{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:FG6UE4BOFU2QG5FGB4HD65E254","short_pith_number":"pith:FG6UE4BO","canonical_record":{"source":{"id":"1107.0498","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-07-03T21:38:41Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"0e7cf578f872c78f0769259e6070c86a4374e016f80d658a4071a668c7c4f178","abstract_canon_sha256":"942ddd0b892a66d4883993d690f56423b5939299808d599551c9fb8e6d58c91a"},"schema_version":"1.0"},"canonical_sha256":"29bd42702e2d350374a60f0e3f749aef13a19d7a5e25e61352622a5c69ba9b66","source":{"kind":"arxiv","id":"1107.0498","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.0498","created_at":"2026-05-18T03:49:47Z"},{"alias_kind":"arxiv_version","alias_value":"1107.0498v3","created_at":"2026-05-18T03:49:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.0498","created_at":"2026-05-18T03:49:47Z"},{"alias_kind":"pith_short_12","alias_value":"FG6UE4BOFU2Q","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"FG6UE4BOFU2QG5FG","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"FG6UE4BO","created_at":"2026-05-18T12:26:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:FG6UE4BOFU2QG5FGB4HD65E254","target":"record","payload":{"canonical_record":{"source":{"id":"1107.0498","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-07-03T21:38:41Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"0e7cf578f872c78f0769259e6070c86a4374e016f80d658a4071a668c7c4f178","abstract_canon_sha256":"942ddd0b892a66d4883993d690f56423b5939299808d599551c9fb8e6d58c91a"},"schema_version":"1.0"},"canonical_sha256":"29bd42702e2d350374a60f0e3f749aef13a19d7a5e25e61352622a5c69ba9b66","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:49:47.525825Z","signature_b64":"tDJrguLXgLHsX1mAF6FekTILgK2D37CrLkJ5VT5+HG+ghuZdeYSR2JTFct0tiwq8wpk24vf7i42XdWcWkub1DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"29bd42702e2d350374a60f0e3f749aef13a19d7a5e25e61352622a5c69ba9b66","last_reissued_at":"2026-05-18T03:49:47.525059Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:49:47.525059Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.0498","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":"2026-05-18T03:49:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"93n3MGGZZ+TvFQuXX8jrN5j892Q2p1hELu9Dk1VAkNKmbJAu9W5pkXhpQdpX/amA004FE2SsuXcLiV7UkX8uAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T06:42:03.718386Z"},"content_sha256":"4cb6956c10aaa140fd74793d4cbad5cd8451a6fea7dda6babe5c2074c0fe065c","schema_version":"1.0","event_id":"sha256:4cb6956c10aaa140fd74793d4cbad5cd8451a6fea7dda6babe5c2074c0fe065c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:FG6UE4BOFU2QG5FGB4HD65E254","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal Contours for High-Order Derivatives","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.NA","authors_text":"Folkmar Bornemann, Georg Wechslberger","submitted_at":"2011-07-03T21:38:41Z","abstract_excerpt":"As a model of more general contour integration problems we consider the numerical calculation of high-order derivatives of holomorphic functions using Cauchy's integral formula. Bornemann (2011) showed that the condition number of the Cauchy integral strongly depends on the chosen contour and solved the problem of minimizing the condition number for circular contours. In this paper we minimize the condition number within the class of grid paths of step size h using Provan's algorithm for finding a shortest enclosing walk in weighted graphs embedded in the plane. Numerical examples show that op"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.0498","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":"2026-05-18T03:49:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4iu6/edM0GlL+hLUWVA23xazHHrUJ7af+hi5em0gBM7lQPPSymCab1ql/wcwLxkZixD/osQnyUhAdY4L4pEpAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T06:42:03.719097Z"},"content_sha256":"9d39d4f1e72a03d8b317b3c5be9d9b88e8b85455587d872dbb5fb9b3c880060a","schema_version":"1.0","event_id":"sha256:9d39d4f1e72a03d8b317b3c5be9d9b88e8b85455587d872dbb5fb9b3c880060a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FG6UE4BOFU2QG5FGB4HD65E254/bundle.json","state