{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:G3IKPMHGWW4X7TLIZ3CBSMBIHH","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":"d32e3dcf6a7cd669b1e73abcd3633917b634d5ded855bb3628328d9824a2a735","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-02-26T09:51:59Z","title_canon_sha256":"73f00eb379f3eb40180755d77759287e81be914fff279e1cc11614731bbfdf4f"},"schema_version":"1.0","source":{"id":"1902.09829","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.09829","created_at":"2026-06-04T20:13:56Z"},{"alias_kind":"arxiv_version","alias_value":"1902.09829v1","created_at":"2026-06-04T20:13:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.09829","created_at":"2026-06-04T20:13:56Z"},{"alias_kind":"pith_short_12","alias_value":"G3IKPMHGWW4X","created_at":"2026-06-04T20:13:56Z"},{"alias_kind":"pith_short_16","alias_value":"G3IKPMHGWW4X7TLI","created_at":"2026-06-04T20:13:56Z"},{"alias_kind":"pith_short_8","alias_value":"G3IKPMHG","created_at":"2026-06-04T20:13:56Z"}],"graph_snapshots":[{"event_id":"sha256:0d125cb290df1647649571eb18d8eaecf9a7a4c6a6ebb6725becf6c1333cbe2c","target":"graph","created_at":"2026-06-04T20:13:56Z","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/1902.09829/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Error estimates of finite element methods for reaction-diffusion problems are often realised in the related energy norm. In the singularly perturbed case, however, this norm is not adequate. A different scaling of the $H^m$ seminorm for $2m$-th order problems leads to a balanced norm which reflects the layer behaviour correctly.\n  We prove error estimates in such balanced norms and improve thereby existing estimates known in literature.","authors_text":"Hans-G. Roos, Sebastian Franz","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-02-26T09:51:59Z","title":"Error estimates in balanced norms of finite element methods for higher order reaction-diffusion problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.09829","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":"sha256:227faa2682837fa5c57ab111abb5c3ad4ea1c4602111e1fc80b9f8be419f2eb0","target":"record","created_at":"2026-06-04T20:13:56Z","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":"d32e3dcf6a7cd669b1e73abcd3633917b634d5ded855bb3628328d9824a2a735","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-02-26T09:51:59Z","title_canon_sha256":"73f00eb379f3eb40180755d77759287e81be914fff279e1cc11614731bbfdf4f"},"schema_version":"1.0","source":{"id":"1902.09829","kind":"arxiv","version":1}},"canonical_sha256":"36d0a7b0e6b5b97fcd68cec419302839ebf7f992848fbce4aa0ebd88892329cc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"36d0a7b0e6b5b97fcd68cec419302839ebf7f992848fbce4aa0ebd88892329cc","first_computed_at":"2026-06-04T20:13:56.403620Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T20:13:56.403620Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WKDeWClmOMjMUx5hNbNEpKvNfkAHaeBEHjIrOkUG1YzA1+T48V5qgl7uIp70zjNgvJ+7Z9l2JRPwhVVwEifxAA==","signature_status":"signed_v1","signed_at":"2026-06-04T20:13:56.404065Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.09829","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:227faa2682837fa5c57ab111abb5c3ad4ea1c4602111e1fc80b9f8be419f2eb0","sha256:0d125cb290df1647649571eb18d8eaecf9a7a4c6a6ebb6725becf6c1333cbe2c"],"state_sha256":"c8b33caca522da895c337c46a83beca7c761790108da77f47e036fceef952eef"}