{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:GMWMB63MJO4UOOFIFIEIBGYKL7","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":"647b4e311770cc385637fabfb7c8120e1fdbdb918e9e7b960aa05827adc916a1","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2017-07-11T09:50:48Z","title_canon_sha256":"8c7bad5936980b7c56c31abd545fc7b8d6d6bf941388097fc87061ea3b350b6e"},"schema_version":"1.0","source":{"id":"1707.03201","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.03201","created_at":"2026-05-18T00:14:59Z"},{"alias_kind":"arxiv_version","alias_value":"1707.03201v3","created_at":"2026-05-18T00:14:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.03201","created_at":"2026-05-18T00:14:59Z"},{"alias_kind":"pith_short_12","alias_value":"GMWMB63MJO4U","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"GMWMB63MJO4UOOFI","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"GMWMB63M","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:b5fc35dcbf72c28a1c7061e0e8698927dad502575a27673363e0cae7d2f6d22d","target":"graph","created_at":"2026-05-18T00:14:59Z","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":"This work presents a numerical study of functional type a posteriori error estimates for IgA approximation schemes in the context of elliptic boundary-value problems. Along with the detailed discussion of the most crucial properties of such estimates, we present the algorithm of a reliable solution approximation together with the scheme of efficient a posteriori error bound generation-based on solving an auxiliary problem with respect to an introduced vector-valued variable. In this approach, we take advantage of B-(THB-)spline's high smoothness for the auxiliary vector function reconstruction","authors_text":"Svetlana Matculevich","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2017-07-11T09:50:48Z","title":"Functional approach to the error control in adaptive IgA schemes for elliptic boundary value problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.03201","kind":"arxiv","version":3},"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":"sha256:1ae5d5239cd5835c91d295a0f89c438acda5978a46a7fc8218f45b0e79bd493f","target":"record","created_at":"2026-05-18T00:14:59Z","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":"647b4e311770cc385637fabfb7c8120e1fdbdb918e9e7b960aa05827adc916a1","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2017-07-11T09:50:48Z","title_canon_sha256":"8c7bad5936980b7c56c31abd545fc7b8d6d6bf941388097fc87061ea3b350b6e"},"schema_version":"1.0","source":{"id":"1707.03201","kind":"arxiv","version":3}},"canonical_sha256":"332cc0fb6c4bb94738a82a08809b0a5ff5ce8581471710a34086ad667cfc4b37","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"332cc0fb6c4bb94738a82a08809b0a5ff5ce8581471710a34086ad667cfc4b37","first_computed_at":"2026-05-18T00:14:59.998190Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:59.998190Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SGctYjiukPnFstkwv4XTPgzrLJ1cWS3uC7WnjOphhQIosslip3bWABglQx/yO4YQqGE7yy2Rd6BnVhKxvqwyCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:59.998718Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.03201","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1ae5d5239cd5835c91d295a0f89c438acda5978a46a7fc8218f45b0e79bd493f","sha256:b5fc35dcbf72c28a1c7061e0e8698927dad502575a27673363e0cae7d2f6d22d"],"state_sha256":"fa753e109ed7e0b87da777452b0bcfc78cf1ea880d74dd25349ac402e8970d8d"}