{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:MCVGIV57CLGOSKKG5O333WNJH4","short_pith_number":"pith:MCVGIV57","canonical_record":{"source":{"id":"1804.08445","kind":"arxiv","version":5},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NA","submitted_at":"2018-04-20T08:11:58Z","cross_cats_sorted":["cs.NA","math-ph","math.CV","math.MP","physics.app-ph","physics.comp-ph"],"title_canon_sha256":"7e1295ace07ee8e0afc4bf0214e79aa4fb9f663d2260a766f7d04cd1500769d6","abstract_canon_sha256":"8bc19a641b95231f59942bda5f682337f524f0a9e221ab6f0ec2a722caf16989"},"schema_version":"1.0"},"canonical_sha256":"60aa6457bf12cce92946ebb7bdd9a93f0f64528c008e7f2f87b688f0dce0d171","source":{"kind":"arxiv","id":"1804.08445","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.08445","created_at":"2026-07-05T08:00:28Z"},{"alias_kind":"arxiv_version","alias_value":"1804.08445v5","created_at":"2026-07-05T08:00:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.08445","created_at":"2026-07-05T08:00:28Z"},{"alias_kind":"pith_short_12","alias_value":"MCVGIV57CLGO","created_at":"2026-07-05T08:00:28Z"},{"alias_kind":"pith_short_16","alias_value":"MCVGIV57CLGOSKKG","created_at":"2026-07-05T08:00:28Z"},{"alias_kind":"pith_short_8","alias_value":"MCVGIV57","created_at":"2026-07-05T08:00:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:MCVGIV57CLGOSKKG5O333WNJH4","target":"record","payload":{"canonical_record":{"source":{"id":"1804.08445","kind":"arxiv","version":5},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NA","submitted_at":"2018-04-20T08:11:58Z","cross_cats_sorted":["cs.NA","math-ph","math.CV","math.MP","physics.app-ph","physics.comp-ph"],"title_canon_sha256":"7e1295ace07ee8e0afc4bf0214e79aa4fb9f663d2260a766f7d04cd1500769d6","abstract_canon_sha256":"8bc19a641b95231f59942bda5f682337f524f0a9e221ab6f0ec2a722caf16989"},"schema_version":"1.0"},"canonical_sha256":"60aa6457bf12cce92946ebb7bdd9a93f0f64528c008e7f2f87b688f0dce0d171","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:00:28.594873Z","signature_b64":"MATrVhK79OBBN5U6rFRKGGaHuQLNJ4olMdpVhxwZ22KY5IUoWCqdEQCDGJNem4CW71//iparWrhLOKGe+J8XCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"60aa6457bf12cce92946ebb7bdd9a93f0f64528c008e7f2f87b688f0dce0d171","last_reissued_at":"2026-07-05T08:00:28.594430Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:00:28.594430Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.08445","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:00:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5f8esy6DEm3cZ7O45HBjBHQr6ixXKZ7m71z/meF5mS7HQo4cNmDQI6yi61k/p6Sj2rmvpctYe3zOmJuVC56/BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T12:03:35.677153Z"},"content_sha256":"ac31417a36cd94447a3b7b189bcf3e1c86ddfd57dd922867bdf00ef36bbd1533","schema_version":"1.0","event_id":"sha256:ac31417a36cd94447a3b7b189bcf3e1c86ddfd57dd922867bdf00ef36bbd1533"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:MCVGIV57CLGOSKKG5O333WNJH4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fractional Newton-Raphson Method Accelerated with Aitken's Method","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["cs.NA","math-ph","math.CV","math.MP","physics.app-ph","physics.comp-ph"],"primary_cat":"math.NA","authors_text":"A. Torres-Hernandez, F. Brambila-Paz, R. Caballero-Cruz, U. Iturrar\\'an-Viveros","submitted_at":"2018-04-20T08:11:58Z","abstract_excerpt":"In the following document, we present a way to obtain the order of convergence of the Fractional Newton-Raphson (F N-R) method, which seems to have an order of convergence at least linearly for the case in which the order $\\alpha$ of the derivative is different from one. A simplified way of constructing the Riemann-Liouville (R-L) fractional operators, fractional integral and fractional derivative, is presented along with examples of its application on different functions. Furthermore, an introduction to the Aitken's method is made and it is explained why it has the ability to accelerate the