{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:H5LLJA7GDS4QEJ5Q6CKNV3QZUB","short_pith_number":"pith:H5LLJA7G","canonical_record":{"source":{"id":"0910.1841","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2009-10-09T20:03:39Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"b2e8cd5cfcc61b82794c9ed82a9a5b33d608859d0f8ffbb99be5e3b36b23b5a7","abstract_canon_sha256":"2baf04be5eaf34acd54c08c19f1e65a56521e2a445f33c80ab4136eb34b1bba0"},"schema_version":"1.0"},"canonical_sha256":"3f56b483e61cb90227b0f094daee19a073e8784839f83c729dd7c6e5cd24b38c","source":{"kind":"arxiv","id":"0910.1841","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.1841","created_at":"2026-05-18T04:25:13Z"},{"alias_kind":"arxiv_version","alias_value":"0910.1841v4","created_at":"2026-05-18T04:25:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.1841","created_at":"2026-05-18T04:25:13Z"},{"alias_kind":"pith_short_12","alias_value":"H5LLJA7GDS4Q","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"H5LLJA7GDS4QEJ5Q","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"H5LLJA7G","created_at":"2026-05-18T12:25:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:H5LLJA7GDS4QEJ5Q6CKNV3QZUB","target":"record","payload":{"canonical_record":{"source":{"id":"0910.1841","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2009-10-09T20:03:39Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"b2e8cd5cfcc61b82794c9ed82a9a5b33d608859d0f8ffbb99be5e3b36b23b5a7","abstract_canon_sha256":"2baf04be5eaf34acd54c08c19f1e65a56521e2a445f33c80ab4136eb34b1bba0"},"schema_version":"1.0"},"canonical_sha256":"3f56b483e61cb90227b0f094daee19a073e8784839f83c729dd7c6e5cd24b38c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:25:13.380301Z","signature_b64":"dLoquFXHWJei3QrCIYKEzUYdwWtg281YRdwhMKa31yxumKkcxXxTNKxYuNY/eK/LnujPZJUxyPHA9WJeeQGpDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3f56b483e61cb90227b0f094daee19a073e8784839f83c729dd7c6e5cd24b38c","last_reissued_at":"2026-05-18T04:25:13.379577Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:25:13.379577Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0910.1841","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:25:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mBq+Hil2sIChw4o0biaWCz79Mrg5Xv8Ki+2fSPRfWv670HaCQ9E3XHQIQd5ISuocQ97nfjHh1CQtNgakCblUBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T21:48:23.040993Z"},"content_sha256":"127ad0429828a3d8beb89928da4e7c015ae44fdb547ce1cb10c3726b8d817716","schema_version":"1.0","event_id":"sha256:127ad0429828a3d8beb89928da4e7c015ae44fdb547ce1cb10c3726b8d817716"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:H5LLJA7GDS4QEJ5Q6CKNV3QZUB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Accuracy and Stability of Computing High-Order Derivatives of Analytic Functions by Cauchy Integrals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.NA","authors_text":"Folkmar Bornemann","submitted_at":"2009-10-09T20:03:39Z","abstract_excerpt":"High-order derivatives of analytic functions are expressible as Cauchy integrals over circular contours, which can very effectively be approximated, e.g., by trapezoidal sums. Whereas analytically each radius r up to the radius of convergence is equal, numerical stability strongly depends on r. We give a comprehensive study of this effect; in particular we show that there is a unique radius that minimizes the loss of accuracy caused by round-off errors. For large classes of functions, though not for all, this radius actually gives about full accuracy; a remarkable fact that we explain by the t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.1841","kind":"arxiv","version":4},"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":"2026-05-18T04:25:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W2TuYsUoQoo9LyEoYaGtp+c9Z02ajqouOt5tObHnKIfUQXVoq4NZX5dhndhdwDP00mU8+7hSwj3k23gekg1rDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T21:48:23.041589Z"},"content_sha256":"84f98098842c2d93ba3da602d5657f8f5c0b69c54cbfbfddcd106d9c988af050","schema_version":"1.0","event_id":"sha256:84f98098842c2d93ba3da602d5657f8f5c0b69c54cbfbfddcd106d9c988af050"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H5LLJA7GDS4QEJ5Q6CKNV3QZUB/bundle.json","state_url":"https