{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:CZ2FTPZUNVKDLYO6Y7JFCSOXRH","short_pith_number":"pith:CZ2FTPZU","canonical_record":{"source":{"id":"1205.6504","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-05-29T22:02:21Z","cross_cats_sorted":[],"title_canon_sha256":"68d5d64333423dace0f0437c75e977f6274a0f12b6e524e0689d15253d08b9cc","abstract_canon_sha256":"d595a27844d5e7cec52fe1c107269377803938d27ee635a3d71322d48d1c30a9"},"schema_version":"1.0"},"canonical_sha256":"167459bf346d5435e1dec7d25149d789e9a7afb2183d1577b4918f97b180193e","source":{"kind":"arxiv","id":"1205.6504","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.6504","created_at":"2026-05-18T03:34:38Z"},{"alias_kind":"arxiv_version","alias_value":"1205.6504v3","created_at":"2026-05-18T03:34:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.6504","created_at":"2026-05-18T03:34:38Z"},{"alias_kind":"pith_short_12","alias_value":"CZ2FTPZUNVKD","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CZ2FTPZUNVKDLYO6","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CZ2FTPZU","created_at":"2026-05-18T12:27:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:CZ2FTPZUNVKDLYO6Y7JFCSOXRH","target":"record","payload":{"canonical_record":{"source":{"id":"1205.6504","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-05-29T22:02:21Z","cross_cats_sorted":[],"title_canon_sha256":"68d5d64333423dace0f0437c75e977f6274a0f12b6e524e0689d15253d08b9cc","abstract_canon_sha256":"d595a27844d5e7cec52fe1c107269377803938d27ee635a3d71322d48d1c30a9"},"schema_version":"1.0"},"canonical_sha256":"167459bf346d5435e1dec7d25149d789e9a7afb2183d1577b4918f97b180193e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:34:38.210760Z","signature_b64":"o0uIU62LiKBRxhQzKiCGXStsL8X75ABt5Yk9H5fcNzDFDmIR21KIGrAOjVMxThuY0MP/QkKAzzUoEa0DyzFQAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"167459bf346d5435e1dec7d25149d789e9a7afb2183d1577b4918f97b180193e","last_reissued_at":"2026-05-18T03:34:38.210173Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:34:38.210173Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.6504","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":"2026-05-18T03:34:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Sa5UtlF17rX2VDEIBtvsWRhKNSSUcHT801c3l0hE4oUAKR1TN7AEI7WsgnoJ2Y0TmWfK87dRIKOu67vgOxg7Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T18:32:44.086501Z"},"content_sha256":"c071b3373d7a3f6f9f59ee2dc6da49be68da61879a37c01cb48dca9185209b4a","schema_version":"1.0","event_id":"sha256:c071b3373d7a3f6f9f59ee2dc6da49be68da61879a37c01cb48dca9185209b4a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:CZ2FTPZUNVKDLYO6Y7JFCSOXRH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Richardson Extrapolation for Linearly Degenerate Discontinuities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"J. W. Banks, T. D. Aslam","submitted_at":"2012-05-29T22:02:21Z","abstract_excerpt":"In this paper we investigate the use of Richardson extrapolation to estimate the convergence rates for numerical solutions to advection problems involving discontinuities. We use modified equation analysis to describe the expectation of the approach. In general, the results do not agree with a-priori estimates of the convergence rates. However, we identify one particular use case where Richardson extrapolation does yield the proper result. We then demonstrate this result using a number of numerical examples."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6504","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":"2026-05-18T03:34:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DE6qxMe+0ESmMLb6eTwdOdfRseuIBZ9sjBCwuiosF4n4AubJ0RNRjEZC/jFU8/jM5AduDU89jqkpVMGPSPiCDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T18:32:44.087214Z"},"content_sha256":"5d3d6f449224384a9aaafb7c873d6380f8fe98a268946e86c3d76e649646b73f","schema_version":"1.0","event_id":"sha256:5d3d6f449224384a9aaafb7c873d6380f8fe98a268946e86c3d76e649646b73f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CZ2FTPZUNVKDLYO6Y7JFCSOXRH/bundle.json","state_url":