{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:KTJWHTYL6SHF3CKL7RKUWWTYQC","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":"fc149d7918c3a233f6c4b7cc664d24223eafa493769777e5e04c02a42de29f6c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-07T07:17:08Z","title_canon_sha256":"733f39ef2f1b0db4e35d65db74455b342b3a06c8612867243f645a97f9e31dba"},"schema_version":"1.0","source":{"id":"1908.02463","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.02463","created_at":"2026-07-04T23:52:09Z"},{"alias_kind":"arxiv_version","alias_value":"1908.02463v1","created_at":"2026-07-04T23:52:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.02463","created_at":"2026-07-04T23:52:09Z"},{"alias_kind":"pith_short_12","alias_value":"KTJWHTYL6SHF","created_at":"2026-07-04T23:52:09Z"},{"alias_kind":"pith_short_16","alias_value":"KTJWHTYL6SHF3CKL","created_at":"2026-07-04T23:52:09Z"},{"alias_kind":"pith_short_8","alias_value":"KTJWHTYL","created_at":"2026-07-04T23:52:09Z"}],"graph_snapshots":[{"event_id":"sha256:6be606aaf280ea9ff99e0c1c5d39f846e40c2db3df4c94439fd35d48838dfafe","target":"graph","created_at":"2026-07-04T23:52:09Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.02463/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper concerns the existence of transonic shock solutions to the 2-D steady compressible Euler system in an almost flat finite nozzle ( in the sense that it is a generic small perturbation of a flat one ), under physical boundary conditions proposed by Courant-Friedrichs in \\cite{CourantFriedrichs1948}, in which the receiver pressure is prescribed at the exit of the nozzle. In the resulting free boundary problem, the location of the shock-front is one of the most desirable information one would like to determine. However, the location of the normal shock-front in a flat nozzle can be anyw","authors_text":"Beixiang Fang, Zhouping Xin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-07T07:17:08Z","title":"On Admissible Locations of Transonic Shock Fronts for Steady Euler Flows in an Almost Flat Finite Nozzle with Prescribed Receiver Pressure"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.02463","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":"sha256:4109c261c5d3d3aef569577a17277b8f21bcab6d0274dbe28361c09c32fee44d","target":"record","created_at":"2026-07-04T23:52:09Z","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":"fc149d7918c3a233f6c4b7cc664d24223eafa493769777e5e04c02a42de29f6c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-07T07:17:08Z","title_canon_sha256":"733f39ef2f1b0db4e35d65db74455b342b3a06c8612867243f645a97f9e31dba"},"schema_version":"1.0","source":{"id":"1908.02463","kind":"arxiv","version":1}},"canonical_sha256":"54d363cf0bf48e5d894bfc554b5a7880b5abef1f4e97b083b61840c2b46b5b3c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"54d363cf0bf48e5d894bfc554b5a7880b5abef1f4e97b083b61840c2b46b5b3c","first_computed_at":"2026-07-04T23:52:09.181779Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:52:09.181779Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2HzncyXIlDHi3nPXeD7WtG0DJMPLXg8QW7TNx8l/sFQR8Gn1Waet96NNPP/O1bAKKp0PuimEpEWZ2bDVsxjMAA==","signature_status":"signed_v1","signed_at":"2026-07-04T23:52:09.182155Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.02463","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4109c261c5d3d3aef569577a17277b8f21bcab6d0274dbe28361c09c32fee44d","sha256:6be606aaf280ea9ff99e0c1c5d39f846e40c2db3df4c94439fd35d48838dfafe"],"state_sha256":"7cfaf07c735e3f2f0d478ac5f7bf3fd7a366976cb5e9a0a48804bca0740b3f73"}