{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:XX4CLWRS6MPDRPYIZGZM24XJKA","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":"345203108ff6952b5acdaf1587f167e02a16fd7f6cc587e779ec5ab4914a0d6d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-22T08:49:26Z","title_canon_sha256":"e9ee4f93170f45957135b0f5461db21be6fe1d5c00a75f6971a73d15ba69abf0"},"schema_version":"1.0","source":{"id":"1704.06766","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.06766","created_at":"2026-05-18T00:45:57Z"},{"alias_kind":"arxiv_version","alias_value":"1704.06766v1","created_at":"2026-05-18T00:45:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.06766","created_at":"2026-05-18T00:45:57Z"},{"alias_kind":"pith_short_12","alias_value":"XX4CLWRS6MPD","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"XX4CLWRS6MPDRPYI","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"XX4CLWRS","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:f648eb89e61ab5ad5a1bb0d0e647e1020303fa963eeb2ea96b2a544d5c2287f9","target":"graph","created_at":"2026-05-18T00:45:57Z","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 investigate the well-posedness theory for the MHD boundary layer system in two-dimensional space. The boundary layer equations are governed by the Prandtl type equations that are derived from the full incompressible MHD system with non-slip boundary condition on the velocity, perfectly conducting condition on the magnetic field, and Dirichlet boundary condition on the temperature when the viscosity coefficient depends on the temperature. To derive the Prandtl type boundary layer system, we require all the hydrodynamic Reynolds numbers, magnetic Reynolds numbers and Nusselt nu","authors_text":"Boling Guo, Daiwen Huang, Jincheng Gao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-22T08:49:26Z","title":"Local-in-time Well-posedness of Boundary Layer System for the Full Incompressible MHD Equations by Energy Methods"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.06766","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":"sha256:0fe793dca3e53d40cd8eca3f9358fc85c1cc9871273ba595b94d14ddb1941cc0","target":"record","created_at":"2026-05-18T00:45:57Z","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":"345203108ff6952b5acdaf1587f167e02a16fd7f6cc587e779ec5ab4914a0d6d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-22T08:49:26Z","title_canon_sha256":"e9ee4f93170f45957135b0f5461db21be6fe1d5c00a75f6971a73d15ba69abf0"},"schema_version":"1.0","source":{"id":"1704.06766","kind":"arxiv","version":1}},"canonical_sha256":"bdf825da32f31e38bf08c9b2cd72e9500773447ba17d48c6af4317ae8af39fb3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bdf825da32f31e38bf08c9b2cd72e9500773447ba17d48c6af4317ae8af39fb3","first_computed_at":"2026-05-18T00:45:57.676105Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:57.676105Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FhrvJYJgzYFjSOSJK0uMsCum1gCpjeIgysSvB3XGA4vDLd3DxRV7gdoOBjYBamxaarlFj0AH0knfh1sEe3w9DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:57.676677Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.06766","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0fe793dca3e53d40cd8eca3f9358fc85c1cc9871273ba595b94d14ddb1941cc0","sha256:f648eb89e61ab5ad5a1bb0d0e647e1020303fa963eeb2ea96b2a544d5c2287f9"],"state_sha256":"98876d4fad248cd49d5121fd0150e36c49b97159378924e75b3ae2624b35ed3a"}