{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:ZC6CZRNHCDGLTZDGEGSN3LRXUR","short_pith_number":"pith:ZC6CZRNH","canonical_record":{"source":{"id":"1408.6037","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-08-26T07:35:48Z","cross_cats_sorted":[],"title_canon_sha256":"1f9f25762023dadd8b785d2effef33d0fedc34a37a89156ab94dd107ca8ee36d","abstract_canon_sha256":"bb6f71ea3f274126f958ff655423a98a47cae72d3833cfb6f18486ea876c3fc6"},"schema_version":"1.0"},"canonical_sha256":"c8bc2cc5a710ccb9e46621a4ddae37a45bfa9964c41d70fda25ced209ad63aa8","source":{"kind":"arxiv","id":"1408.6037","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.6037","created_at":"2026-05-18T02:17:33Z"},{"alias_kind":"arxiv_version","alias_value":"1408.6037v2","created_at":"2026-05-18T02:17:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.6037","created_at":"2026-05-18T02:17:33Z"},{"alias_kind":"pith_short_12","alias_value":"ZC6CZRNHCDGL","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZC6CZRNHCDGLTZDG","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZC6CZRNH","created_at":"2026-05-18T12:28:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:ZC6CZRNHCDGLTZDGEGSN3LRXUR","target":"record","payload":{"canonical_record":{"source":{"id":"1408.6037","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-08-26T07:35:48Z","cross_cats_sorted":[],"title_canon_sha256":"1f9f25762023dadd8b785d2effef33d0fedc34a37a89156ab94dd107ca8ee36d","abstract_canon_sha256":"bb6f71ea3f274126f958ff655423a98a47cae72d3833cfb6f18486ea876c3fc6"},"schema_version":"1.0"},"canonical_sha256":"c8bc2cc5a710ccb9e46621a4ddae37a45bfa9964c41d70fda25ced209ad63aa8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:17:33.647870Z","signature_b64":"0skCZb3av3EKdE+JAX3gDac9vL8lHnTLD2iUQR2N3PZC67Waj03XmYwEqLSm6O81WXo8VVhIhoOOuU6YDjeUDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c8bc2cc5a710ccb9e46621a4ddae37a45bfa9964c41d70fda25ced209ad63aa8","last_reissued_at":"2026-05-18T02:17:33.647219Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:17:33.647219Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1408.6037","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:17:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p8Z2XcVuXocoHA0sg1/w2XqqqtSlScbL3KMiPlBpzDtLk799+AnpyhsF4O3QbWaeSnjg+bBaaW+YwdDpVmU2Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T19:05:29.227645Z"},"content_sha256":"a5e2abd726b4c2d556f8f83c3948b29a92322efce3e1dff0baba4c3c80b9c6ef","schema_version":"1.0","event_id":"sha256:a5e2abd726b4c2d556f8f83c3948b29a92322efce3e1dff0baba4c3c80b9c6ef"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:ZC6CZRNHCDGLTZDGEGSN3LRXUR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Posteriori Error Analysis of $hp$-FEM for singularly perturbed problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Jens M. Melenk, Thomas P. Wihler","submitted_at":"2014-08-26T07:35:48Z","abstract_excerpt":"We consider the approximation of singularly perturbed linear second-order boundary value problems by $hp$-finite element methods. In particular, we include the case where the associated differential operator may not be coercive. Within this setting we derive an a posteriori error estimate for a natural residual norm. The error bound is robust with respect to the perturbation parameter and fully explicit with respect to both the local mesh size $h$ and the polynomial degree $p$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.6037","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T02:17:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1eoP/SC7AviBM6T/xgY9HFiae8rMQzrfbwhOyaBDLSyhWxYkJlzfhfGxnjG3hWBrtVTfiuC2qkAVISClDrOADw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T19:05:29.227990Z"},"content_sha256":"1298dd99f087fc30c0e17727137e86394f4862186c23bb3e063e32d6ada8ce61","schema_version":"1.0","event_id":"sha256:1298dd99f087fc30c0e17727137e86394f4862186c23bb3e063e32d6ada8ce61"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZC6CZRNHCDGLTZDGEGSN3LRXUR/bundle.json","state_url":"https://pith.science/pith/ZC