{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:7NVJFMUXKES7WJHLTX2EZU7QMR","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":"86eedfef14935fa5bec42b5c3acd05cba036f2950acd692b99982a33c9c4984f","cross_cats_sorted":["cs.NA","math.AP"],"license":"","primary_cat":"math.NA","submitted_at":"2004-10-06T20:29:45Z","title_canon_sha256":"dba2fd41067cce29f18b59cc10745de891f40f200351957888aae27474ce2a7a"},"schema_version":"1.0","source":{"id":"math/0410184","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0410184","created_at":"2026-06-03T22:06:15Z"},{"alias_kind":"arxiv_version","alias_value":"math/0410184v1","created_at":"2026-06-03T22:06:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0410184","created_at":"2026-06-03T22:06:15Z"},{"alias_kind":"pith_short_12","alias_value":"7NVJFMUXKES7","created_at":"2026-06-03T22:06:15Z"},{"alias_kind":"pith_short_16","alias_value":"7NVJFMUXKES7WJHL","created_at":"2026-06-03T22:06:15Z"},{"alias_kind":"pith_short_8","alias_value":"7NVJFMUX","created_at":"2026-06-03T22:06:15Z"}],"graph_snapshots":[{"event_id":"sha256:0cbad94f25686f1888d4b449d80e29dae7c7c185f73edd62c469b67aaf9d27bb","target":"graph","created_at":"2026-06-03T22:06:15Z","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/math/0410184/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the approximation properties of a harmonic function $u \\in H\\sp{1-k}(\\Omega)$, $k > 0$, on relatively compact sub-domain $A$ of $\\Omega$, using the Generalized Finite Element Method. For smooth, bounded domains $\\Omega$, we obtain that the GFEM--approximation $u_S$ satisfies $\\|u - u_S\\|_{H\\sp{1}(A)} \\le C h^{\\gamma}\\|u\\|_{H\\sp{1-k}(\\Omega)}$, where $h$ is the typical size of the ``elements'' defining the GFEM--space $S$ and $\\gamma \\ge 0 $ is such that the local approximation spaces contain all polynomials of degree $k + \\gamma + 1$. The main technical result is an extension of the c","authors_text":"Ivo Babuska, Victor Nistor","cross_cats":["cs.NA","math.AP"],"headline":"","license":"","primary_cat":"math.NA","submitted_at":"2004-10-06T20:29:45Z","title":"Interior numerical approximation of boundary value problems with a distributional data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0410184","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":"sha256:63542b01b6fc9e05cb74c58322a2618d38a311baee672f18fbe5fa99858e3a25","target":"record","created_at":"2026-06-03T22:06:15Z","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":"86eedfef14935fa5bec42b5c3acd05cba036f2950acd692b99982a33c9c4984f","cross_cats_sorted":["cs.NA","math.AP"],"license":"","primary_cat":"math.NA","submitted_at":"2004-10-06T20:29:45Z","title_canon_sha256":"dba2fd41067cce29f18b59cc10745de891f40f200351957888aae27474ce2a7a"},"schema_version":"1.0","source":{"id":"math/0410184","kind":"arxiv","version":1}},"canonical_sha256":"fb6a92b2975125fb24eb9df44cd3f06472e9bdeebb42db692ead915a95111185","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fb6a92b2975125fb24eb9df44cd3f06472e9bdeebb42db692ead915a95111185","first_computed_at":"2026-06-03T22:06:15.818549Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T22:06:15.818549Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UCSdfh/DVh+befxl00JSfolNbs7N6gvADH+hv3Nb2couemIaZJfPmKHAoONlc3OZk7arUdv+Wu90eS57VTAiCQ==","signature_status":"signed_v1","signed_at":"2026-06-03T22:06:15.818977Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0410184","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:63542b01b6fc9e05cb74c58322a2618d38a311baee672f18fbe5fa99858e3a25","sha256:0cbad94f25686f1888d4b449d80e29dae7c7c185f73edd62c469b67aaf9d27bb"],"state_sha256":"2c703ab57474e1bc9d849c810f3ee3d868e7de87d9e7d69663650ff8f5b5e6f7"}