{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:5QVIWS4LZTZ47H7RKD6O23MXAT","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":"4869370ae02ce58876009742601f3393e17ceca1152c70a4eb320815238402cb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-09T22:46:59Z","title_canon_sha256":"2fb36d6c161be5477e5a6cf599c008104a4bd2b79ad9ad96a089ac52cd43eee2"},"schema_version":"1.0","source":{"id":"1401.2197","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.2197","created_at":"2026-05-18T00:56:53Z"},{"alias_kind":"arxiv_version","alias_value":"1401.2197v1","created_at":"2026-05-18T00:56:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.2197","created_at":"2026-05-18T00:56:53Z"},{"alias_kind":"pith_short_12","alias_value":"5QVIWS4LZTZ4","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"5QVIWS4LZTZ47H7R","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"5QVIWS4L","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:60f620ab0c4a5b7208671cbc24ad74e328a2e362e7cf965530e4651edc8c4c4d","target":"graph","created_at":"2026-05-18T00:56:53Z","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 work of Texier and Zumbrun in the semilinear non-re ection symmetric case, we study O(2) transverse Hopf bifurcation, or \\cellular instability,\" of viscous shock waves in a channel, for a class of quasilinear hyperbolic{parabolic systems including the equations of thermoviscoelasticity. The main difficulties are to (i) obtain Fr'echet differentiability of the time-T solution operator by appropriate hyperbolic{parabolic energy estimates, and (ii) handle O(2) symmetry in the absence of either center manifold reduction (due to lack of spectral gap) or (due to nonstandard quasilinear hyp","authors_text":"Alin Pogan, Jinghua Yao, Kevin Zumbrun","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-09T22:46:59Z","title":"O(2) Hopf bifurcation of viscous shock waves in a channel"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.2197","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":"sha256:1089f70ad6ef4a6f2591830c15522e14d8d86d6faf6e405646951833f514b49c","target":"record","created_at":"2026-05-18T00:56:53Z","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":"4869370ae02ce58876009742601f3393e17ceca1152c70a4eb320815238402cb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-09T22:46:59Z","title_canon_sha256":"2fb36d6c161be5477e5a6cf599c008104a4bd2b79ad9ad96a089ac52cd43eee2"},"schema_version":"1.0","source":{"id":"1401.2197","kind":"arxiv","version":1}},"canonical_sha256":"ec2a8b4b8bccf3cf9ff150fced6d9704d1daf6f8792d0b7fb9fbc31a84abfcee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ec2a8b4b8bccf3cf9ff150fced6d9704d1daf6f8792d0b7fb9fbc31a84abfcee","first_computed_at":"2026-05-18T00:56:53.222859Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:56:53.222859Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GfAfMT2hnfxUe+FxcfFsfQdq46F7ygqgbDFA26sjOxBpuc0rzxv50+LvwW8zyH7Pz5TXB10kOZNOE+G0aKfJCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:56:53.223431Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.2197","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1089f70ad6ef4a6f2591830c15522e14d8d86d6faf6e405646951833f514b49c","sha256:60f620ab0c4a5b7208671cbc24ad74e328a2e362e7cf965530e4651edc8c4c4d"],"state_sha256":"54c71c5b246b80d024441024ee388bc074f72c2c9416b0167e3f0a3d0aef3918"}