{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:G3IKPMHGWW4X7TLIZ3CBSMBIHH","short_pith_number":"pith:G3IKPMHG","canonical_record":{"source":{"id":"1902.09829","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-02-26T09:51:59Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"73f00eb379f3eb40180755d77759287e81be914fff279e1cc11614731bbfdf4f","abstract_canon_sha256":"d32e3dcf6a7cd669b1e73abcd3633917b634d5ded855bb3628328d9824a2a735"},"schema_version":"1.0"},"canonical_sha256":"36d0a7b0e6b5b97fcd68cec419302839ebf7f992848fbce4aa0ebd88892329cc","source":{"kind":"arxiv","id":"1902.09829","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:G3IKPMHGWW4X7TLIZ3CBSMBIHH","target":"record","payload":{"canonical_record":{"source":{"id":"1902.09829","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-02-26T09:51:59Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"73f00eb379f3eb40180755d77759287e81be914fff279e1cc11614731bbfdf4f","abstract_canon_sha256":"d32e3dcf6a7cd669b1e73abcd3633917b634d5ded855bb3628328d9824a2a735"},"schema_version":"1.0"},"canonical_sha256":"36d0a7b0e6b5b97fcd68cec419302839ebf7f992848fbce4aa0ebd88892329cc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T20:13:56.404065Z","signature_b64":"WKDeWClmOMjMUx5hNbNEpKvNfkAHaeBEHjIrOkUG1YzA1+T48V5qgl7uIp70zjNgvJ+7Z9l2JRPwhVVwEifxAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"36d0a7b0e6b5b97fcd68cec419302839ebf7f992848fbce4aa0ebd88892329cc","last_reissued_at":"2026-06-04T20:13:56.403620Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T20:13:56.403620Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.09829","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-04T20:13:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"muuOjpWXYmyPxf93BrFDFLFvnDhTBLtsYRv6LWfXAlwWEcuuwqxmPSR2Aw/LTNFK0bWjSEU9cwsUuuUoymV1Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T23:47:09.354684Z"},"content_sha256":"227faa2682837fa5c57ab111abb5c3ad4ea1c4602111e1fc80b9f8be419f2eb0","schema_version":"1.0","event_id":"sha256:227faa2682837fa5c57ab111abb5c3ad4ea1c4602111e1fc80b9f8be419f2eb0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:G3IKPMHGWW4X7TLIZ3CBSMBIHH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Error estimates in balanced norms of finite element methods for higher order reaction-diffusion problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Hans-G. Roos, Sebastian Franz","submitted_at":"2019-02-26T09:51:59Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.09829","kind":"arxiv","version":1},"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/1902.09829/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":"2026-06-04T20:13:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WrlLE4N+63Us+nA/h58uQ5Hccy4XLt2fgyk5Z02Nt75b4YK/diZI8GzA6rlQc6wV0Z5K6l/OQHHthotlADvhBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T23:47:09.355059Z"},"content_sha256":"0d125cb290df1647649571eb18d8eaecf9a7a4c6a6ebb6725becf6c1333cbe2c","schema_version":"1.0","event_id":"sha256:0d125cb290df1647649571eb18d8eaecf9a7a4c6a6ebb6725becf6c1333cbe2c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G3IKPMHGWW4X7TLIZ3CBSMBIHH/bundle.json","state_url":"https://pith.science/pith/G3IKPMHGWW4X7TLIZ3CBSMBIHH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G3IKPMHGWW4X7TLIZ3CBSMBIHH/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":"2026-06-08T23:47:09Z","links":{"resolver":"https://pith.science/pith/G3IKPMHGWW4X7TLIZ3CBSMBIHH","bundle":"https://pith.science/pith/G3IKPMHGWW4X7TLIZ3CBSMBIHH/bundle.json","state":"https://pith.science/pith/G3IKPMHGWW4X7TLIZ3CBSMBIHH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G3IKPMHGWW4X7TLIZ3CBSMBIHH/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8sGH1WcVdGWqnnMWaaF0IyDki3TP+PqCYgH2BZT2tofS1ovcK26gLGk6ny6idOA/4oKtRb2Nso2FezcVNNchBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T23:47:09.357001Z","bundle_sha256":"6895b9ea74f6d557bfa72e2235228f642998777a064740fd6fc3fb1cd0960db9"}}