{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:ZKQJD7BZWNMZHY6HZWSNW5R67G","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":"03ee59197930b4f1c6b216ac339710feacf0bd4bebf0fc81f57000f906445008","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2009-11-06T13:27:24Z","title_canon_sha256":"2362c3add7a06791f4f30754b09a2ef8b1355dbbf90b4e10c33445da9f2c4e42"},"schema_version":"1.0","source":{"id":"0911.1245","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.1245","created_at":"2026-05-18T03:07:41Z"},{"alias_kind":"arxiv_version","alias_value":"0911.1245v2","created_at":"2026-05-18T03:07:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.1245","created_at":"2026-05-18T03:07:41Z"},{"alias_kind":"pith_short_12","alias_value":"ZKQJD7BZWNMZ","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"ZKQJD7BZWNMZHY6H","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"ZKQJD7BZ","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:675ea852fbab8fcd8f9475d42d7a82c53305f0104f3a6d64cf37318799791fe5","target":"graph","created_at":"2026-05-18T03:07:41Z","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":"In most recent substructuring methods, a fundamental role is played by the coarse space. For some of these methods (e.g. BDDC and FETI-DP), its definition relies on a 'minimal' set of coarse nodes (sometimes called corners) which assures invertibility of local subdomain problems and also of the global coarse problem. This basic set is typically enhanced by enforcing continuity of functions at some generalized degrees of freedom, such as average values on edges or faces of subdomains. We revisit existing algorithms for selection of corners. The main contribution of this paper consists of propos","authors_text":"Jakub \\v{S}\\'istek, Jaroslav Novotn\\'y, Marta \\v{C}ert\\'ikov\\'a, Pavel Burda","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2009-11-06T13:27:24Z","title":"Face-based Selection of Corners in 3D Substructuring"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.1245","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":"sha256:9449b0ceaa63dd58c8ec898e8a77848de49b6aabed8e20304c648dd96053f472","target":"record","created_at":"2026-05-18T03:07:41Z","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":"03ee59197930b4f1c6b216ac339710feacf0bd4bebf0fc81f57000f906445008","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2009-11-06T13:27:24Z","title_canon_sha256":"2362c3add7a06791f4f30754b09a2ef8b1355dbbf90b4e10c33445da9f2c4e42"},"schema_version":"1.0","source":{"id":"0911.1245","kind":"arxiv","version":2}},"canonical_sha256":"caa091fc39b35993e3c7cda4db763ef9aee1e7d36eefc9d2ab04fa69cad9426a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"caa091fc39b35993e3c7cda4db763ef9aee1e7d36eefc9d2ab04fa69cad9426a","first_computed_at":"2026-05-18T03:07:41.626779Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:07:41.626779Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lKVh9NgOVrHNsXhOP35/HrRrTFCrj9roNjTYivT21pZ6nVtjDAciXnJxbamPb02GML5jBtDyVuhviVfwSgDHDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:07:41.627246Z","signed_message":"canonical_sha256_bytes"},"source_id":"0911.1245","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9449b0ceaa63dd58c8ec898e8a77848de49b6aabed8e20304c648dd96053f472","sha256:675ea852fbab8fcd8f9475d42d7a82c53305f0104f3a6d64cf37318799791fe5"],"state_sha256":"0b2b1f99c63e05b203ad88e039dc0545cdb3b254b95491e61e760ab9b26857c8"}