{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:AZOR64V6AWOYRC4NYR3BMXWLTK","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":"bb23737fa4d3bcfcdacd1f268a7ed1e0aba912072fc3219d912ab64a4af7ea0d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-06-21T12:25:42Z","title_canon_sha256":"7b5fcea036f3b1452d53a15e86bdd664d858cfc043f7f290254b41be8e1d0045"},"schema_version":"1.0","source":{"id":"1306.5115","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.5115","created_at":"2026-05-18T02:56:32Z"},{"alias_kind":"arxiv_version","alias_value":"1306.5115v1","created_at":"2026-05-18T02:56:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.5115","created_at":"2026-05-18T02:56:32Z"},{"alias_kind":"pith_short_12","alias_value":"AZOR64V6AWOY","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"AZOR64V6AWOYRC4N","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"AZOR64V6","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:1ba357815bdadb13a0644addc814b54d46a6b09bd44b68004735b0e371170212","target":"graph","created_at":"2026-05-18T02:56:32Z","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 solution of second order elliptic PDEs in $\\R^d$ with inhomogeneous Dirichlet data by means of an $h$-adaptive FEM with fixed polynomial order $p\\in\\N$. As model example serves the Poisson equation with mixed Dirichlet-Neumann boundary conditions, where the inhomogeneous Dirichlet data are discretized by use of an $H^{1/2}$-stable projection, for instance, the $L^2$-projection for $p=1$ or the Scott-Zhang projection for general $p\\ge1$. For error estimation, we use a residual error estimator which includes the Dirichlet data oscillations. We prove that each $H^{1/2}$-stable pro","authors_text":"Dirk Praetorius, Josef Kemetm\\\"uller, Marcus Page, Markus Aurada, Michael Feischl","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-06-21T12:25:42Z","title":"Each H^{1/2}-stable projection yields convergence and quasi-optimality of adaptive FEM with inhomogeneous Dirichlet data in R^d"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.5115","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":"sha256:6b8042114353165302dd39d87b503353e65b1c3335768846b4bb2deb38673d39","target":"record","created_at":"2026-05-18T02:56:32Z","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":"bb23737fa4d3bcfcdacd1f268a7ed1e0aba912072fc3219d912ab64a4af7ea0d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-06-21T12:25:42Z","title_canon_sha256":"7b5fcea036f3b1452d53a15e86bdd664d858cfc043f7f290254b41be8e1d0045"},"schema_version":"1.0","source":{"id":"1306.5115","kind":"arxiv","version":1}},"canonical_sha256":"065d1f72be059d888b8dc476165ecb9a8c17ca5accc4ea6e0579e4fde983e18f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"065d1f72be059d888b8dc476165ecb9a8c17ca5accc4ea6e0579e4fde983e18f","first_computed_at":"2026-05-18T02:56:32.647248Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:56:32.647248Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hv7EgjHWYiAHVEVvuwBG5LU4OReuuwytA2u017QsObUCAKzVDrn9iOjRtspuEp5tqv2YTd8Ih8dfcj4eNy4pDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:56:32.647941Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.5115","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6b8042114353165302dd39d87b503353e65b1c3335768846b4bb2deb38673d39","sha256:1ba357815bdadb13a0644addc814b54d46a6b09bd44b68004735b0e371170212"],"state_sha256":"49f4a26b6fdfe8233af225f3a0ea78b1e2ed204ad9893bec5266d14c1afd315c"}