{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:BVC6X36CMZBERPLKMJL65MK4GN","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":"c2995e00faacd9ffb44493851f715931a4616c3503be2cca68dc7f0ea168147b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-11-19T16:41:20Z","title_canon_sha256":"9d21e5dc36f71e591901261217f7d9cbd330ac470806876c5516effdbadbf953"},"schema_version":"1.0","source":{"id":"1211.4489","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.4489","created_at":"2026-05-18T03:40:26Z"},{"alias_kind":"arxiv_version","alias_value":"1211.4489v1","created_at":"2026-05-18T03:40:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.4489","created_at":"2026-05-18T03:40:26Z"},{"alias_kind":"pith_short_12","alias_value":"BVC6X36CMZBE","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"BVC6X36CMZBERPLK","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"BVC6X36C","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:12a7642ce1db0be3ed3908201d560868b1598dc4428fc280674e4bf6ffb7dfa8","target":"graph","created_at":"2026-05-18T03:40:26Z","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 by a combination of analytical and numerical techniques some basic questions regarding the relations between inviscid and viscous stability and existence of a convex entropy. Specifically, for a system possessing a convex entropy, in particular for the equations of gas dynamics with a convex equation of state, we ask: (i) can inviscid instability occur? (ii) can there occur viscous instability not detected by inviscid theory? (iii) can there occur the ---necessarily viscous--- effect of Hopf bifurcation, or \"galloping instability\"? and, perhaps most important from a practical point","authors_text":"Blake Barker, Heinrich Freist\\\"uhler, Kevin Zumbrun","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-11-19T16:41:20Z","title":"Convex entropy, Hopf bifurcation, and viscous and inviscid shock stability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.4489","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":"sha256:2967142ee10d6c1743873590158dd742187ff4627b7051778ee1e2ba11ef4b11","target":"record","created_at":"2026-05-18T03:40:26Z","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":"c2995e00faacd9ffb44493851f715931a4616c3503be2cca68dc7f0ea168147b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-11-19T16:41:20Z","title_canon_sha256":"9d21e5dc36f71e591901261217f7d9cbd330ac470806876c5516effdbadbf953"},"schema_version":"1.0","source":{"id":"1211.4489","kind":"arxiv","version":1}},"canonical_sha256":"0d45ebefc2664248bd6a6257eeb15c33561d6998d16fb85f1ccb2136b5ae9a05","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0d45ebefc2664248bd6a6257eeb15c33561d6998d16fb85f1ccb2136b5ae9a05","first_computed_at":"2026-05-18T03:40:26.730849Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:40:26.730849Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aqlEZUHt6t7rTlJCeF56ARfSQCp7ZznGIkWvd2Qk+zxb71Ljd8B3RxnARzuERsIdp9LvqXuTMlSoBBrStbsoAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:40:26.731258Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.4489","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2967142ee10d6c1743873590158dd742187ff4627b7051778ee1e2ba11ef4b11","sha256:12a7642ce1db0be3ed3908201d560868b1598dc4428fc280674e4bf6ffb7dfa8"],"state_sha256":"fb2947ca75da2400a94fa57ab1bd5625a5ad86b8d0b5ad97da0fb3484a866c79"}