{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:Y6G5UTFQWYZGMXXZMDOWBXDVDA","short_pith_number":"pith:Y6G5UTFQ","schema_version":"1.0","canonical_sha256":"c78dda4cb0b632665ef960dd60dc751827f4473f6cd459aad2346101ccf8431d","source":{"kind":"arxiv","id":"2508.09609","version":1},"attestation_state":"computed","paper":{"title":"Global uniform regularity for the 3D incompressible MHD equations with slip boundary condition near a background magnetic field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jiahong Wu, Jincheng Gao, Lianyun Peng, Zheng-an Yao","submitted_at":"2025-08-13T08:41:51Z","abstract_excerpt":"This paper resolves the global regularity problem for the three-dimensional incompressible magnetohydrodynamics (MHD) equations in the upper half-space with slip boundary conditions, in the presence of a background magnetic field. Motivated by geophysical applications, we consider an anisotropic MHD system with weak dissipation in the $x_2$ and $x_3$ directions and small vertical magnetic diffusion. By exploiting the stabilizing effect induced by the background magnetic field and constructing a hierarchy of four energy functionals, we establish global-in-time uniform bounds that are independen"},"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":"2508.09609","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-08-13T08:41:51Z","cross_cats_sorted":[],"title_canon_sha256":"93bcb29da65bc22a6e07770c822aa2bb17ee24f8177e384ffade2cb8339ac1df","abstract_canon_sha256":"1be390b552ac64ce5d3c13c1cdbaa5af9a83305b1313e32328b3c4f04d1a1fe9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:53:18.193922Z","signature_b64":"48tbFx7xpZ130usKALle2XPmGfTn/RxOYQz/SsWYWwHcJ1eVag/jcP/8FQHSLIds/HhBhfVf3u/JNpYnHQzRDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c78dda4cb0b632665ef960dd60dc751827f4473f6cd459aad2346101ccf8431d","last_reissued_at":"2026-07-05T11:53:18.193394Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:53:18.193394Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Global uniform regularity for the 3D incompressible MHD equations with slip boundary condition near a background magnetic field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jiahong Wu, Jincheng Gao, Lianyun Peng, Zheng-an Yao","submitted_at":"2025-08-13T08:41:51Z","abstract_excerpt":"This paper resolves the global regularity problem for the three-dimensional incompressible magnetohydrodynamics (MHD) equations in the upper half-space with slip boundary conditions, in the presence of a background magnetic field. Motivated by geophysical applications, we consider an anisotropic MHD system with weak dissipation in the $x_2$ and $x_3$ directions and small vertical magnetic diffusion. By exploiting the stabilizing effect induced by the background magnetic field and constructing a hierarchy of four energy functionals, we establish global-in-time uniform bounds that are independen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.09609","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2508.09609/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":"2508.09609","created_at":"2026-07-05T11:53:18.193454+00:00"},{"alias_kind":"arxiv_version","alias_value":"2508.09609v1","created_at":"2026-07-05T11:53:18.193454+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.09609","created_at":"2026-07-05T11:53:18.193454+00:00"},{"alias_kind":"pith_short_12","alias_value":"Y6G5UTFQWYZG","created_at":"2026-07-05T11:53:18.193454+00:00"},{"alias_kind":"pith_short_16","alias_value":"Y6G5UTFQWYZGMXXZ","created_at":"2026-07-05T11:53:18.193454+00:00"},{"alias_kind":"pith_short_8","alias_value":"Y6G5UTFQ","created_at":"2026-07-05T11:53:18.193454+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2607.06910","citing_title":"Nonlinear stability of a background magnetic field for the 3D compressible MHD equations with anisotropic dissipation","ref_index":21,"is_internal_anchor":true},{"citing_arxiv_id":"2605.10506","citing_title":"Global uniform regularity for the 3D compressible MHD equations near a background magnetic field","ref_index":35,"is_internal_anchor":false},{"citing_arxiv_id":"2605.10506","citing_title":"Global uniform regularity for the 3D compressible MHD equations near a background magnetic field","ref_index":35,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/Y6G5UTFQWYZGMXXZMDOWBXDVDA","json":"https://pith.science/pith/Y6G5UTFQWYZGMXXZMDOWBXDVDA.json","graph_json":"https://pith.science/api/pith-number/Y6G5UTFQWYZGMXXZMDOWBXDVDA/graph.json","events_json":"https://pith.science/api/pith-number/Y6G5UTFQWYZGMXXZMDOWBXDVDA/events.json","paper":"https://pith.science/paper/Y6G5UTFQ"},"agent_actions":{"view_html":"https://pith.science/pith/Y6G5UTFQWYZGMXXZMDOWBXDVDA","download_json":"https://pith.science/pith/Y6G5UTFQWYZGMXXZMDOWBXDVDA.json","view_paper":"https://pith.science/paper/Y6G5UTFQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2508.09609&json=true","fetch_graph":"https://pith.science/api/pith-number/Y6G5UTFQWYZGMXXZMDOWBXDVDA/graph.json","fetch_events":"https://pith.science/api/pith-number/Y6G5UTFQWYZGMXXZMDOWBXDVDA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Y6G5UTFQWYZGMXXZMDOWBXDVDA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Y6G5UTFQWYZGMXXZMDOWBXDVDA/action/storage_attestation","attest_author":"https://pith.science/pith/Y6G5UTFQWYZGMXXZMDOWBXDVDA/action/author_attestation","sign_citation":"https://pith.science/pith/Y6G5UTFQWYZGMXXZMDOWBXDVDA/action/citation_signature","submit_replication":"https://pith.science/pith/Y6G5UTFQWYZGMXXZMDOWBXDVDA/action/replication_record"}},"created_at":"2026-07-05T11:53:18.193454+00:00","updated_at":"2026-07-05T11:53:18.193454+00:00"}