{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:GAWRZGIIYDSN6CIFWNKMDPNEY6","short_pith_number":"pith:GAWRZGII","canonical_record":{"source":{"id":"1507.03493","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-07-13T15:29:03Z","cross_cats_sorted":[],"title_canon_sha256":"a012cb7de523888cc2057c835f8149b0ca8626e169fd85392d1a77f9eba6d905","abstract_canon_sha256":"534e9f965c5870e7e57e66b49dc5bf443cdb60970e782f3655d359538ec3e337"},"schema_version":"1.0"},"canonical_sha256":"302d1c9908c0e4df0905b354c1bda4c7a67ac5e1deb1c69ac27f1afc1c5f1aaf","source":{"kind":"arxiv","id":"1507.03493","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.03493","created_at":"2026-05-18T01:36:58Z"},{"alias_kind":"arxiv_version","alias_value":"1507.03493v1","created_at":"2026-05-18T01:36:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.03493","created_at":"2026-05-18T01:36:58Z"},{"alias_kind":"pith_short_12","alias_value":"GAWRZGIIYDSN","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GAWRZGIIYDSN6CIF","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GAWRZGII","created_at":"2026-05-18T12:29:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:GAWRZGIIYDSN6CIFWNKMDPNEY6","target":"record","payload":{"canonical_record":{"source":{"id":"1507.03493","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-07-13T15:29:03Z","cross_cats_sorted":[],"title_canon_sha256":"a012cb7de523888cc2057c835f8149b0ca8626e169fd85392d1a77f9eba6d905","abstract_canon_sha256":"534e9f965c5870e7e57e66b49dc5bf443cdb60970e782f3655d359538ec3e337"},"schema_version":"1.0"},"canonical_sha256":"302d1c9908c0e4df0905b354c1bda4c7a67ac5e1deb1c69ac27f1afc1c5f1aaf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:58.706815Z","signature_b64":"F+I+pdyF45xqBAooGlXBXOFvU2c27A1quWsewDQxCMzxzZY+9G29mSZmr9t2Esz+vb0bFCO5QWfyd9lNlKkfBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"302d1c9908c0e4df0905b354c1bda4c7a67ac5e1deb1c69ac27f1afc1c5f1aaf","last_reissued_at":"2026-05-18T01:36:58.706211Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:58.706211Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.03493","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":"2026-05-18T01:36:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"htQ6QTYSMgwmFH94Xd/Xh1VBmk6r2Fq5rMETBaTtcqecqQQKOGsv+U3/Q6F5Fg4Gm7JPET0Nqjh1WmNqx9I4BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T14:31:51.434394Z"},"content_sha256":"e5329b1a98087dd49570fc3b38475984d4e2cfb2e709739807c722ec9ec4ae8d","schema_version":"1.0","event_id":"sha256:e5329b1a98087dd49570fc3b38475984d4e2cfb2e709739807c722ec9ec4ae8d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:GAWRZGIIYDSN6CIFWNKMDPNEY6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Computing multiple zeros by using a parameter in Newton-Secant method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Massimiliano Ferrara, Mehdi Salimi, Somayeh Sharifi","submitted_at":"2015-07-13T15:29:03Z","abstract_excerpt":"In this paper, we modify the Newton-Secant method with third order of convergence for finding multiple roots of nonlinear equations. Per iteration this method requires two evaluations of the function and one evaluation of its first derivative. This method has the efficiency index equal to $3^{\\frac{1}{3}}\\approx 1.44225$. We describe the analysis of the proposed method along with numerical experiments including comparison with existing methods. Moreover, the dynamics of the proposed method are shown with some comparisons to the other existing methods."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.03493","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":"2026-05-18T01:36:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AinoihF3oBYQgZG5j/8t1X5qNGlyUVZNaCYstPbgQIqvfmF5PvrO9uOIjXHu6/Jk1YBGzoPmRGh0gUSteVGCAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T14:31:51.434865Z"},"content_sha256":"a35bf906baf679e5e376264afce7cc3b734f8ec5892daa0912f9b8321b772afe","schema_version":"1.0","event_id":"sha256:a35bf906baf679e5e376264afce7cc3b734f8ec5892daa0912f9b8321b772afe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GAWRZGIIYDSN6CIFWNKMDPNEY6/bundle.json","state