{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:N3SRFAUZU2CC552RAXBRFFHLDT","short_pith_number":"pith:N3SRFAUZ","canonical_record":{"source":{"id":"1908.08698","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-08-23T07:12:55Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"b528f1b4a6e97339fda59d7b4c9bb3cd049d52708b7d5495c5685d3e73ed8e43","abstract_canon_sha256":"1981579a3f244d5f9716e22f1cef037063369af69f84e40ed37229de0637a84d"},"schema_version":"1.0"},"canonical_sha256":"6ee5128299a6842ef75105c31294eb1cd4b4c4af46f7226b8c37b9b1496558ee","source":{"kind":"arxiv","id":"1908.08698","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.08698","created_at":"2026-07-05T00:38:33Z"},{"alias_kind":"arxiv_version","alias_value":"1908.08698v3","created_at":"2026-07-05T00:38:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.08698","created_at":"2026-07-05T00:38:33Z"},{"alias_kind":"pith_short_12","alias_value":"N3SRFAUZU2CC","created_at":"2026-07-05T00:38:33Z"},{"alias_kind":"pith_short_16","alias_value":"N3SRFAUZU2CC552R","created_at":"2026-07-05T00:38:33Z"},{"alias_kind":"pith_short_8","alias_value":"N3SRFAUZ","created_at":"2026-07-05T00:38:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:N3SRFAUZU2CC552RAXBRFFHLDT","target":"record","payload":{"canonical_record":{"source":{"id":"1908.08698","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-08-23T07:12:55Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"b528f1b4a6e97339fda59d7b4c9bb3cd049d52708b7d5495c5685d3e73ed8e43","abstract_canon_sha256":"1981579a3f244d5f9716e22f1cef037063369af69f84e40ed37229de0637a84d"},"schema_version":"1.0"},"canonical_sha256":"6ee5128299a6842ef75105c31294eb1cd4b4c4af46f7226b8c37b9b1496558ee","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:38:33.469922Z","signature_b64":"5rSwqK4qHGaf5pR3PgGMe4w8kImziC7aEAWnxXb4233n/3EbcvK43ECxhmv7+iU+hYuCScq6OLPO9c5AKB5uDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6ee5128299a6842ef75105c31294eb1cd4b4c4af46f7226b8c37b9b1496558ee","last_reissued_at":"2026-07-05T00:38:33.469376Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:38:33.469376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.08698","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:38:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RGGz0JiA4/x7gYH3fduaKQoejXS3p2Sb+IB7+YbUkLdOEFV2mK2REUv/zmcSVWJ90OK/bhM0SmojzMhGvKx0AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T15:12:16.740591Z"},"content_sha256":"f644134ae05116a8926d3432a01eedcfb7a137571c8575b38bd995ee36c21fd8","schema_version":"1.0","event_id":"sha256:f644134ae05116a8926d3432a01eedcfb7a137571c8575b38bd995ee36c21fd8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:N3SRFAUZU2CC552RAXBRFFHLDT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Convergence Rate of Multiscale Finite Element Method for Various Boundary Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Changqing Ye, Hao Dong, JunZhi Cui","submitted_at":"2019-08-23T07:12:55Z","abstract_excerpt":"In this paper, we examine the effectiveness of classic multiscale finite element method (MsFEM) (Hou and Wu, 1997; Hou et al., 1999) for mixed Dirichlet-Neumann, Robin and hemivariational inequality boundary problems. Constructing so-called boundary correctors is a common technique in existing methods to prove the convergence rate of MsFEM, while we think not reflects the essence of those problems. Instead, we focus on the first-order expansion structure. Through recently developed estimations in homogenization theory, our convergence rate is provided with milder assumptions and in neat forms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.08698","kind":"arxiv","version":3},"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/1908.08698/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:38:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"epxO7M5yXKJ0OcvycqH7q41wZSpaMpO/sEGM+KrnqKmivBYr7iJ+srsliMjkeEuq4TRZWClryHMgWj3+mqR0BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T15:12:16.741517Z"},"content_sha256":"25fec3f5cb11398dfc375e610572314c9f420b915f8dc4e4076a61e45b778bff","schema_version":"1.0","event_id":"sha256:25fec3f5cb11398dfc375e610572314c9f420b915f8dc4e4076a61e45b778bff"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N3SRFAUZU2CC552RAXBRFFHLDT/bundle.json","state_