{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:634FPMDRTYHR2G2P4HHAJ6QPTZ","short_pith_number":"pith:634FPMDR","schema_version":"1.0","canonical_sha256":"f6f857b0719e0f1d1b4fe1ce04fa0f9e487f20ff7947b41c2d5c6e6caeafed4c","source":{"kind":"arxiv","id":"2001.00324","version":2},"attestation_state":"computed","paper":{"title":"Verification of Prandtl boundary layer ansatz for the steady electrically conducting fluids with a moving physical boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Feng Xie, Shijin Ding, Zhilin Lin","submitted_at":"2020-01-02T04:41:46Z","abstract_excerpt":"In this paper, we are concerned with the validity of Prandtl boundary layer expansion for the solutions to two dimensional (2D) steady viscous incompressible magnetohydrodynamics (MHD) equations in a domain $\\{(X, Y)\\in[0, L]\\times\\mathbb{R}_+\\}$ with a moving flat boundary $\\{Y=0\\}$. As a direct consequence, even though there exist strong boundary layers, the inviscid type limit is still established for the solutions of 2D steady viscous incompressible MHD equations in Sobolev spaces provided that the following three assumptions hold: the hydrodynamics and magnetic Reynolds numbers take the s"},"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":"2001.00324","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-01-02T04:41:46Z","cross_cats_sorted":[],"title_canon_sha256":"0288a085d2877512a69750032229925767a3ee722180aa2677d0843951c1f588","abstract_canon_sha256":"506878cf3de083fffc211adb21efb062ef6b72f1bb6511abf577e7db569b4529"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:34:05.124759Z","signature_b64":"zONIlczC1CT5A26pjCRYz7/iNgjboN8q3NjR6Jvj8gRi7STCMYaHyuy/U//1VPrv7MoNsI3aopd4k0y8qxutDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f6f857b0719e0f1d1b4fe1ce04fa0f9e487f20ff7947b41c2d5c6e6caeafed4c","last_reissued_at":"2026-07-05T00:34:05.124329Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:34:05.124329Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Verification of Prandtl boundary layer ansatz for the steady electrically conducting fluids with a moving physical boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Feng Xie, Shijin Ding, Zhilin Lin","submitted_at":"2020-01-02T04:41:46Z","abstract_excerpt":"In this paper, we are concerned with the validity of Prandtl boundary layer expansion for the solutions to two dimensional (2D) steady viscous incompressible magnetohydrodynamics (MHD) equations in a domain $\\{(X, Y)\\in[0, L]\\times\\mathbb{R}_+\\}$ with a moving flat boundary $\\{Y=0\\}$. As a direct consequence, even though there exist strong boundary layers, the inviscid type limit is still established for the solutions of 2D steady viscous incompressible MHD equations in Sobolev spaces provided that the following three assumptions hold: the hydrodynamics and magnetic Reynolds numbers take the s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2001.00324","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/2001.00324/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":"2001.00324","created_at":"2026-07-05T00:34:05.124399+00:00"},{"alias_kind":"arxiv_version","alias_value":"2001.00324v2","created_at":"2026-07-05T00:34:05.124399+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2001.00324","created_at":"2026-07-05T00:34:05.124399+00:00"},{"alias_kind":"pith_short_12","alias_value":"634FPMDRTYHR","created_at":"2026-07-05T00:34:05.124399+00:00"},{"alias_kind":"pith_short_16","alias_value":"634FPMDRTYHR2G2P","created_at":"2026-07-05T00:34:05.124399+00:00"},{"alias_kind":"pith_short_8","alias_value":"634FPMDR","created_at":"2026-07-05T00:34:05.124399+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/634FPMDRTYHR2G2P4HHAJ6QPTZ","json":"https://pith.science/pith/634FPMDRTYHR2G2P4HHAJ6QPTZ.json","graph_json":"https://pith.science/api/pith-number/634FPMDRTYHR2G2P4HHAJ6QPTZ/graph.json","events_json":"https://pith.science/api/pith-number/634FPMDRTYHR2G2P4HHAJ6QPTZ/events.json","paper":"https://pith.science/paper/634FPMDR"},"agent_actions":{"view_html":"https://pith.science/pith/634FPMDRTYHR2G2P4HHAJ6QPTZ","download_json":"https://pith.science/pith/634FPMDRTYHR2G2P4HHAJ6QPTZ.json","view_paper":"https://pith.science/paper/634FPMDR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2001.00324&json=true","fetch_graph":"https://pith.science/api/pith-number/634FPMDRTYHR2G2P4HHAJ6QPTZ/graph.json","fetch_events":"https://pith.science/api/pith-number/634FPMDRTYHR2G2P4HHAJ6QPTZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/634FPMDRTYHR2G2P4HHAJ6QPTZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/634FPMDRTYHR2G2P4HHAJ6QPTZ/action/storage_attestation","attest_author":"https://pith.science/pith/634FPMDRTYHR2G2P4HHAJ6QPTZ/action/author_attestation","sign_citation":"https://pith.science/pith/634FPMDRTYHR2G2P4HHAJ6QPTZ/action/citation_signature","submit_replication":"https://pith.science/pith/634FPMDRTYHR2G2P4HHAJ6QPTZ/action/replication_record"}},"created_at":"2026-07-05T00:34:05.124399+00:00","updated_at":"2026-07-05T00:34:05.124399+00:00"}