{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:JGBSLQZCCMQRI7262YHUSPYMGJ","short_pith_number":"pith:JGBSLQZC","schema_version":"1.0","canonical_sha256":"498325c3221321147f5ed60f493f0c3256152cacc70ad61fd07be4fd94e468a3","source":{"kind":"arxiv","id":"1908.01694","version":2},"attestation_state":"computed","paper":{"title":"Structural stability of the transonic shock problem in a divergent three dimensional axisymmetric perturbed nozzle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chunjing Xie, Shangkun Weng, Zhouping Xin","submitted_at":"2019-08-05T15:38:59Z","abstract_excerpt":"In this paper, we prove the structural stability of the transonic shocks for three dimensional axisymmetric Euler system with swirl velocity under the perturbations for the incoming supersonic flow, the nozzle boundary, and the exit pressure. Compared with the known results on the stability of transonic shocks, one of the major difficulties for the axisymmetric flows with swirls is that corner singularities near the intersection point of the shock surface and nozzle boundary and the artificial singularity near the axis appear simultaneously. One of the key points in the analysis for this paper"},"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":"1908.01694","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-05T15:38:59Z","cross_cats_sorted":[],"title_canon_sha256":"567aedc6ff4cf4354a0e5bd0598aa719447f1e1f52f92f3680f14fa592e562f7","abstract_canon_sha256":"79563b72c0a4d79c820343d7f3d9c1024335d5e8f252b194271245110a17f65d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:40:25.136961Z","signature_b64":"jXIXP3GtIJo7imeGPhWWYBjP8NdGDS8Ik+6YkQpUcQLUzkqZ4rpKkP+EtYWwvmiG/eXdlQBoNLVCp79Iw2MzBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"498325c3221321147f5ed60f493f0c3256152cacc70ad61fd07be4fd94e468a3","last_reissued_at":"2026-07-05T00:40:25.136499Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:40:25.136499Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Structural stability of the transonic shock problem in a divergent three dimensional axisymmetric perturbed nozzle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chunjing Xie, Shangkun Weng, Zhouping Xin","submitted_at":"2019-08-05T15:38:59Z","abstract_excerpt":"In this paper, we prove the structural stability of the transonic shocks for three dimensional axisymmetric Euler system with swirl velocity under the perturbations for the incoming supersonic flow, the nozzle boundary, and the exit pressure. Compared with the known results on the stability of transonic shocks, one of the major difficulties for the axisymmetric flows with swirls is that corner singularities near the intersection point of the shock surface and nozzle boundary and the artificial singularity near the axis appear simultaneously. One of the key points in the analysis for this paper"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.01694","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.01694/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1908.01694","created_at":"2026-07-05T00:40:25.136564+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.01694v2","created_at":"2026-07-05T00:40:25.136564+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.01694","created_at":"2026-07-05T00:40:25.136564+00:00"},{"alias_kind":"pith_short_12","alias_value":"JGBSLQZCCMQR","created_at":"2026-07-05T00:40:25.136564+00:00"},{"alias_kind":"pith_short_16","alias_value":"JGBSLQZCCMQRI726","created_at":"2026-07-05T00:40:25.136564+00:00"},{"alias_kind":"pith_short_8","alias_value":"JGBSLQZC","created_at":"2026-07-05T00:40:25.136564+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/JGBSLQZCCMQRI7262YHUSPYMGJ","json":"https://pith.science/pith/JGBSLQZCCMQRI7262YHUSPYMGJ.json","graph_json":"https://pith.science/api/pith-number/JGBSLQZCCMQRI7262YHUSPYMGJ/graph.json","events_json":"https://pith.science/api/pith-number/JGBSLQZCCMQRI7262YHUSPYMGJ/events.json","paper":"https://pith.science/paper/JGBSLQZC"},"agent_actions":{"view_html":"https://pith.science/pith/JGBSLQZCCMQRI7262YHUSPYMGJ","download_json":"https://pith.science/pith/JGBSLQZCCMQRI7262YHUSPYMGJ.json","view_paper":"https://pith.science/paper/JGBSLQZC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.01694&json=true","fetch_graph":"https://pith.science/api/pith-number/JGBSLQZCCMQRI7262YHUSPYMGJ/graph.json","fetch_events":"https://pith.science/api/pith-number/JGBSLQZCCMQRI7262YHUSPYMGJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JGBSLQZCCMQRI7262YHUSPYMGJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JGBSLQZCCMQRI7262YHUSPYMGJ/action/storage_attestation","attest_author":"https://pith.science/pith/JGBSLQZCCMQRI7262YHUSPYMGJ/action/author_attestation","sign_citation":"https://pith.science/pith/JGBSLQZCCMQRI7262YHUSPYMGJ/action/citation_signature","submit_replication":"https://pith.science/pith/JGBSLQZCCMQRI7262YHUSPYMGJ/action/replication_record"}},"created_at":"2026-07-05T00:40:25.136564+00:00","updated_at":"2026-07-05T00:40:25.136564+00:00"}