{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:YKCJKSKA2FJB2JO5YKVCZ7KTVZ","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":"ea111bc0b417d726f018ba219857533a54e2d8f810186f6d7376e641f85354e8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-02-12T16:29:13Z","title_canon_sha256":"9f6a71966a78b9e499bc91becae45b50bb931a3d07abae7f7ad759baa23f120e"},"schema_version":"1.0","source":{"id":"0902.2153","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0902.2153","created_at":"2026-05-18T02:14:48Z"},{"alias_kind":"arxiv_version","alias_value":"0902.2153v1","created_at":"2026-05-18T02:14:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.2153","created_at":"2026-05-18T02:14:48Z"},{"alias_kind":"pith_short_12","alias_value":"YKCJKSKA2FJB","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"YKCJKSKA2FJB2JO5","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"YKCJKSKA","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:4dc7a7dbcba5c76ca6bb8773ba1937cd797648bdee2545ba2f87d8107a5414ae","target":"graph","created_at":"2026-05-18T02:14:48Z","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":"Extending our previous work in the strictly parabolic case, we show that a linearly unstable Lax-type viscous shock solution of a general quasilinear hyperbolic--parabolic system of conservation laws possesses a translation-invariant center stable manifold within which it is nonlinearly orbitally stable with respect to small $L^1\\cap H^3$ perturbations, converging time-asymptotically to a translate of the unperturbed wave. That is, for a shock with $p$ unstable eigenvalues, we establish conditional stability on a codimension-$p$ manifold of initial data, with sharp rates of decay in all $L^p$.","authors_text":"Kevin Zumbrun","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-02-12T16:29:13Z","title":"Conditional stability of unstable viscous shock waves in compressible gas dynamics and MHD"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.2153","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:a4ddf596fb874a06fc1c1c49e84c96580bf927303c93d34a05ff8e163f205168","target":"record","created_at":"2026-05-18T02:14:48Z","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":"ea111bc0b417d726f018ba219857533a54e2d8f810186f6d7376e641f85354e8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-02-12T16:29:13Z","title_canon_sha256":"9f6a71966a78b9e499bc91becae45b50bb931a3d07abae7f7ad759baa23f120e"},"schema_version":"1.0","source":{"id":"0902.2153","kind":"arxiv","version":1}},"canonical_sha256":"c284954940d1521d25ddc2aa2cfd53ae501e59c10da8d4baa3c8a4765c96191b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c284954940d1521d25ddc2aa2cfd53ae501e59c10da8d4baa3c8a4765c96191b","first_computed_at":"2026-05-18T02:14:48.125102Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:14:48.125102Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FhbXLZMDqv3I5FvI5zhOQLwN/aAqrtXOm1FWTHHEOPbpmq4kxdkM/MDMEEkvP3bhxFj2VijaczDiBpNm8uZlCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:14:48.125675Z","signed_message":"canonical_sha256_bytes"},"source_id":"0902.2153","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a4ddf596fb874a06fc1c1c49e84c96580bf927303c93d34a05ff8e163f205168","sha256:4dc7a7dbcba5c76ca6bb8773ba1937cd797648bdee2545ba2f87d8107a5414ae"],"state_sha256":"3b31bd0c4dbb3b9b56d152f7d7b028aa5504d2973096fa581177a814b6fd7c2e"}