{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:KAQJDDAPJRYUQLRMSKLBJOYPMA","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":"2da77615bff9f9c8b555cd3ffe1c57f36b36e744448fab67cef350090f7a03f1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-05-12T19:21:54Z","title_canon_sha256":"758c623a9e9183841dca77a221f505c4846130a9df7f491d1c9ceb812e67751e"},"schema_version":"1.0","source":{"id":"1505.03125","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.03125","created_at":"2026-05-18T01:33:58Z"},{"alias_kind":"arxiv_version","alias_value":"1505.03125v3","created_at":"2026-05-18T01:33:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.03125","created_at":"2026-05-18T01:33:58Z"},{"alias_kind":"pith_short_12","alias_value":"KAQJDDAPJRYU","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"KAQJDDAPJRYUQLRM","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"KAQJDDAP","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:bbf2406e6f78a9b4ab422c339af986839bb9154460215938fb94c6966731b908","target":"graph","created_at":"2026-05-18T01:33:58Z","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":"Summation-by-parts (SBP) finite-difference discretizations share many attractive properties with Galerkin finite-element methods (FEMs), including time stability and superconvergent functionals; however, unlike FEMs, SBP operators are not completely determined by a basis, so the potential exists to tailor SBP operators to meet different objectives. To date, application of high-order SBP discretizations to multiple dimensions has been limited to tensor product domains. This paper presents a definition for multi-dimensional SBP finite-difference operators that is a natural extension of one-dimen","authors_text":"David C. Del Rey Fern\\'andez, David W. Zingg, Jason E. Hicken","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-05-12T19:21:54Z","title":"Multidimensional Summation-By-Parts Operators: General Theory and Application to Simplex Elements"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.03125","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":"sha256:722e0a07a05f72683bd2ef0fede7a34665cfd0ef12d0f6ebc7375cd56de9c9c6","target":"record","created_at":"2026-05-18T01:33:58Z","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":"2da77615bff9f9c8b555cd3ffe1c57f36b36e744448fab67cef350090f7a03f1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-05-12T19:21:54Z","title_canon_sha256":"758c623a9e9183841dca77a221f505c4846130a9df7f491d1c9ceb812e67751e"},"schema_version":"1.0","source":{"id":"1505.03125","kind":"arxiv","version":3}},"canonical_sha256":"5020918c0f4c71482e2c929614bb0f60202cba6e62873dd90aebd2230d463a7c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5020918c0f4c71482e2c929614bb0f60202cba6e62873dd90aebd2230d463a7c","first_computed_at":"2026-05-18T01:33:58.351057Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:33:58.351057Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wnnMJFq1ZZBP+D7qEBi4K/nB507njJZ6wZ06TdQIZqIo8B9xWUtb1GnlK0blzIYCpt3LwUWBztrLvvNRDvzzCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:33:58.351472Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.03125","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:722e0a07a05f72683bd2ef0fede7a34665cfd0ef12d0f6ebc7375cd56de9c9c6","sha256:bbf2406e6f78a9b4ab422c339af986839bb9154460215938fb94c6966731b908"],"state_sha256":"d974f6eef704d85656005e857104bdda54a22c4b63f937f5178685c5fe53621e"}