6CZRNHCDGLTZDGEGSN3LRXUR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZC6CZRNHCDGLTZDGEGSN3LRXUR/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":"2026-05-22T19:05:29Z","links":{"resolver":"https://pith.science/pith/ZC6CZRNHCDGLTZDGEGSN3LRXUR","bundle":"https://pith.science/pith/ZC6CZRNHCDGLTZDGEGSN3LRXUR/bundle.json","state":"https://pith.science/pith/ZC6CZRNHCDGLTZDGEGSN3LRXUR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZC6CZRNHCDGLTZDGEGSN3LRXUR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ZC6CZRNHCDGLTZDGEGSN3LRXUR","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":"bb6f71ea3f274126f958ff655423a98a47cae72d3833cfb6f18486ea876c3fc6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-08-26T07:35:48Z","title_canon_sha256":"1f9f25762023dadd8b785d2effef33d0fedc34a37a89156ab94dd107ca8ee36d"},"schema_version":"1.0","source":{"id":"1408.6037","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.6037","created_at":"2026-05-18T02:17:33Z"},{"alias_kind":"arxiv_version","alias_value":"1408.6037v2","created_at":"2026-05-18T02:17:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.6037","created_at":"2026-05-18T02:17:33Z"},{"alias_kind":"pith_short_12","alias_value":"ZC6CZRNHCDGL","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZC6CZRNHCDGLTZDG","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZC6CZRNH","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:1298dd99f087fc30c0e17727137e86394f4862186c23bb3e063e32d6ada8ce61","target":"graph","created_at":"2026-05-18T02:17:33Z","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"},"paper":{"abstract_excerpt":"We consider the approximation of singularly perturbed linear second-order boundary value problems by $hp$-finite element methods. In particular, we include the case where the associated differential operator may not be coercive. Within this setting we derive an a posteriori error estimate for a natural residual norm. The error bound is robust with respect to the perturbation parameter and fully explicit with respect to both the local mesh size $h$ and the polynomial degree $p$.","authors_text":"Jens M. Melenk, Thomas P. Wihler","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-08-26T07:35:48Z","title":"A Posteriori Error Analysis of $hp$-FEM for singularly perturbed problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.6037","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:a5e2abd726b4c2d556f8f83c3948b29a92322efce3e1dff0baba4c3c80b9c6ef","target":"record","created_at":"2026-05-18T02:17:33Z","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":"bb6f71ea3f274126f958ff655423a98a47cae72d3833cfb6f18486ea876c3fc6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-08-26T07:35:48Z","title_canon_sha256":"1f9f25762023dadd8b785d2effef33d0fedc34a37a89156ab94dd107ca8ee36d"},"schema_version":"1.0","source":{"id":"1408.6037","kind":"arxiv","version":2}},"canonical_sha256":"c8bc2cc5a710ccb9e46621a4ddae37a45bfa9964c41d70fda25ced209ad63aa8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c8bc2cc5a710ccb9e46621a4ddae37a45bfa9964c41d70fda25ced209ad63aa8","first_computed_at":"2026-05-18T02:17:33.647219Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:17:33.647219Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0skCZb3av3EKdE+JAX3gDac9vL8lHnTLD2iUQR2N3PZC67Waj03XmYwEqLSm6O81WXo8VVhIhoOOuU6YDjeUDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:17:33.647870Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.6037","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a5e2abd726b4c2d556f8f83c3948b29a92322efce3e1dff0baba4c3c80b9c6ef","sha256:1298dd99f087fc30c0e17727137e86394f4862186c23bb3e063e32d6ada8ce61"],"state_sha256":"dd516cd3204f9642a0c188e940511982f3cc1ad41d5d6ba025ad35be9de7cd75"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EhhYasdwgKPdVH5MaIwP+Z4OFvAvZtxrtwve6ID8bqj1b6UvLfUt8J9mH963BDukX0AFenDTxqSd2a5dBLekDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T19:05:29.230214Z","bundle_sha256":"e9fe6077a6b81750449c9e9a01f8dafa961759ef4154f62f67715d0bfcb1a1c2"}}