{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:PYPO2W4SLZVQ3CFZXTD3LJKD5G","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":"5e91458d6a9c4104a84966dc50152abb85b22cd461e7e16c56ae648a3c999b93","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-21T20:44:18Z","title_canon_sha256":"40f0ab565c8b8920034eedb310e3c9da546c8de35dac4b41612e27b51760e307"},"schema_version":"1.0","source":{"id":"1903.09234","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.09234","created_at":"2026-05-17T23:50:40Z"},{"alias_kind":"arxiv_version","alias_value":"1903.09234v1","created_at":"2026-05-17T23:50:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.09234","created_at":"2026-05-17T23:50:40Z"},{"alias_kind":"pith_short_12","alias_value":"PYPO2W4SLZVQ","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"PYPO2W4SLZVQ3CFZ","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"PYPO2W4S","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:d2125f6841edcc6611f013a59a9357daa684f61eda49bfc973307ae3d4c5eb38","target":"graph","created_at":"2026-05-17T23:50:40Z","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":"We study an ocean related system with a small viscosity parameter, which is the linearized version of the modified Primitive Equations. As the parameter goes to zero, a $L^\\infty$ convergence result is obtained together with the estimation on the thickness of the boundary layer.","authors_text":"Wenshu Zhou, Xiaodan Wei, Xulong Qin, Xu Zhao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-21T20:44:18Z","title":"Boundary Layer Study for an Ocean Related System with a Small Viscosity Parameter"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.09234","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:f67f68bc86e5fd3189664bd2694b5ec1601afde809540835642490c7eeb1c92e","target":"record","created_at":"2026-05-17T23:50:40Z","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":"5e91458d6a9c4104a84966dc50152abb85b22cd461e7e16c56ae648a3c999b93","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-21T20:44:18Z","title_canon_sha256":"40f0ab565c8b8920034eedb310e3c9da546c8de35dac4b41612e27b51760e307"},"schema_version":"1.0","source":{"id":"1903.09234","kind":"arxiv","version":1}},"canonical_sha256":"7e1eed5b925e6b0d88b9bcc7b5a543e99fa3b3a836f25f5cdbb1c943a080cdca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7e1eed5b925e6b0d88b9bcc7b5a543e99fa3b3a836f25f5cdbb1c943a080cdca","first_computed_at":"2026-05-17T23:50:40.269376Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:40.269376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"txg3Co5VVG+umNo2wnPUdcqsW8L836+t+RQBWF4jXZaBHn9ZH9YFOmJBr+gBw8rHkVbghZUPLfB8denfd5vKCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:40.269982Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.09234","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f67f68bc86e5fd3189664bd2694b5ec1601afde809540835642490c7eeb1c92e","sha256:d2125f6841edcc6611f013a59a9357daa684f61eda49bfc973307ae3d4c5eb38"],"state_sha256":"4eebd5089be68dec864535064ba639357eba4b555013a8e1bd89908410a4a93e"}