{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:QDW4EK5WJ7CPVNJZ3OTKETXJFA","short_pith_number":"pith:QDW4EK5W","canonical_record":{"source":{"id":"1410.5029","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2014-10-19T02:31:57Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"cf6fe26fae948fb49a18933f86248fc67d6d24467f6f7e8cc37596fbbf8e3ba8","abstract_canon_sha256":"50a12acc03587501d16b8071e707bbe8c1dba89c0befee8a45c6ab36b71cce04"},"schema_version":"1.0"},"canonical_sha256":"80edc22bb64fc4fab539dba6a24ee928341225af308823d3777fee9971cca807","source":{"kind":"arxiv","id":"1410.5029","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.5029","created_at":"2026-05-18T02:39:47Z"},{"alias_kind":"arxiv_version","alias_value":"1410.5029v1","created_at":"2026-05-18T02:39:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.5029","created_at":"2026-05-18T02:39:47Z"},{"alias_kind":"pith_short_12","alias_value":"QDW4EK5WJ7CP","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"QDW4EK5WJ7CPVNJZ","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"QDW4EK5W","created_at":"2026-05-18T12:28:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:QDW4EK5WJ7CPVNJZ3OTKETXJFA","target":"record","payload":{"canonical_record":{"source":{"id":"1410.5029","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2014-10-19T02:31:57Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"cf6fe26fae948fb49a18933f86248fc67d6d24467f6f7e8cc37596fbbf8e3ba8","abstract_canon_sha256":"50a12acc03587501d16b8071e707bbe8c1dba89c0befee8a45c6ab36b71cce04"},"schema_version":"1.0"},"canonical_sha256":"80edc22bb64fc4fab539dba6a24ee928341225af308823d3777fee9971cca807","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:39:47.148862Z","signature_b64":"zK5ptoVDsTEQxD5rzpopPGGqhcwEynOb8U2m5c5FbfFIhRYFPNIqehLgSTRK6NKJOWchquY9ChFZNFgtqJfrBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"80edc22bb64fc4fab539dba6a24ee928341225af308823d3777fee9971cca807","last_reissued_at":"2026-05-18T02:39:47.148372Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:39:47.148372Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.5029","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:39:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RrtRjEhGEcCl5mAHxakwyu6qvU/Ie9OZRbx1bZi0RaE/82x2BgcIWon+x8r6n8iCHEc1l12uqXVUFY3gyOVGAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T21:14:14.379021Z"},"content_sha256":"d5b4036c4efc58527113910017a1f4b412a32a1f3f00cd856bb06575d019378c","schema_version":"1.0","event_id":"sha256:d5b4036c4efc58527113910017a1f4b412a32a1f3f00cd856bb06575d019378c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:QDW4EK5WJ7CPVNJZ3OTKETXJFA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized Summation-by-Parts Operators for the Second Derivative with Variable Coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"cs.NA","authors_text":"David C. Del Rey Fern\\'andez, David W. Zingg","submitted_at":"2014-10-19T02:31:57Z","abstract_excerpt":"The comprehensive generalization of summation-by-parts of Del Rey Fern\\'andez et al.\\ (J. Comput. Phys., 266, 2014) is extended to approximations of second derivatives with variable coefficients. This enables the construction of second-derivative operators with one or more of the following characteristics: i) non-repeating interior stencil, ii) nonuniform nodal distributions, and iii) exclusion of one or both boundary nodes. Definitions are proposed that give rise to generalized SBP operators that result in consistent, conservative, and stable discretizations of PDEs with or without mixed deri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.5029","kind":"arxiv","version":1},"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":"2026-05-18T02:39:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JF+KLP8T93hvJWxXJxUo4yMztIJmumKz2/Z9VX5jEN7VIqQE0ASmHnBMGaMWc4879CJ1o5X/ezryoFv2Zko+Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T21:14:14.379739Z"},"content_sha256":"cd8f50ecae7673ffc30bb1faeb2dc9693cef0ddb769914d06afeb22c2c2eb42a","schema_version":"1.0","event_id":"sha256:cd8f50ecae7673ffc30bb1faeb2dc9693cef0ddb769914d06afeb22c2c2eb42a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QDW4EK5WJ7CPVNJZ3OTKETXJFA/bundle.json","state_url":