{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:QKGZ4LHEVIMURD44WKNO53KDYW","short_pith_number":"pith:QKGZ4LHE","schema_version":"1.0","canonical_sha256":"828d9e2ce4aa19488f9cb29aeeed43c5a802828a869b63f196582813ce35a496","source":{"kind":"arxiv","id":"1403.5750","version":3},"attestation_state":"computed","paper":{"title":"An algorithmic exploration of the existence of high-order summation by parts operators with diagonal norm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Joshua Klarmann, Nathan Albin","submitted_at":"2014-03-23T13:18:43Z","abstract_excerpt":"This paper explores a common class of diagonal-norm summation by parts (SBP) operators found in the literature, which can be parameterized by an integer triple $(s,t,r)$ representing the interior order of accuracy ($2s)$, the boundary order of accuracy ($t$), and the dimension of the boundary closure ($r$). There is no simple formula for determining whether or not an SBP operator exists for a given triple of parameters. Instead, one must check that certain compatibility conditions are met: namely that a particular linear system of equations has a positive solution. Partly because of the comple"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1403.5750","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-03-23T13:18:43Z","cross_cats_sorted":[],"title_canon_sha256":"1fe0a8d0f8d073db95b1d879432e8b66d0b49613d6aa196afaa5386690a13667","abstract_canon_sha256":"ae08156bb6354901af6f0300c4214cf983dd50a51ee1e610c772fe778d6bec89"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:29.241334Z","signature_b64":"2iuyvkmn1gtwRvsaGfWPTaTzVLWwBDsoWDLoQ7im91Dmoqyh15eRGoId638qP2ifzPASTF4tGtgrncag+8MYAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"828d9e2ce4aa19488f9cb29aeeed43c5a802828a869b63f196582813ce35a496","last_reissued_at":"2026-05-18T01:08:29.240868Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:29.240868Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An algorithmic exploration of the existence of high-order summation by parts operators with diagonal norm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Joshua Klarmann, Nathan Albin","submitted_at":"2014-03-23T13:18:43Z","abstract_excerpt":"This paper explores a common class of diagonal-norm summation by parts (SBP) operators found in the literature, which can be parameterized by an integer triple $(s,t,r)$ representing the interior order of accuracy ($2s)$, the boundary order of accuracy ($t$), and the dimension of the boundary closure ($r$). There is no simple formula for determining whether or not an SBP operator exists for a given triple of parameters. Instead, one must check that certain compatibility conditions are met: namely that a particular linear system of equations has a positive solution. Partly because of the comple"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5750","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1403.5750","created_at":"2026-05-18T01:08:29.240948+00:00"},{"alias_kind":"arxiv_version","alias_value":"1403.5750v3","created_at":"2026-05-18T01:08:29.240948+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.5750","created_at":"2026-05-18T01:08:29.240948+00:00"},{"alias_kind":"pith_short_12","alias_value":"QKGZ4LHEVIMU","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_16","alias_value":"QKGZ4LHEVIMURD44","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_8","alias_value":"QKGZ4LHE","created_at":"2026-05-18T12:28:46.137349+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QKGZ4LHEVIMURD44WKNO53KDYW","json":"https://pith.science/pith/QKGZ4LHEVIMURD44WKNO53KDYW.json","graph_json":"https://pith.science/api/pith-number/QKGZ4LHEVIMURD44WKNO53KDYW/graph.json","events_json":"https://pith.science/api/pith-number/QKGZ4LHEVIMURD44WKNO53KDYW/events.json","paper":"https://pith.science/paper/QKGZ4LHE"},"agent_actions":{"view_html":"https://pith.science/pith/QKGZ4LHEVIMURD44WKNO53KDYW","download_json":"https://pith.science/pith/QKGZ4LHEVIMURD44WKNO53KDYW.json","view_paper":"https://pith.science/paper/QKGZ4LHE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1403.5750&json=true","fetch_graph":"https://pith.science/api/pith-number/QKGZ4LHEVIMURD44WKNO53KDYW/graph.json","fetch_events":"https://pith.science/api/pith-number/QKGZ4LHEVIMURD44WKNO53KDYW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QKGZ4LHEVIMURD44WKNO53KDYW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QKGZ4LHEVIMURD44WKNO53KDYW/action/storage_attestation","attest_author":"https://pith.science/pith/QKGZ4LHEVIMURD44WKNO53KDYW/action/author_attestation","sign_citation":"https://pith.science/pith/QKGZ4LHEVIMURD44WKNO53KDYW/action/citation_signature","submit_replication":"https://pith.science/pith/QKGZ4LHEVIMURD44WKNO53KDYW/action/replication_record"}},"created_at":"2026-05-18T01:08:29.240948+00:00","updated_at":"2026-05-18T01:08:29.240948+00:00"}