{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:BBUV2WQKTSBZMM4BVJ3YAVPZ2A","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":"4959c92e0f63511914a9d5ba482a4058d54e918246db2db0ca11257fd952c98c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-05-28T09:37:59Z","title_canon_sha256":"b7ed88bb3ecfd21c9137629622b8d98a6694f2a4a792609276a79fb893a03523"},"schema_version":"1.0","source":{"id":"1505.07611","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.07611","created_at":"2026-05-18T01:29:45Z"},{"alias_kind":"arxiv_version","alias_value":"1505.07611v2","created_at":"2026-05-18T01:29:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.07611","created_at":"2026-05-18T01:29:45Z"},{"alias_kind":"pith_short_12","alias_value":"BBUV2WQKTSBZ","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"BBUV2WQKTSBZMM4B","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"BBUV2WQK","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:8bc5d38a9d5e2706b949bc90df67acf9b5e6817931372e5e04de9afa73a0b569","target":"graph","created_at":"2026-05-18T01:29:45Z","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":"This paper addresses the variational multiscale stabilization of standard finite element methods for linear partial differential equations that exhibit multiscale features. The stabilization is of Petrov-Galerkin type with a standard finite element trial space and a problem-dependent test space based on pre-computed fine-scale correctors. The exponential decay of these correctors and their localisation to local cell problems is rigorously justified. The stabilization eliminates scale-dependent pre-asymptotic effects as they appear for standard finite element discretizations of highly oscillato","authors_text":"Daniel Peterseim","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-05-28T09:37:59Z","title":"Variational Multiscale Stabilization and the Exponential Decay of Fine-scale Correctors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.07611","kind":"arxiv","version":2},"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":"sha256:0146fe8cc3ae17da0a0d7ee947867d7ce8b578defc99ed450d7bc9f5e38e0cbc","target":"record","created_at":"2026-05-18T01:29:45Z","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":"4959c92e0f63511914a9d5ba482a4058d54e918246db2db0ca11257fd952c98c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-05-28T09:37:59Z","title_canon_sha256":"b7ed88bb3ecfd21c9137629622b8d98a6694f2a4a792609276a79fb893a03523"},"schema_version":"1.0","source":{"id":"1505.07611","kind":"arxiv","version":2}},"canonical_sha256":"08695d5a0a9c83963381aa778055f9d012acb3e55824972411b6cf776f22d1e0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"08695d5a0a9c83963381aa778055f9d012acb3e55824972411b6cf776f22d1e0","first_computed_at":"2026-05-18T01:29:45.877823Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:29:45.877823Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uAIa60rAvUMTg27x74cWAsRQANopqOhGBCh+s2IruYWhdoIA8HVLCG7xf4gVCI3qeiTZVPWSVGDeuMzUxy0zDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:29:45.878369Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.07611","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0146fe8cc3ae17da0a0d7ee947867d7ce8b578defc99ed450d7bc9f5e38e0cbc","sha256:8bc5d38a9d5e2706b949bc90df67acf9b5e6817931372e5e04de9afa73a0b569"],"state_sha256":"982c0b04555c5f433d0b0385e8c0fd11cce9932379aae5ed52bda2600e271af8"}