_url":"https://pith.science/pith/FG6UE4BOFU2QG5FGB4HD65E254/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FG6UE4BOFU2QG5FGB4HD65E254/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":"2026-05-26T06:42:03Z","links":{"resolver":"https://pith.science/pith/FG6UE4BOFU2QG5FGB4HD65E254","bundle":"https://pith.science/pith/FG6UE4BOFU2QG5FGB4HD65E254/bundle.json","state":"https://pith.science/pith/FG6UE4BOFU2QG5FGB4HD65E254/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FG6UE4BOFU2QG5FGB4HD65E254/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:FG6UE4BOFU2QG5FGB4HD65E254","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":"942ddd0b892a66d4883993d690f56423b5939299808d599551c9fb8e6d58c91a","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-07-03T21:38:41Z","title_canon_sha256":"0e7cf578f872c78f0769259e6070c86a4374e016f80d658a4071a668c7c4f178"},"schema_version":"1.0","source":{"id":"1107.0498","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.0498","created_at":"2026-05-18T03:49:47Z"},{"alias_kind":"arxiv_version","alias_value":"1107.0498v3","created_at":"2026-05-18T03:49:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.0498","created_at":"2026-05-18T03:49:47Z"},{"alias_kind":"pith_short_12","alias_value":"FG6UE4BOFU2Q","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"FG6UE4BOFU2QG5FG","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"FG6UE4BO","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:9d39d4f1e72a03d8b317b3c5be9d9b88e8b85455587d872dbb5fb9b3c880060a","target":"graph","created_at":"2026-05-18T03:49:47Z","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":"As a model of more general contour integration problems we consider the numerical calculation of high-order derivatives of holomorphic functions using Cauchy's integral formula. Bornemann (2011) showed that the condition number of the Cauchy integral strongly depends on the chosen contour and solved the problem of minimizing the condition number for circular contours. In this paper we minimize the condition number within the class of grid paths of step size h using Provan's algorithm for finding a shortest enclosing walk in weighted graphs embedded in the plane. Numerical examples show that op","authors_text":"Folkmar Bornemann, Georg Wechslberger","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-07-03T21:38:41Z","title":"Optimal Contours for High-Order Derivatives"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.0498","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":"sha256:4cb6956c10aaa140fd74793d4cbad5cd8451a6fea7dda6babe5c2074c0fe065c","target":"record","created_at":"2026-05-18T03:49:47Z","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":"942ddd0b892a66d4883993d690f56423b5939299808d599551c9fb8e6d58c91a","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-07-03T21:38:41Z","title_canon_sha256":"0e7cf578f872c78f0769259e6070c86a4374e016f80d658a4071a668c7c4f178"},"schema_version":"1.0","source":{"id":"1107.0498","kind":"arxiv","version":3}},"canonical_sha256":"29bd42702e2d350374a60f0e3f749aef13a19d7a5e25e61352622a5c69ba9b66","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"29bd42702e2d350374a60f0e3f749aef13a19d7a5e25e61352622a5c69ba9b66","first_computed_at":"2026-05-18T03:49:47.525059Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:49:47.525059Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tDJrguLXgLHsX1mAF6FekTILgK2D37CrLkJ5VT5+HG+ghuZdeYSR2JTFct0tiwq8wpk24vf7i42XdWcWkub1DA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:49:47.525825Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.0498","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4cb6956c10aaa140fd74793d4cbad5cd8451a6fea7dda6babe5c2074c0fe065c","sha256:9d39d4f1e72a03d8b317b3c5be9d9b88e8b85455587d872dbb5fb9b3c880060a"],"state_sha256":"80a4a5624f45b256c79eedb5fc801ccf8573309c1717b6231df7a74b220d800d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ez+rmV/a6di4E3Uht2+/jlw6VUj0IDV8GLhyhRF2QMIi5Du9/HGUwUuuTGtVqBnNcamRwfGy38ert/Ir4ov/CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T06:42:03.722498Z","bundle_sha256":"a2eb538573b76546da824dfb4de4ee189b36ecafcf2724a25cad45b2c767410d"}}