{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:EBMM47P5OHTFH4B5JZYVCEM4NF","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":"e1601fbbf35f2f7e99ff853e511793bd5a37b2b5cfe58840d90e939d316564b0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-09-28T16:33:23Z","title_canon_sha256":"41fb1e6a8f83411ef8dd0502d3bd8e18be818425505fa00af4258de59bc0eade"},"schema_version":"1.0","source":{"id":"1509.08384","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.08384","created_at":"2026-05-18T01:09:29Z"},{"alias_kind":"arxiv_version","alias_value":"1509.08384v3","created_at":"2026-05-18T01:09:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.08384","created_at":"2026-05-18T01:09:29Z"},{"alias_kind":"pith_short_12","alias_value":"EBMM47P5OHTF","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"EBMM47P5OHTFH4B5","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"EBMM47P5","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:502422f7603ebbf1687f4a2f9b63634dc15cddb75f239f0d00608f00cd8b1ffa","target":"graph","created_at":"2026-05-18T01:09:29Z","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 develop a new multiscale finite element method for Laplace equation with oscillating Neumann boundary conditions on rough boundaries. The key point is the introduction of a new boundary condition that incorporates both the microscopically geometrical and physical information of the rough boundary. We prove the method has optimal convergence rate in the energy norm with a weak resonance term for periodic roughness. Numerical results are reported for both periodic and nonperiodic roughness.","authors_text":"P.B. Ming, X. Xu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-09-28T16:33:23Z","title":"A multiscale finite element method for oscillating Neumann problem on rough domain"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.08384","kind":"arxiv","version":3},"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:b4639138b0db264af70ca24e67488985ef1f4c97b19c7e379812bb0aa7311fb5","target":"record","created_at":"2026-05-18T01:09:29Z","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":"e1601fbbf35f2f7e99ff853e511793bd5a37b2b5cfe58840d90e939d316564b0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-09-28T16:33:23Z","title_canon_sha256":"41fb1e6a8f83411ef8dd0502d3bd8e18be818425505fa00af4258de59bc0eade"},"schema_version":"1.0","source":{"id":"1509.08384","kind":"arxiv","version":3}},"canonical_sha256":"2058ce7dfd71e653f03d4e7151119c696a410738dee68f67fd864f7debc9c6f2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2058ce7dfd71e653f03d4e7151119c696a410738dee68f67fd864f7debc9c6f2","first_computed_at":"2026-05-18T01:09:29.689345Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:29.689345Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gtlUwrdf4HUdBjH92t0GWidGr0vZ44oGd8LYyjB7WAS2OR0b8WHXV6hu/woX/nDgPpo/0yx7iWYxuHYPkX5XBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:29.689712Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.08384","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b4639138b0db264af70ca24e67488985ef1f4c97b19c7e379812bb0aa7311fb5","sha256:502422f7603ebbf1687f4a2f9b63634dc15cddb75f239f0d00608f00cd8b1ffa"],"state_sha256":"2fe6c6146c90f8cbf02a6c899be5281af0084b47714d328dbe890d4bdfb5c1ce"}