"https://pith.science/pith/QDW4EK5WJ7CPVNJZ3OTKETXJFA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QDW4EK5WJ7CPVNJZ3OTKETXJFA/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":"2026-06-05T21:14:14Z","links":{"resolver":"https://pith.science/pith/QDW4EK5WJ7CPVNJZ3OTKETXJFA","bundle":"https://pith.science/pith/QDW4EK5WJ7CPVNJZ3OTKETXJFA/bundle.json","state":"https://pith.science/pith/QDW4EK5WJ7CPVNJZ3OTKETXJFA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QDW4EK5WJ7CPVNJZ3OTKETXJFA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:QDW4EK5WJ7CPVNJZ3OTKETXJFA","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":"50a12acc03587501d16b8071e707bbe8c1dba89c0befee8a45c6ab36b71cce04","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2014-10-19T02:31:57Z","title_canon_sha256":"cf6fe26fae948fb49a18933f86248fc67d6d24467f6f7e8cc37596fbbf8e3ba8"},"schema_version":"1.0","source":{"id":"1410.5029","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.5029","created_at":"2026-05-18T02:39:47Z"},{"alias_kind":"arxiv_version","alias_value":"1410.5029v1","created_at":"2026-05-18T02:39:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.5029","created_at":"2026-05-18T02:39:47Z"},{"alias_kind":"pith_short_12","alias_value":"QDW4EK5WJ7CP","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"QDW4EK5WJ7CPVNJZ","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"QDW4EK5W","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:cd8f50ecae7673ffc30bb1faeb2dc9693cef0ddb769914d06afeb22c2c2eb42a","target":"graph","created_at":"2026-05-18T02:39:47Z","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":"The comprehensive generalization of summation-by-parts of Del Rey Fern\\'andez et al.\\ (J. Comput. Phys., 266, 2014) is extended to approximations of second derivatives with variable coefficients. This enables the construction of second-derivative operators with one or more of the following characteristics: i) non-repeating interior stencil, ii) nonuniform nodal distributions, and iii) exclusion of one or both boundary nodes. Definitions are proposed that give rise to generalized SBP operators that result in consistent, conservative, and stable discretizations of PDEs with or without mixed deri","authors_text":"David C. Del Rey Fern\\'andez, David W. Zingg","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2014-10-19T02:31:57Z","title":"Generalized Summation-by-Parts Operators for the Second Derivative with Variable Coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.5029","kind":"arxiv","version":1},"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:d5b4036c4efc58527113910017a1f4b412a32a1f3f00cd856bb06575d019378c","target":"record","created_at":"2026-05-18T02:39:47Z","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":"50a12acc03587501d16b8071e707bbe8c1dba89c0befee8a45c6ab36b71cce04","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2014-10-19T02:31:57Z","title_canon_sha256":"cf6fe26fae948fb49a18933f86248fc67d6d24467f6f7e8cc37596fbbf8e3ba8"},"schema_version":"1.0","source":{"id":"1410.5029","kind":"arxiv","version":1}},"canonical_sha256":"80edc22bb64fc4fab539dba6a24ee928341225af308823d3777fee9971cca807","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"80edc22bb64fc4fab539dba6a24ee928341225af308823d3777fee9971cca807","first_computed_at":"2026-05-18T02:39:47.148372Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:39:47.148372Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zK5ptoVDsTEQxD5rzpopPGGqhcwEynOb8U2m5c5FbfFIhRYFPNIqehLgSTRK6NKJOWchquY9ChFZNFgtqJfrBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:39:47.148862Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.5029","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d5b4036c4efc58527113910017a1f4b412a32a1f3f00cd856bb06575d019378c","sha256:cd8f50ecae7673ffc30bb1faeb2dc9693cef0ddb769914d06afeb22c2c2eb42a"],"state_sha256":"e0bba9e0e45a76c7f4bd52b10fa134b5322f30d7c8ebfe138d0a29c06b7d44cf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lhgcu8mlYnMdsJTvYreRei0rn/GG+zSE9I+zeDGLN/IXR9NsfZqTqAHSog+OdO0XDSUiZGYbqI0e725r9Ik1Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T21:14:14.383555Z","bundle_sha256":"e51ad78e3b6305ce822423f437705b48f3b6522c717ba117811a1f5ac99cfd66"}}