{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:5QVIWS4LZTZ47H7RKD6O23MXAT","short_pith_number":"pith:5QVIWS4L","schema_version":"1.0","canonical_sha256":"ec2a8b4b8bccf3cf9ff150fced6d9704d1daf6f8792d0b7fb9fbc31a84abfcee","source":{"kind":"arxiv","id":"1401.2197","version":1},"attestation_state":"computed","paper":{"title":"O(2) Hopf bifurcation of viscous shock waves in a channel","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alin Pogan, Jinghua Yao, Kevin Zumbrun","submitted_at":"2014-01-09T22:46:59Z","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1401.2197","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-09T22:46:59Z","cross_cats_sorted":[],"title_canon_sha256":"2fb36d6c161be5477e5a6cf599c008104a4bd2b79ad9ad96a089ac52cd43eee2","abstract_canon_sha256":"4869370ae02ce58876009742601f3393e17ceca1152c70a4eb320815238402cb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:53.223431Z","signature_b64":"GfAfMT2hnfxUe+FxcfFsfQdq46F7ygqgbDFA26sjOxBpuc0rzxv50+LvwW8zyH7Pz5TXB10kOZNOE+G0aKfJCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ec2a8b4b8bccf3cf9ff150fced6d9704d1daf6f8792d0b7fb9fbc31a84abfcee","last_reissued_at":"2026-05-18T00:56:53.222859Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:53.222859Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"O(2) Hopf bifurcation of viscous shock waves in a channel","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alin Pogan, Jinghua Yao, Kevin Zumbrun","submitted_at":"2014-01-09T22:46:59Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.2197","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1401.2197","created_at":"2026-05-18T00:56:53.222941+00:00"},{"alias_kind":"arxiv_version","alias_value":"1401.2197v1","created_at":"2026-05-18T00:56:53.222941+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.2197","created_at":"2026-05-18T00:56:53.222941+00:00"},{"alias_kind":"pith_short_12","alias_value":"5QVIWS4LZTZ4","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_16","alias_value":"5QVIWS4LZTZ47H7R","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_8","alias_value":"5QVIWS4L","created_at":"2026-05-18T12:28:14.216126+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/5QVIWS4LZTZ47H7RKD6O23MXAT","json":"https://pith.science/pith/5QVIWS4LZTZ47H7RKD6O23MXAT.json","graph_json":"https://pith.science/api/pith-number/5QVIWS4LZTZ47H7RKD6O23MXAT/graph.json","events_json":"https://pith.science/api/pith-number/5QVIWS4LZTZ47H7RKD6O23MXAT/events.json","paper":"https://pith.science/paper/5QVIWS4L"},"agent_actions":{"view_html":"https://pith.science/pith/5QVIWS4LZTZ47H7RKD6O23MXAT","download_json":"https://pith.science/pith/5QVIWS4LZTZ47H7RKD6O23MXAT.json","view_paper":"https://pith.science/paper/5QVIWS4L","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1401.2197&json=true","fetch_graph":"https://pith.science/api/pith-number/5QVIWS4LZTZ47H7RKD6O23MXAT/graph.json","fetch_events":"https://pith.science/api/pith-number/5QVIWS4LZTZ47H7RKD6O23MXAT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5QVIWS4LZTZ47H7RKD6O23MXAT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5QVIWS4LZTZ47H7RKD6O23MXAT/action/storage_attestation","attest_author":"https://pith.science/pith/5QVIWS4LZTZ47H7RKD6O23MXAT/action/author_attestation","sign_citation":"https://pith.science/pith/5QVIWS4LZTZ47H7RKD6O23MXAT/action/citation_signature","submit_replication":"https://pith.science/pith/5QVIWS4LZTZ47H7RKD6O23MXAT/action/replication_record"}},"created_at":"2026-05-18T00:56:53.222941+00:00","updated_at":"2026-05-18T00:56:53.222941+00:00"}