{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:KAQJDDAPJRYUQLRMSKLBJOYPMA","short_pith_number":"pith:KAQJDDAP","canonical_record":{"source":{"id":"1505.03125","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-05-12T19:21:54Z","cross_cats_sorted":[],"title_canon_sha256":"758c623a9e9183841dca77a221f505c4846130a9df7f491d1c9ceb812e67751e","abstract_canon_sha256":"2da77615bff9f9c8b555cd3ffe1c57f36b36e744448fab67cef350090f7a03f1"},"schema_version":"1.0"},"canonical_sha256":"5020918c0f4c71482e2c929614bb0f60202cba6e62873dd90aebd2230d463a7c","source":{"kind":"arxiv","id":"1505.03125","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:KAQJDDAPJRYUQLRMSKLBJOYPMA","target":"record","payload":{"canonical_record":{"source":{"id":"1505.03125","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-05-12T19:21:54Z","cross_cats_sorted":[],"title_canon_sha256":"758c623a9e9183841dca77a221f505c4846130a9df7f491d1c9ceb812e67751e","abstract_canon_sha256":"2da77615bff9f9c8b555cd3ffe1c57f36b36e744448fab67cef350090f7a03f1"},"schema_version":"1.0"},"canonical_sha256":"5020918c0f4c71482e2c929614bb0f60202cba6e62873dd90aebd2230d463a7c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:58.351472Z","signature_b64":"wnnMJFq1ZZBP+D7qEBi4K/nB507njJZ6wZ06TdQIZqIo8B9xWUtb1GnlK0blzIYCpt3LwUWBztrLvvNRDvzzCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5020918c0f4c71482e2c929614bb0f60202cba6e62873dd90aebd2230d463a7c","last_reissued_at":"2026-05-18T01:33:58.351057Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:58.351057Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.03125","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:33:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VSIxlI1QCCil6t9KYq0lwZCObiSWolg1ih5Lb6O05q/3ZFC8Hkq85VOA3E3eh3TJCf/2ztbW3KNlu2FlkYrjBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T02:21:01.282611Z"},"content_sha256":"722e0a07a05f72683bd2ef0fede7a34665cfd0ef12d0f6ebc7375cd56de9c9c6","schema_version":"1.0","event_id":"sha256:722e0a07a05f72683bd2ef0fede7a34665cfd0ef12d0f6ebc7375cd56de9c9c6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:KAQJDDAPJRYUQLRMSKLBJOYPMA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multidimensional Summation-By-Parts Operators: General Theory and Application to Simplex Elements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"David C. Del Rey Fern\\'andez, David W. Zingg, Jason E. Hicken","submitted_at":"2015-05-12T19:21:54Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.03125","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:33:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SLAe6NKar7G2Mm6zfm2tRx4QCJRnbKLMMXjEzmHRCbpjK5dbsAOzUleGOZX55YI15nRW/eOgyR0u/0GrQn5XCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T02:21:01.283180Z"},"content_sha256":"bbf2406e6f78a9b4ab422c339af986839bb9154460215938fb94c6966731b908","schema_version":"1.0","event_id":"sha256:bbf2406e6f78a9b4ab422c339af986839bb9154460215938fb94c6966731b908"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KAQJDDAPJRYUQLRMSKLBJOYPMA/bundle.json","state_url":"https://pith.science/pith/KAQJDDAPJRYUQLRMSKLBJOYPMA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KAQJDDAPJRYUQLRMSKLBJOYPMA/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-05T02:21:01Z","links":{"resolver":"https://pith.science/pith/KAQJDDAPJRYUQLRMSKLBJOYPMA","bundle":"https://pith.science/pith/KAQJDDAPJRYUQLRMSKLBJOYPMA/bundle.json","state":"https://pith.science/pith/KAQJDDAPJRYUQLRMSKLBJOYPMA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KAQJDDAPJRYUQLRMSKLBJOYPMA/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JXIRzlnYRhCJg5sgjLLuRk0fFEwMLAi1eaHIH5b5Ygi0VgZOHa6vBAC3CQ86SIkjCREymplpgCw6wKnPn8c1Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T02:21:01.286156Z","bundle_sha256":"3bb6c5a084c453d23f7f6bbb12a717ad4c64ba25332f89f4b9419f5297c34421"}}