{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:C4I2TBZ6XV5UIK24Q6OH4RSTTJ","short_pith_number":"pith:C4I2TBZ6","canonical_record":{"source":{"id":"1110.2281","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-10-11T06:14:47Z","cross_cats_sorted":[],"title_canon_sha256":"121f44799ce20a416a8ae52da2c4f96c0958eacfd6a1e9575e1fb9d27680c6c0","abstract_canon_sha256":"8954fb85c42a7bcf33121c504aba7fcdf88d8a9c734ccde86c3621cc821d199f"},"schema_version":"1.0"},"canonical_sha256":"1711a9873ebd7b442b5c879c7e46539a7fb14a4011de7916fec09f0f6ec85402","source":{"kind":"arxiv","id":"1110.2281","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.2281","created_at":"2026-05-18T04:11:17Z"},{"alias_kind":"arxiv_version","alias_value":"1110.2281v1","created_at":"2026-05-18T04:11:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.2281","created_at":"2026-05-18T04:11:17Z"},{"alias_kind":"pith_short_12","alias_value":"C4I2TBZ6XV5U","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"C4I2TBZ6XV5UIK24","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"C4I2TBZ6","created_at":"2026-05-18T12:26:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:C4I2TBZ6XV5UIK24Q6OH4RSTTJ","target":"record","payload":{"canonical_record":{"source":{"id":"1110.2281","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-10-11T06:14:47Z","cross_cats_sorted":[],"title_canon_sha256":"121f44799ce20a416a8ae52da2c4f96c0958eacfd6a1e9575e1fb9d27680c6c0","abstract_canon_sha256":"8954fb85c42a7bcf33121c504aba7fcdf88d8a9c734ccde86c3621cc821d199f"},"schema_version":"1.0"},"canonical_sha256":"1711a9873ebd7b442b5c879c7e46539a7fb14a4011de7916fec09f0f6ec85402","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:11:17.133072Z","signature_b64":"2Va5t5oIJn50Swp+Kxc9TQccOkd+MlLfUNw00rKO4GHVVPKT0qWT+T1TMLzFX59bZQ7F+ZZf5VipS+QsX/WaDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1711a9873ebd7b442b5c879c7e46539a7fb14a4011de7916fec09f0f6ec85402","last_reissued_at":"2026-05-18T04:11:17.132421Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:11:17.132421Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.2281","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":"2026-05-18T04:11:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KZwYgJUzpsaGlkv0kD0tBOetSMocAgUpFmvXRUhhCfLpS16ggnJmh/pwWp5TYmbvjeaYwVKWZxKobbfp7b1xBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T10:40:44.550815Z"},"content_sha256":"550facc1738f16b400db42e43ea4c3a0498f2fd8a69f9850e2febfb56cdeb900","schema_version":"1.0","event_id":"sha256:550facc1738f16b400db42e43ea4c3a0498f2fd8a69f9850e2febfb56cdeb900"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:C4I2TBZ6XV5UIK24Q6OH4RSTTJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the approximation of derivatives using divided difference operators preserving the local convergence order of iterative methods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Miquel Grau-S\\'anchez, Miquel Noguera, Sergio Amat","submitted_at":"2011-10-11T06:14:47Z","abstract_excerpt":"A development of an inverse first-order divided difference operator for functions of several variables is presented. Two generalized derivative-free algorithms builded up from Ostrowski's method for solving systems of nonlinear equations are written and analyzed. A direct computation of the local order of convergence for these variants of Ostrowski's method is given. In order to preserve the local order of convergence, any divided difference operator is not valid. Two counterexamples of computation of a classical divided difference operator without preserving the order are presented. A new div"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.2281","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":"2026-05-18T04:11:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fu9sjzfTm3JdxFEFhUWpU+BYbV2sS8HPyHZ0k5vjXD+nTV+SzsU7fiMWBhijMnAbM8cL1nu9AhgAKm3fc8hjAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T10:40:44.551440Z"},"content_sha256":"d3e4105133b36eb782fee81ea15c2c8b57392acce6d96622129d56326e2dd795","schema_version":"1.0","event_id":"sha256:d3e4105133b36eb782fee81ea15c2c8b57392acce6d96622129d56326e2dd795"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C4I2TBZ6XV5UIK24Q6OH4RSTTJ/bundle.json","state_url":"https://