai Ni, Luqi Wang, Zhipeng Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-08-01T06:12:26Z","title":"Compressible Navier--Stokes equations with a potential force: global well-posedness and optimal time-decay rates for arbitrarily large $L^2$ initial data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.00465","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":"sha256:72a847b473663bd590172c3e7e3140665886b1e7e7fbfb5b27fa19943d12ea3f","target":"record","created_at":"2026-08-04T00:36:44Z","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":"fcb4dfa6cf22c1e8ee6c12e3635ccc81eb0e17640c42fbbecd05692f81c40256","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-08-01T06:12:26Z","title_canon_sha256":"9e04e0847a4f4d57211eb8fb9f9bcbbf09e624064c420c26b3e7c86ad0a92ae2"},"schema_version":"1.0","source":{"id":"2608.00465","kind":"arxiv","version":1}},"canonical_sha256":"1965810e76add43048c4097a5652d9edb22abd870cdb961a216dcebc2b4bd45d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1965810e76add43048c4097a5652d9edb22abd870cdb961a216dcebc2b4bd45d","first_computed_at":"2026-08-04T00:36:44.183164Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-04T00:36:44.183164Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"prEG5i1IC4bZ0sp/RyTdUUhhgRwH3IX+f047GD9hTyfDQ6ZyRbZwcRedvXp6t5VBknMd2WbwOf0dcoD86OzZCQ==","signature_status":"signed_v1","signed_at":"2026-08-04T00:36:44.184616Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.00465","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:72a847b473663bd590172c3e7e3140665886b1e7e7fbfb5b27fa19943d12ea3f","sha256:45fa72aeadb6b395d2ee98361eb797efe037d89abe9017d28be932cb7a582516"],"state_sha256":"84fa732a90f83a15c1c96ef924d642b9a2fe5b475401b7773e8dce723614d82a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fiWkLaoyIBQtQ/RKOu9yTnpvaAifN9pCIf7pEItUiFeYtlOM+0eLOInoSvDMBLxGOc5uxhQgXFVAD52ADk7DDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T09:09:53.295722Z","bundle_sha256":"cf00043038344fe6c5afb24e0d99114f4a3c61f2b72ef97bfaa2996e1bab9730"}}