{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:KHUAS6L57BUIOVT7K5PM2XACYK","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":"9ee8b7adbff92a8fe5c1e5895be123d77b05b58dad7458e05f77ed49f991d4f3","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-08-01T22:52:59Z","title_canon_sha256":"9b61f27feb591242e5231c531df475d307f3aeabd84f7402145fe2c45a7f97e8"},"schema_version":"1.0","source":{"id":"1908.00652","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.00652","created_at":"2026-07-05T02:00:29Z"},{"alias_kind":"arxiv_version","alias_value":"1908.00652v1","created_at":"2026-07-05T02:00:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.00652","created_at":"2026-07-05T02:00:29Z"},{"alias_kind":"pith_short_12","alias_value":"KHUAS6L57BUI","created_at":"2026-07-05T02:00:29Z"},{"alias_kind":"pith_short_16","alias_value":"KHUAS6L57BUIOVT7","created_at":"2026-07-05T02:00:29Z"},{"alias_kind":"pith_short_8","alias_value":"KHUAS6L5","created_at":"2026-07-05T02:00:29Z"}],"graph_snapshots":[{"event_id":"sha256:9ea072f21a85555c798239b91cf8887a357d77cb0b616302e3ca007b25a1d423","target":"graph","created_at":"2026-07-05T02:00:29Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.00652/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we study elliptic partial differential equations with rapidly varying diffusion coefficient that can be represented as a perturbation of a reference coefficient. We develop a numerical method for efficiently solving multiple perturbed problems by reusing local computations performed with the reference coefficient. The proposed method is based on the Petrov--Galerkin Localized Orthogonal Decomposition (PG-LOD) which allows for straightforward parallelization with low communcation overhead and memory consumption. We focus on two types of perturbations: local defects which we treat ","authors_text":"Axel M{\\aa}lqvist, Fredrik Hellman, Tim Keil","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-08-01T22:52:59Z","title":"Numerical upscaling of perturbed diffusion problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.00652","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":"sha256:0d555f84ac68a1b9b87222c082a77470f9fb7577237a648e0ab17f79c4dcec4e","target":"record","created_at":"2026-07-05T02:00:29Z","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":"9ee8b7adbff92a8fe5c1e5895be123d77b05b58dad7458e05f77ed49f991d4f3","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-08-01T22:52:59Z","title_canon_sha256":"9b61f27feb591242e5231c531df475d307f3aeabd84f7402145fe2c45a7f97e8"},"schema_version":"1.0","source":{"id":"1908.00652","kind":"arxiv","version":1}},"canonical_sha256":"51e809797df86887567f575ecd5c02c2a57de88ac650f2841d829816bc0031f2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"51e809797df86887567f575ecd5c02c2a57de88ac650f2841d829816bc0031f2","first_computed_at":"2026-07-05T02:00:29.205341Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:00:29.205341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tdIgDLOGtLmXuZUxb7sEoZz39Eml39jWHLFwI2LKRv3kmapmHQKHkkV2AtiY66Xe256ETxt8Y9pp0rZL/0TJCw==","signature_status":"signed_v1","signed_at":"2026-07-05T02:00:29.205798Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.00652","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0d555f84ac68a1b9b87222c082a77470f9fb7577237a648e0ab17f79c4dcec4e","sha256:9ea072f21a85555c798239b91cf8887a357d77cb0b616302e3ca007b25a1d423"],"state_sha256":"0f311e8b0d2be0f4eda99a0e17f1c4ab1742ac9e50d6361e7bdec8e88ece6589"}