pith.science/pith/C4I2TBZ6XV5UIK24Q6OH4RSTTJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C4I2TBZ6XV5UIK24Q6OH4RSTTJ/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":"2026-06-07T10:40:44Z","links":{"resolver":"https://pith.science/pith/C4I2TBZ6XV5UIK24Q6OH4RSTTJ","bundle":"https://pith.science/pith/C4I2TBZ6XV5UIK24Q6OH4RSTTJ/bundle.json","state":"https://pith.science/pith/C4I2TBZ6XV5UIK24Q6OH4RSTTJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C4I2TBZ6XV5UIK24Q6OH4RSTTJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:C4I2TBZ6XV5UIK24Q6OH4RSTTJ","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":"8954fb85c42a7bcf33121c504aba7fcdf88d8a9c734ccde86c3621cc821d199f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-10-11T06:14:47Z","title_canon_sha256":"121f44799ce20a416a8ae52da2c4f96c0958eacfd6a1e9575e1fb9d27680c6c0"},"schema_version":"1.0","source":{"id":"1110.2281","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.2281","created_at":"2026-05-18T04:11:17Z"},{"alias_kind":"arxiv_version","alias_value":"1110.2281v1","created_at":"2026-05-18T04:11:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.2281","created_at":"2026-05-18T04:11:17Z"},{"alias_kind":"pith_short_12","alias_value":"C4I2TBZ6XV5U","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"C4I2TBZ6XV5UIK24","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"C4I2TBZ6","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:d3e4105133b36eb782fee81ea15c2c8b57392acce6d96622129d56326e2dd795","target":"graph","created_at":"2026-05-18T04:11:17Z","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":"A development of an inverse first-order divided difference operator for functions of several variables is presented. Two generalized derivative-free algorithms builded up from Ostrowski's method for solving systems of nonlinear equations are written and analyzed. A direct computation of the local order of convergence for these variants of Ostrowski's method is given. In order to preserve the local order of convergence, any divided difference operator is not valid. Two counterexamples of computation of a classical divided difference operator without preserving the order are presented. A new div","authors_text":"Miquel Grau-S\\'anchez, Miquel Noguera, Sergio Amat","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-10-11T06:14:47Z","title":"On the approximation of derivatives using divided difference operators preserving the local convergence order of iterative methods"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.2281","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":"sha256:550facc1738f16b400db42e43ea4c3a0498f2fd8a69f9850e2febfb56cdeb900","target":"record","created_at":"2026-05-18T04:11:17Z","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":"8954fb85c42a7bcf33121c504aba7fcdf88d8a9c734ccde86c3621cc821d199f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-10-11T06:14:47Z","title_canon_sha256":"121f44799ce20a416a8ae52da2c4f96c0958eacfd6a1e9575e1fb9d27680c6c0"},"schema_version":"1.0","source":{"id":"1110.2281","kind":"arxiv","version":1}},"canonical_sha256":"1711a9873ebd7b442b5c879c7e46539a7fb14a4011de7916fec09f0f6ec85402","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1711a9873ebd7b442b5c879c7e46539a7fb14a4011de7916fec09f0f6ec85402","first_computed_at":"2026-05-18T04:11:17.132421Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:11:17.132421Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2Va5t5oIJn50Swp+Kxc9TQccOkd+MlLfUNw00rKO4GHVVPKT0qWT+T1TMLzFX59bZQ7F+ZZf5VipS+QsX/WaDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:11:17.133072Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.2281","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:550facc1738f16b400db42e43ea4c3a0498f2fd8a69f9850e2febfb56cdeb900","sha256:d3e4105133b36eb782fee81ea15c2c8b57392acce6d96622129d56326e2dd795"],"state_sha256":"d84f5f81e024841bebaa0b1cdcfc4cfc6b0d00d3c36a34960881415160161c2d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0b5L347z+Qk3ojYyClFJMU3rsVG8jvbX+th5eIt8B9sUTcMYJv5lqrVJAwG+5I1Uzo1d8Tn2suQz/NLFrCRlAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T10:40:44.554282Z","bundle_sha256":"bae59565d11dbdf89ed4ccc98a353c99c75b093bf2d9cf7e0d664da675766f00"}}