{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:4XI2XBU745CNO5WENEADI7UFJB","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":"78d121e2dc9a0c9d9a93ebce5ba811d3a3cd1bf698e4cf6f006976a774e8324b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-03-25T15:48:14Z","title_canon_sha256":"e451c53f930589fc28950106cd4f073322b54924e46c01faee33f0107fbd283d"},"schema_version":"1.0","source":{"id":"1903.10409","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.10409","created_at":"2026-05-17T23:50:18Z"},{"alias_kind":"arxiv_version","alias_value":"1903.10409v2","created_at":"2026-05-17T23:50:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.10409","created_at":"2026-05-17T23:50:18Z"},{"alias_kind":"pith_short_12","alias_value":"4XI2XBU745CN","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"4XI2XBU745CNO5WE","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"4XI2XBU7","created_at":"2026-05-18T12:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:a85573ff2a9fa6a35d4cf29f77402a162124e68d201332a321846b54e73b2a29","target":"graph","created_at":"2026-05-17T23:50:18Z","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":"For the discretization of the integral fractional Laplacian $(-\\Delta)^s$, $0 < s < 1$, based on piecewise linear functions, we present and analyze a reliable weighted residual a posteriori error estimator. In order to compensate for a lack of $L^2$-regularity of the residual in the regime $3/4 < s < 1$, this weighted residual error estimator includes as an additional weight a power of the distance from the mesh skeleton. We prove optimal convergence rates for an $h$-adaptive algorithm driven by this error estimator. Key to the analysis of the adaptive algorithm are local inverse estimates for","authors_text":"Dirk Praetorius, Jens Markus Melenk, Markus Faustmann","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-03-25T15:48:14Z","title":"Quasi-optimal convergence rate for an adaptive method for the integral fractional Laplacian"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.10409","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":"sha256:460dffb2330d7032f42c4933ed0558b54c90003e67cf25fae30ee6823c60f946","target":"record","created_at":"2026-05-17T23:50:18Z","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":"78d121e2dc9a0c9d9a93ebce5ba811d3a3cd1bf698e4cf6f006976a774e8324b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-03-25T15:48:14Z","title_canon_sha256":"e451c53f930589fc28950106cd4f073322b54924e46c01faee33f0107fbd283d"},"schema_version":"1.0","source":{"id":"1903.10409","kind":"arxiv","version":2}},"canonical_sha256":"e5d1ab869fe744d776c46900347e8548456902c7973a1dc95a0b9576bf88c338","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e5d1ab869fe744d776c46900347e8548456902c7973a1dc95a0b9576bf88c338","first_computed_at":"2026-05-17T23:50:18.618440Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:18.618440Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b0/4BiNcoscMKc1yJDZYdhsTzkApQR+4lamqpZr/l6yLz6Y1qwDPbR1JA4ubb0xPkv7JCwnfIItQXdBi4eBDBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:18.619008Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.10409","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:460dffb2330d7032f42c4933ed0558b54c90003e67cf25fae30ee6823c60f946","sha256:a85573ff2a9fa6a35d4cf29f77402a162124e68d201332a321846b54e73b2a29"],"state_sha256":"de4ee74275ba94edc86adf16233c1459e3b56b4b51945abdf645cba978cbb8d9"}