{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:YYATWPFE2RXY25JVV3ZT5E62HN","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":"83bf570d7ea9fc50468763156f1d470c1e1c28be4e821e0241f05a38ba918524","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-08-25T12:30:28Z","title_canon_sha256":"807b0b88800baa43655655f21035bb23da606f903e77d30fb765d165e5e44475"},"schema_version":"1.0","source":{"id":"1508.06127","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.06127","created_at":"2026-05-18T01:34:46Z"},{"alias_kind":"arxiv_version","alias_value":"1508.06127v1","created_at":"2026-05-18T01:34:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.06127","created_at":"2026-05-18T01:34:46Z"},{"alias_kind":"pith_short_12","alias_value":"YYATWPFE2RXY","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"YYATWPFE2RXY25JV","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"YYATWPFE","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:1ea12fa36b559df5b6484919d7a2686aeecf3581f101939817089b30ad896a57","target":"graph","created_at":"2026-05-18T01:34:46Z","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":"We consider viscous compressible barotropic motions in a bounded domain $\\Omega \\subset \\mathbb{R}^3$ with the Dirichlet boundary conditions for velocity. We assume the existence of some special sufficiently regular solutions $v_s$ (velocity), $\\varrho_s$ (density) of the problem. By the special solutions we can choose spherically symmetric solutions. Let $v$, $\\varrho$ be a~solution to our problem. Then we are looking for differences $u=v-v_s$, $\\eta=\\varrho-\\varrho_s$. We prove existence of $u$, $\\eta$ such that $u,\\eta\\in L_\\infty(kT,(k+1)T;H^2(\\Omega))$, $u_t,\\eta_t\\in L_\\infty(kT,(k+1)T;H","authors_text":"H-O. Bae, Wojciech M. Zaj\\k{a}czkowski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-08-25T12:30:28Z","title":"Global regular motions for compressible barotropic viscous fluids. Stability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.06127","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:d619298f9c156e0fcee4743fd0ba3094d3c322ba4c619fa6fb61603396541f15","target":"record","created_at":"2026-05-18T01:34:46Z","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":"83bf570d7ea9fc50468763156f1d470c1e1c28be4e821e0241f05a38ba918524","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-08-25T12:30:28Z","title_canon_sha256":"807b0b88800baa43655655f21035bb23da606f903e77d30fb765d165e5e44475"},"schema_version":"1.0","source":{"id":"1508.06127","kind":"arxiv","version":1}},"canonical_sha256":"c6013b3ca4d46f8d7535aef33e93da3b69d6bf2bc9e828d294afd025ba2de0cc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c6013b3ca4d46f8d7535aef33e93da3b69d6bf2bc9e828d294afd025ba2de0cc","first_computed_at":"2026-05-18T01:34:46.742097Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:46.742097Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"H7kaS6tIVQ39y+ihts0CSRHUUDjzK48j1YD7AMuXayh9KpvnQU5l89F6BwfHSHL1O5s57+BDYzFGjZp9ZEMkDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:46.742725Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.06127","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d619298f9c156e0fcee4743fd0ba3094d3c322ba4c619fa6fb61603396541f15","sha256:1ea12fa36b559df5b6484919d7a2686aeecf3581f101939817089b30ad896a57"],"state_sha256":"a82dedfc31124707adcb142878abcc478f17e211e10f5aa605088409946bc3ae"}