{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:J4ZI6BJRGNCM2IJXTKEVHZZSWM","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":"f9b11b13b5bd09c89d559105dfb611bc5eae6f3ca0d9ef54d39b6addc0c38640","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-02-12T13:43:44Z","title_canon_sha256":"9d60878c55570728fe708cd6559bac4ec810d19742cf005697378b8b54cd50f1"},"schema_version":"1.0","source":{"id":"1802.04039","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.04039","created_at":"2026-05-18T00:23:49Z"},{"alias_kind":"arxiv_version","alias_value":"1802.04039v1","created_at":"2026-05-18T00:23:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.04039","created_at":"2026-05-18T00:23:49Z"},{"alias_kind":"pith_short_12","alias_value":"J4ZI6BJRGNCM","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"J4ZI6BJRGNCM2IJX","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"J4ZI6BJR","created_at":"2026-05-18T12:32:31Z"}],"graph_snapshots":[{"event_id":"sha256:bfb05d3428e6f37a9f77baa42db822b1d1a6cde79bd181d2ec49556b7aab7996","target":"graph","created_at":"2026-05-18T00:23:49Z","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":"In this paper, we prove that separation occurs for the stationary Prandtl equation, in the case of adverse pressure gradient, for a large class of boundary data at $x=0$.We justify the Goldstein singularity: more precisely, we prove that under suitable assumptions on the boundary data at $x=0$, there exists $x^*>0$ such that $\\p\\_y u\\_{y=0}(x)\\sim C \\sqrt{x^* -x}$ as  $x\\to x^*$ for some positive constant $C$, where $u$ is the solution of the stationary Prandtl equation in the domain $\\{0<x<x^*,\\ y>0\\}$. Our proof relies on three main ingredients: the computation of a \"stable\" approximate solu","authors_text":"Anne-Laure Dalibard (LJLL), Nader Masmoudi (CIMS)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-02-12T13:43:44Z","title":"Separation for the stationary Prandtl equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.04039","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:af24fc5749831f405fb88c36ca454d386bbbd1fc73ec888add30c2ebb37134ea","target":"record","created_at":"2026-05-18T00:23:49Z","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":"f9b11b13b5bd09c89d559105dfb611bc5eae6f3ca0d9ef54d39b6addc0c38640","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-02-12T13:43:44Z","title_canon_sha256":"9d60878c55570728fe708cd6559bac4ec810d19742cf005697378b8b54cd50f1"},"schema_version":"1.0","source":{"id":"1802.04039","kind":"arxiv","version":1}},"canonical_sha256":"4f328f05313344cd21379a8953e732b33fce56743d5adf6ab1c67860d69e4006","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f328f05313344cd21379a8953e732b33fce56743d5adf6ab1c67860d69e4006","first_computed_at":"2026-05-18T00:23:49.613449Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:49.613449Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KqiL/uccoUMvbFid810EEW2qa9IwLoySNKYlZlAD/EWe+wFGY5SfNDFvlhkbdnrU3CdodWDI90YI5omRDjSSAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:49.614060Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.04039","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:af24fc5749831f405fb88c36ca454d386bbbd1fc73ec888add30c2ebb37134ea","sha256:bfb05d3428e6f37a9f77baa42db822b1d1a6cde79bd181d2ec49556b7aab7996"],"state_sha256":"8989ce29592399fb7efb10c46cd76f0d722ead72144925d119597e2b7d818d38"}