{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:O7QPAYQRH3RZALZTDI3WEYCYYE","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":"3d2717255173d45b6f3db9eaae4fb5e9e74efe9d3279dfb6c86e1c10e08caf8a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-10-28T13:50:12Z","title_canon_sha256":"635af258651dc1860baa20202c735783b386f65df9a16456c16e1f9a669b9920"},"schema_version":"1.0","source":{"id":"1610.09211","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.09211","created_at":"2026-05-18T00:21:57Z"},{"alias_kind":"arxiv_version","alias_value":"1610.09211v2","created_at":"2026-05-18T00:21:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.09211","created_at":"2026-05-18T00:21:57Z"},{"alias_kind":"pith_short_12","alias_value":"O7QPAYQRH3RZ","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"O7QPAYQRH3RZALZT","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"O7QPAYQR","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:8cdc9cf93058912367faf098e73487ca63ed3489b28124b4cd4451c3a32a7174","target":"graph","created_at":"2026-05-18T00:21:57Z","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":"The hp-version of the finite element method is applied to singularly perturbed reaction-diffusion type equations on polygonal domains. The solution exhibits boundary layers as well as corner layers. On a class of meshes that are suitable refined near the boundary and the corners, robust exponential convergence (in the polynomial degree) is shown in both a balanced norm and the maximum norm.","authors_text":"Jens Markus Melenk, Markus Faustmann","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-10-28T13:50:12Z","title":"Robust exponential convergence of hp-FEM in balanced norms for singularly perturbed reaction-diffusion problems: corner domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09211","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:e223d23dfd816f2f1188527694d791e6584c41bf84c06a7cc97b4de8b2b4aec0","target":"record","created_at":"2026-05-18T00:21:57Z","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":"3d2717255173d45b6f3db9eaae4fb5e9e74efe9d3279dfb6c86e1c10e08caf8a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-10-28T13:50:12Z","title_canon_sha256":"635af258651dc1860baa20202c735783b386f65df9a16456c16e1f9a669b9920"},"schema_version":"1.0","source":{"id":"1610.09211","kind":"arxiv","version":2}},"canonical_sha256":"77e0f062113ee3902f331a37626058c12e6bf6dbe6579104f000f192af6ff668","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"77e0f062113ee3902f331a37626058c12e6bf6dbe6579104f000f192af6ff668","first_computed_at":"2026-05-18T00:21:57.177211Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:21:57.177211Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"adS2O64+bHMdn9wnySubXhMmm9aP7u6pWN18Z8BlTh1Nr4qTW4nsKSxpYyveeufcZgPJM+mQRlm4MkwjvDtmCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:21:57.177936Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.09211","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e223d23dfd816f2f1188527694d791e6584c41bf84c06a7cc97b4de8b2b4aec0","sha256:8cdc9cf93058912367faf098e73487ca63ed3489b28124b4cd4451c3a32a7174"],"state_sha256":"14b9a94166ac518cf362fbcb1e4b460a37eb67839508b7710e03fdfc8dba9d95"}