{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:BAVAGWP2UN52HCJG3GSJUHXCUH","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":"61fb858f729e831f979c155dac0731423a753e742e5bf32f4c02c26c26049e31","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.AP","submitted_at":"2012-03-29T14:18:27Z","title_canon_sha256":"8264b41cce17a41cb261c574846cf4870adfe1a00e76b933f8360671d1d3a61c"},"schema_version":"1.0","source":{"id":"1203.6529","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.6529","created_at":"2026-05-18T03:59:02Z"},{"alias_kind":"arxiv_version","alias_value":"1203.6529v1","created_at":"2026-05-18T03:59:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.6529","created_at":"2026-05-18T03:59:02Z"},{"alias_kind":"pith_short_12","alias_value":"BAVAGWP2UN52","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"BAVAGWP2UN52HCJG","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"BAVAGWP2","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:0e487948a3f83806794a432b6fa9fa06fd2aa24fdd31d22de161fce61d348da7","target":"graph","created_at":"2026-05-18T03:59:02Z","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":"This paper is concerned with the existence, uniqueness and time-asymptotic stability of time periodic solutions to the compressible Navier-Stokes-Korteweg system effected by a time periodic external force in $\\mathbb{R}^n$. Our analysis is based on a combination of the energy method and the time decay estimates of solutions to the linearized system.","authors_text":"Huijiang Zhao, Qinghua Xiao, Zhengzheng Chen","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.AP","submitted_at":"2012-03-29T14:18:27Z","title":"Time periodic solutions of compressible fluid models of Korteweg type"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.6529","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:bdc70c480f1a3db03242edb79762fb01e6ca1c7bd26dec8695ba5c87e3a4d25b","target":"record","created_at":"2026-05-18T03:59:02Z","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":"61fb858f729e831f979c155dac0731423a753e742e5bf32f4c02c26c26049e31","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.AP","submitted_at":"2012-03-29T14:18:27Z","title_canon_sha256":"8264b41cce17a41cb261c574846cf4870adfe1a00e76b933f8360671d1d3a61c"},"schema_version":"1.0","source":{"id":"1203.6529","kind":"arxiv","version":1}},"canonical_sha256":"082a0359faa37ba38926d9a49a1ee2a1f239edd8ea95c40775002cbb0f3fd460","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"082a0359faa37ba38926d9a49a1ee2a1f239edd8ea95c40775002cbb0f3fd460","first_computed_at":"2026-05-18T03:59:02.305481Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:59:02.305481Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xxlLIswiQDjL4rFT+4APR+CtEAsvE3JNqxqFgLiwW+jhQUx/aiQBPAJq00zMG4JV3L6Ye6RfZ106pXRdMwyuBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:59:02.306440Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.6529","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bdc70c480f1a3db03242edb79762fb01e6ca1c7bd26dec8695ba5c87e3a4d25b","sha256:0e487948a3f83806794a432b6fa9fa06fd2aa24fdd31d22de161fce61d348da7"],"state_sha256":"98b24fd9d7ba187be3d0cc7d019945bc9b5ae08aad0559157d6f764a82c4e528"}