{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:4GGPCTC7FR2GQT3SWTW3LZ4P22","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":"e05bd6a3e74d5ca08cf2053f4d19fc870f268658a6e245e7e080c987ae7653bb","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-15T16:43:01Z","title_canon_sha256":"7484ea033592a9875f7cb9275954db17bb0284af76d5624ba35441f6dcf69915"},"schema_version":"1.0","source":{"id":"1705.05323","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.05323","created_at":"2026-05-18T00:44:30Z"},{"alias_kind":"arxiv_version","alias_value":"1705.05323v1","created_at":"2026-05-18T00:44:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.05323","created_at":"2026-05-18T00:44:30Z"},{"alias_kind":"pith_short_12","alias_value":"4GGPCTC7FR2G","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"4GGPCTC7FR2GQT3S","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"4GGPCTC7","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:ae5a86f8d9cb6b3614ca0310f73442467f49ab267a33180b1bca7ac16a34f196","target":"graph","created_at":"2026-05-18T00:44:30Z","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":"This is a continuation and completion of the program (initiated in \\cite{GrN1,GrN2}) to derive pointwise estimates on the Green function and sharp bounds on the semigroup of linearized Navier-Stokes around a generic stationary boundary layer profile. This is done via a spectral analysis approach and a careful study of the Orr-Sommerfeld equations, or equivalently the Navier-Stokes resolvent operator $(\\lambda - L)^{-1}$. The earlier work (\\cite{GrN1,GrN2}) treats the Orr-Sommerfeld equations away from critical layers: this is the case when the phase velocity is away from the range of the backg","authors_text":"Emmanuel Grenier, Toan T. Nguyen","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-15T16:43:01Z","title":"Green function for linearized Navier-Stokes around a boundary layer profile: near critical layers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.05323","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":"sha256:72b3b21d8448bf8b66578997e629c7133c9fcc727384fb64787d59db1166e8e3","target":"record","created_at":"2026-05-18T00:44:30Z","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":"e05bd6a3e74d5ca08cf2053f4d19fc870f268658a6e245e7e080c987ae7653bb","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-15T16:43:01Z","title_canon_sha256":"7484ea033592a9875f7cb9275954db17bb0284af76d5624ba35441f6dcf69915"},"schema_version":"1.0","source":{"id":"1705.05323","kind":"arxiv","version":1}},"canonical_sha256":"e18cf14c5f2c74684f72b4edb5e78fd6854b25bab370816bf785adc5c927b6ba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e18cf14c5f2c74684f72b4edb5e78fd6854b25bab370816bf785adc5c927b6ba","first_computed_at":"2026-05-18T00:44:30.819973Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:30.819973Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YlVcjFFqpJQk43IgBUheKiBuB6UKBL90k22dMYnjERManeJN6Dv6zD7uUcFUCy9iN8ZJCW0HOcQU9UQV9KPUAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:30.820693Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.05323","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:72b3b21d8448bf8b66578997e629c7133c9fcc727384fb64787d59db1166e8e3","sha256:ae5a86f8d9cb6b3614ca0310f73442467f49ab267a33180b1bca7ac16a34f196"],"state_sha256":"30da0067223526842fc5179d811379534345613e181e28883a2247e08a2767d3"}