"https://pith.science/pith/CZ2FTPZUNVKDLYO6Y7JFCSOXRH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CZ2FTPZUNVKDLYO6Y7JFCSOXRH/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":"2026-06-07T18:32:44Z","links":{"resolver":"https://pith.science/pith/CZ2FTPZUNVKDLYO6Y7JFCSOXRH","bundle":"https://pith.science/pith/CZ2FTPZUNVKDLYO6Y7JFCSOXRH/bundle.json","state":"https://pith.science/pith/CZ2FTPZUNVKDLYO6Y7JFCSOXRH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CZ2FTPZUNVKDLYO6Y7JFCSOXRH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:CZ2FTPZUNVKDLYO6Y7JFCSOXRH","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":"d595a27844d5e7cec52fe1c107269377803938d27ee635a3d71322d48d1c30a9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-05-29T22:02:21Z","title_canon_sha256":"68d5d64333423dace0f0437c75e977f6274a0f12b6e524e0689d15253d08b9cc"},"schema_version":"1.0","source":{"id":"1205.6504","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.6504","created_at":"2026-05-18T03:34:38Z"},{"alias_kind":"arxiv_version","alias_value":"1205.6504v3","created_at":"2026-05-18T03:34:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.6504","created_at":"2026-05-18T03:34:38Z"},{"alias_kind":"pith_short_12","alias_value":"CZ2FTPZUNVKD","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CZ2FTPZUNVKDLYO6","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CZ2FTPZU","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:5d3d6f449224384a9aaafb7c873d6380f8fe98a268946e86c3d76e649646b73f","target":"graph","created_at":"2026-05-18T03:34:38Z","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 this paper we investigate the use of Richardson extrapolation to estimate the convergence rates for numerical solutions to advection problems involving discontinuities. We use modified equation analysis to describe the expectation of the approach. In general, the results do not agree with a-priori estimates of the convergence rates. However, we identify one particular use case where Richardson extrapolation does yield the proper result. We then demonstrate this result using a number of numerical examples.","authors_text":"J. W. Banks, T. D. Aslam","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-05-29T22:02:21Z","title":"Richardson Extrapolation for Linearly Degenerate Discontinuities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6504","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:c071b3373d7a3f6f9f59ee2dc6da49be68da61879a37c01cb48dca9185209b4a","target":"record","created_at":"2026-05-18T03:34:38Z","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":"d595a27844d5e7cec52fe1c107269377803938d27ee635a3d71322d48d1c30a9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-05-29T22:02:21Z","title_canon_sha256":"68d5d64333423dace0f0437c75e977f6274a0f12b6e524e0689d15253d08b9cc"},"schema_version":"1.0","source":{"id":"1205.6504","kind":"arxiv","version":3}},"canonical_sha256":"167459bf346d5435e1dec7d25149d789e9a7afb2183d1577b4918f97b180193e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"167459bf346d5435e1dec7d25149d789e9a7afb2183d1577b4918f97b180193e","first_computed_at":"2026-05-18T03:34:38.210173Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:34:38.210173Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o0uIU62LiKBRxhQzKiCGXStsL8X75ABt5Yk9H5fcNzDFDmIR21KIGrAOjVMxThuY0MP/QkKAzzUoEa0DyzFQAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:34:38.210760Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.6504","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c071b3373d7a3f6f9f59ee2dc6da49be68da61879a37c01cb48dca9185209b4a","sha256:5d3d6f449224384a9aaafb7c873d6380f8fe98a268946e86c3d76e649646b73f"],"state_sha256":"3aae5cbc4aa90f853c8b02f635f86e218ccf2acf919cf9c3d8c10bbb0e79e00f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GvpXcVGDKjuvsfQEXwfur+9e1RmFrwPR6ZMKn7IWstbLfqS/3Fb2gYIDc4Kwf5GP/CGBkp7IF1Sky8HB3YNMCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T18:32:44.091010Z","bundle_sha256":"82907eeab5435404e18721a6596f0fa85add42780c9504d3de64185b06d614a4"}}