{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:4GGPCTC7FR2GQT3SWTW3LZ4P22","short_pith_number":"pith:4GGPCTC7","schema_version":"1.0","canonical_sha256":"e18cf14c5f2c74684f72b4edb5e78fd6854b25bab370816bf785adc5c927b6ba","source":{"kind":"arxiv","id":"1705.05323","version":1},"attestation_state":"computed","paper":{"title":"Green function for linearized Navier-Stokes around a boundary layer profile: near critical layers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Emmanuel Grenier, Toan T. Nguyen","submitted_at":"2017-05-15T16:43:01Z","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"},"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":"1705.05323","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-15T16:43:01Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"7484ea033592a9875f7cb9275954db17bb0284af76d5624ba35441f6dcf69915","abstract_canon_sha256":"e05bd6a3e74d5ca08cf2053f4d19fc870f268658a6e245e7e080c987ae7653bb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:30.820693Z","signature_b64":"YlVcjFFqpJQk43IgBUheKiBuB6UKBL90k22dMYnjERManeJN6Dv6zD7uUcFUCy9iN8ZJCW0HOcQU9UQV9KPUAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e18cf14c5f2c74684f72b4edb5e78fd6854b25bab370816bf785adc5c927b6ba","last_reissued_at":"2026-05-18T00:44:30.819973Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:30.819973Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Green function for linearized Navier-Stokes around a boundary layer profile: near critical layers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Emmanuel Grenier, Toan T. Nguyen","submitted_at":"2017-05-15T16:43:01Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.05323","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":"1705.05323","created_at":"2026-05-18T00:44:30.820083+00:00"},{"alias_kind":"arxiv_version","alias_value":"1705.05323v1","created_at":"2026-05-18T00:44:30.820083+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.05323","created_at":"2026-05-18T00:44:30.820083+00:00"},{"alias_kind":"pith_short_12","alias_value":"4GGPCTC7FR2G","created_at":"2026-05-18T12:30:58.224056+00:00"},{"alias_kind":"pith_short_16","alias_value":"4GGPCTC7FR2GQT3S","created_at":"2026-05-18T12:30:58.224056+00:00"},{"alias_kind":"pith_short_8","alias_value":"4GGPCTC7","created_at":"2026-05-18T12:30:58.224056+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/4GGPCTC7FR2GQT3SWTW3LZ4P22","json":"https://pith.science/pith/4GGPCTC7FR2GQT3SWTW3LZ4P22.json","graph_json":"https://pith.science/api/pith-number/4GGPCTC7FR2GQT3SWTW3LZ4P22/graph.json","events_json":"https://pith.science/api/pith-number/4GGPCTC7FR2GQT3SWTW3LZ4P22/events.json","paper":"https://pith.science/paper/4GGPCTC7"},"agent_actions":{"view_html":"https://pith.science/pith/4GGPCTC7FR2GQT3SWTW3LZ4P22","download_json":"https://pith.science/pith/4GGPCTC7FR2GQT3SWTW3LZ4P22.json","view_paper":"https://pith.science/paper/4GGPCTC7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1705.05323&json=true","fetch_graph":"https://pith.science/api/pith-number/4GGPCTC7FR2GQT3SWTW3LZ4P22/graph.json","fetch_events":"https://pith.science/api/pith-number/4GGPCTC7FR2GQT3SWTW3LZ4P22/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4GGPCTC7FR2GQT3SWTW3LZ4P22/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4GGPCTC7FR2GQT3SWTW3LZ4P22/action/storage_attestation","attest_author":"https://pith.science/pith/4GGPCTC7FR2GQT3SWTW3LZ4P22/action/author_attestation","sign_citation":"https://pith.science/pith/4GGPCTC7FR2GQT3SWTW3LZ4P22/action/citation_signature","submit_replication":"https://pith.science/pith/4GGPCTC7FR2GQT3SWTW3LZ4P22/action/replication_record"}},"created_at":"2026-05-18T00:44:30.820083+00:00","updated_at":"2026-05-18T00:44:30.820083+00:00"}