url":"https://pith.science/pith/N3SRFAUZU2CC552RAXBRFFHLDT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N3SRFAUZU2CC552RAXBRFFHLDT/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-04T15:12:16Z","links":{"resolver":"https://pith.science/pith/N3SRFAUZU2CC552RAXBRFFHLDT","bundle":"https://pith.science/pith/N3SRFAUZU2CC552RAXBRFFHLDT/bundle.json","state":"https://pith.science/pith/N3SRFAUZU2CC552RAXBRFFHLDT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N3SRFAUZU2CC552RAXBRFFHLDT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:N3SRFAUZU2CC552RAXBRFFHLDT","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":"1981579a3f244d5f9716e22f1cef037063369af69f84e40ed37229de0637a84d","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-08-23T07:12:55Z","title_canon_sha256":"b528f1b4a6e97339fda59d7b4c9bb3cd049d52708b7d5495c5685d3e73ed8e43"},"schema_version":"1.0","source":{"id":"1908.08698","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.08698","created_at":"2026-07-05T00:38:33Z"},{"alias_kind":"arxiv_version","alias_value":"1908.08698v3","created_at":"2026-07-05T00:38:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.08698","created_at":"2026-07-05T00:38:33Z"},{"alias_kind":"pith_short_12","alias_value":"N3SRFAUZU2CC","created_at":"2026-07-05T00:38:33Z"},{"alias_kind":"pith_short_16","alias_value":"N3SRFAUZU2CC552R","created_at":"2026-07-05T00:38:33Z"},{"alias_kind":"pith_short_8","alias_value":"N3SRFAUZ","created_at":"2026-07-05T00:38:33Z"}],"graph_snapshots":[{"event_id":"sha256:25fec3f5cb11398dfc375e610572314c9f420b915f8dc4e4076a61e45b778bff","target":"graph","created_at":"2026-07-05T00:38:33Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.08698/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we examine the effectiveness of classic multiscale finite element method (MsFEM) (Hou and Wu, 1997; Hou et al., 1999) for mixed Dirichlet-Neumann, Robin and hemivariational inequality boundary problems. Constructing so-called boundary correctors is a common technique in existing methods to prove the convergence rate of MsFEM, while we think not reflects the essence of those problems. Instead, we focus on the first-order expansion structure. Through recently developed estimations in homogenization theory, our convergence rate is provided with milder assumptions and in neat forms.","authors_text":"Changqing Ye, Hao Dong, JunZhi Cui","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-08-23T07:12:55Z","title":"Convergence Rate of Multiscale Finite Element Method for Various Boundary Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.08698","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:f644134ae05116a8926d3432a01eedcfb7a137571c8575b38bd995ee36c21fd8","target":"record","created_at":"2026-07-05T00:38:33Z","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":"1981579a3f244d5f9716e22f1cef037063369af69f84e40ed37229de0637a84d","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-08-23T07:12:55Z","title_canon_sha256":"b528f1b4a6e97339fda59d7b4c9bb3cd049d52708b7d5495c5685d3e73ed8e43"},"schema_version":"1.0","source":{"id":"1908.08698","kind":"arxiv","version":3}},"canonical_sha256":"6ee5128299a6842ef75105c31294eb1cd4b4c4af46f7226b8c37b9b1496558ee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6ee5128299a6842ef75105c31294eb1cd4b4c4af46f7226b8c37b9b1496558ee","first_computed_at":"2026-07-05T00:38:33.469376Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:38:33.469376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5rSwqK4qHGaf5pR3PgGMe4w8kImziC7aEAWnxXb4233n/3EbcvK43ECxhmv7+iU+hYuCScq6OLPO9c5AKB5uDw==","signature_status":"signed_v1","signed_at":"2026-07-05T00:38:33.469922Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.08698","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f644134ae05116a8926d3432a01eedcfb7a137571c8575b38bd995ee36c21fd8","sha256:25fec3f5cb11398dfc375e610572314c9f420b915f8dc4e4076a61e45b778bff"],"state_sha256":"57bb9f3d35217beb3a3c2d4ea1067ea2dc490ed4be86e9bf2fff5c219aaeda6f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LgFgsMWx3qYxJDOlYpAscvYSpjesUhRMb9V5YQtMouK0RPKGqZGMRPMp0yeeBvnR9kaMzV2iLDQRRv3oF0NNDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T15:12:16.748784Z","bundle_sha256":"08c1a55d1aeb0b26c81cc93d1f868ec5b0d3472e9deba1652212eb37878375fc"}}