_url":"https://pith.science/pith/GAWRZGIIYDSN6CIFWNKMDPNEY6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GAWRZGIIYDSN6CIFWNKMDPNEY6/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":"2026-05-29T14:31:51Z","links":{"resolver":"https://pith.science/pith/GAWRZGIIYDSN6CIFWNKMDPNEY6","bundle":"https://pith.science/pith/GAWRZGIIYDSN6CIFWNKMDPNEY6/bundle.json","state":"https://pith.science/pith/GAWRZGIIYDSN6CIFWNKMDPNEY6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GAWRZGIIYDSN6CIFWNKMDPNEY6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:GAWRZGIIYDSN6CIFWNKMDPNEY6","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":"534e9f965c5870e7e57e66b49dc5bf443cdb60970e782f3655d359538ec3e337","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-07-13T15:29:03Z","title_canon_sha256":"a012cb7de523888cc2057c835f8149b0ca8626e169fd85392d1a77f9eba6d905"},"schema_version":"1.0","source":{"id":"1507.03493","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.03493","created_at":"2026-05-18T01:36:58Z"},{"alias_kind":"arxiv_version","alias_value":"1507.03493v1","created_at":"2026-05-18T01:36:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.03493","created_at":"2026-05-18T01:36:58Z"},{"alias_kind":"pith_short_12","alias_value":"GAWRZGIIYDSN","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GAWRZGIIYDSN6CIF","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GAWRZGII","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:a35bf906baf679e5e376264afce7cc3b734f8ec5892daa0912f9b8321b772afe","target":"graph","created_at":"2026-05-18T01:36:58Z","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 modify the Newton-Secant method with third order of convergence for finding multiple roots of nonlinear equations. Per iteration this method requires two evaluations of the function and one evaluation of its first derivative. This method has the efficiency index equal to $3^{\\frac{1}{3}}\\approx 1.44225$. We describe the analysis of the proposed method along with numerical experiments including comparison with existing methods. Moreover, the dynamics of the proposed method are shown with some comparisons to the other existing methods.","authors_text":"Massimiliano Ferrara, Mehdi Salimi, Somayeh Sharifi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-07-13T15:29:03Z","title":"Computing multiple zeros by using a parameter in Newton-Secant method"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.03493","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:e5329b1a98087dd49570fc3b38475984d4e2cfb2e709739807c722ec9ec4ae8d","target":"record","created_at":"2026-05-18T01:36:58Z","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":"534e9f965c5870e7e57e66b49dc5bf443cdb60970e782f3655d359538ec3e337","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-07-13T15:29:03Z","title_canon_sha256":"a012cb7de523888cc2057c835f8149b0ca8626e169fd85392d1a77f9eba6d905"},"schema_version":"1.0","source":{"id":"1507.03493","kind":"arxiv","version":1}},"canonical_sha256":"302d1c9908c0e4df0905b354c1bda4c7a67ac5e1deb1c69ac27f1afc1c5f1aaf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"302d1c9908c0e4df0905b354c1bda4c7a67ac5e1deb1c69ac27f1afc1c5f1aaf","first_computed_at":"2026-05-18T01:36:58.706211Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:58.706211Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F+I+pdyF45xqBAooGlXBXOFvU2c27A1quWsewDQxCMzxzZY+9G29mSZmr9t2Esz+vb0bFCO5QWfyd9lNlKkfBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:58.706815Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.03493","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e5329b1a98087dd49570fc3b38475984d4e2cfb2e709739807c722ec9ec4ae8d","sha256:a35bf906baf679e5e376264afce7cc3b734f8ec5892daa0912f9b8321b772afe"],"state_sha256":"9d0cca05f4bb9ef312a0490bdfa37ade6ef0eaa96fe6aa851289589000237804"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dCS4MBvPSyrCxX2IJl/ZlOY7s/B2KPQw4AemBOkYG2YgTN2Q8z/QqUgyX7c5Aqza+vKgoEQUsfzBFLm4fBsbBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T14:31:51.438849Z","bundle_sha256":"86e9a790e1f7a4918ea2a8701781ff76f71460a457892d1b9413c1ec569b70ae"}}