://pith.science/pith/H5LLJA7GDS4QEJ5Q6CKNV3QZUB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H5LLJA7GDS4QEJ5Q6CKNV3QZUB/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":"2026-06-06T21:48:23Z","links":{"resolver":"https://pith.science/pith/H5LLJA7GDS4QEJ5Q6CKNV3QZUB","bundle":"https://pith.science/pith/H5LLJA7GDS4QEJ5Q6CKNV3QZUB/bundle.json","state":"https://pith.science/pith/H5LLJA7GDS4QEJ5Q6CKNV3QZUB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H5LLJA7GDS4QEJ5Q6CKNV3QZUB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:H5LLJA7GDS4QEJ5Q6CKNV3QZUB","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":"2baf04be5eaf34acd54c08c19f1e65a56521e2a445f33c80ab4136eb34b1bba0","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2009-10-09T20:03:39Z","title_canon_sha256":"b2e8cd5cfcc61b82794c9ed82a9a5b33d608859d0f8ffbb99be5e3b36b23b5a7"},"schema_version":"1.0","source":{"id":"0910.1841","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.1841","created_at":"2026-05-18T04:25:13Z"},{"alias_kind":"arxiv_version","alias_value":"0910.1841v4","created_at":"2026-05-18T04:25:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.1841","created_at":"2026-05-18T04:25:13Z"},{"alias_kind":"pith_short_12","alias_value":"H5LLJA7GDS4Q","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"H5LLJA7GDS4QEJ5Q","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"H5LLJA7G","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:84f98098842c2d93ba3da602d5657f8f5c0b69c54cbfbfddcd106d9c988af050","target":"graph","created_at":"2026-05-18T04:25:13Z","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":"High-order derivatives of analytic functions are expressible as Cauchy integrals over circular contours, which can very effectively be approximated, e.g., by trapezoidal sums. Whereas analytically each radius r up to the radius of convergence is equal, numerical stability strongly depends on r. We give a comprehensive study of this effect; in particular we show that there is a unique radius that minimizes the loss of accuracy caused by round-off errors. For large classes of functions, though not for all, this radius actually gives about full accuracy; a remarkable fact that we explain by the t","authors_text":"Folkmar Bornemann","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2009-10-09T20:03:39Z","title":"Accuracy and Stability of Computing High-Order Derivatives of Analytic Functions by Cauchy Integrals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.1841","kind":"arxiv","version":4},"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":"sha256:127ad0429828a3d8beb89928da4e7c015ae44fdb547ce1cb10c3726b8d817716","target":"record","created_at":"2026-05-18T04:25:13Z","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":"2baf04be5eaf34acd54c08c19f1e65a56521e2a445f33c80ab4136eb34b1bba0","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2009-10-09T20:03:39Z","title_canon_sha256":"b2e8cd5cfcc61b82794c9ed82a9a5b33d608859d0f8ffbb99be5e3b36b23b5a7"},"schema_version":"1.0","source":{"id":"0910.1841","kind":"arxiv","version":4}},"canonical_sha256":"3f56b483e61cb90227b0f094daee19a073e8784839f83c729dd7c6e5cd24b38c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3f56b483e61cb90227b0f094daee19a073e8784839f83c729dd7c6e5cd24b38c","first_computed_at":"2026-05-18T04:25:13.379577Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:25:13.379577Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dLoquFXHWJei3QrCIYKEzUYdwWtg281YRdwhMKa31yxumKkcxXxTNKxYuNY/eK/LnujPZJUxyPHA9WJeeQGpDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:25:13.380301Z","signed_message":"canonical_sha256_bytes"},"source_id":"0910.1841","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:127ad0429828a3d8beb89928da4e7c015ae44fdb547ce1cb10c3726b8d817716","sha256:84f98098842c2d93ba3da602d5657f8f5c0b69c54cbfbfddcd106d9c988af050"],"state_sha256":"2c12ff59f8b51429c28daa8d174590f3e34a5d2c586341a31982619718a760ee"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B3czmxYQ4xpJPAg4I2D5okMpx1fOFbWH2eCgqlQRG5N8V9ornEZqdfE0Mi/trRi1Ms8zO1qpw1F/vMSX54/NAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T21:48:23.045428Z","bundle_sha256":"edd0a0c42c19afa1f95f95847f9f6f0e5043e195f28f2b88ec29f0014e9fd77f"}}