c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.08445","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1804.08445/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T08:00:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/0V0uXBfepcw2actc42w/fuNLWCCJ5zyKTc/32MWRjm5Giq5rE7tmC+OQN2lx300nLa5aIOldtDSZTWtcjh1Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T12:03:35.677672Z"},"content_sha256":"0548476a12cf27ace72a8901213662f44005040fffc94b7fc7119c7357c9ef4d","schema_version":"1.0","event_id":"sha256:0548476a12cf27ace72a8901213662f44005040fffc94b7fc7119c7357c9ef4d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MCVGIV57CLGOSKKG5O333WNJH4/bundle.json","state_url":"https://pith.science/pith/MCVGIV57CLGOSKKG5O333WNJH4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MCVGIV57CLGOSKKG5O333WNJH4/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":"2026-08-16T12:03:35Z","links":{"resolver":"https://pith.science/pith/MCVGIV57CLGOSKKG5O333WNJH4","bundle":"https://pith.science/pith/MCVGIV57CLGOSKKG5O333WNJH4/bundle.json","state":"https://pith.science/pith/MCVGIV57CLGOSKKG5O333WNJH4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MCVGIV57CLGOSKKG5O333WNJH4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:MCVGIV57CLGOSKKG5O333WNJH4","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":"8bc19a641b95231f59942bda5f682337f524f0a9e221ab6f0ec2a722caf16989","cross_cats_sorted":["cs.NA","math-ph","math.CV","math.MP","physics.app-ph","physics.comp-ph"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NA","submitted_at":"2018-04-20T08:11:58Z","title_canon_sha256":"7e1295ace07ee8e0afc4bf0214e79aa4fb9f663d2260a766f7d04cd1500769d6"},"schema_version":"1.0","source":{"id":"1804.08445","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.08445","created_at":"2026-07-05T08:00:28Z"},{"alias_kind":"arxiv_version","alias_value":"1804.08445v5","created_at":"2026-07-05T08:00:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.08445","created_at":"2026-07-05T08:00:28Z"},{"alias_kind":"pith_short_12","alias_value":"MCVGIV57CLGO","created_at":"2026-07-05T08:00:28Z"},{"alias_kind":"pith_short_16","alias_value":"MCVGIV57CLGOSKKG","created_at":"2026-07-05T08:00:28Z"},{"alias_kind":"pith_short_8","alias_value":"MCVGIV57","created_at":"2026-07-05T08:00:28Z"}],"graph_snapshots":[{"event_id":"sha256:0548476a12cf27ace72a8901213662f44005040fffc94b7fc7119c7357c9ef4d","target":"graph","created_at":"2026-07-05T08:00:28Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1804.08445/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In the following document, we present a way to obtain the order of convergence of the Fractional Newton-Raphson (F N-R) method, which seems to have an order of convergence at least linearly for the case in which the order $\\alpha$ of the derivative is different from one. A simplified way of constructing the Riemann-Liouville (R-L) fractional operators, fractional integral and fractional derivative, is presented along with examples of its application on different functions. Furthermore, an introduction to the Aitken's method is made and it is explained why it has the ability to accelerate the c","authors_text":"A. Torres-Hernandez, F. Brambila-Paz, R. Caballero-Cruz, U. Iturrar\\'an-Viveros","cross_cats":["cs.NA","math-ph","math.CV","math.MP","physics.app-ph","physics.comp-ph"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NA","submitted_at":"2018-04-20T08:11:58Z","title":"Fractional Newton-Raphson Method Accelerated with Aitken's Method"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.08445","kind":"arxiv","version":5},"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:ac31417a36cd94447a3b7b189bcf3e1c86ddfd57dd922867bdf00ef36bbd1533","target":"record","created_at":"2026-07-05T08:00:28Z","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":"8bc19a641b95231f59942bda5f682337f524f0a9e221ab6f0ec2a722caf16989","cross_cats_sorted":["cs.NA","math-ph","math.CV","math.MP","physics.app-ph","physics.comp-ph"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NA","submitted_at":"2018-04-20T08:11:58Z","title_canon_sha256":"7e1295ace07ee8e0afc4bf0214e79aa4fb9f663d2260a766f7d04cd1500769d6"},"schema_version":"1.0","source":{"id":"1804.08445","kind":"arxiv","version":5}},"canonical_sha256":"60aa6457bf12cce92946ebb7bdd9a93f0f64528c008e7f2f87b688f0dce0d171","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"60aa6457bf12cce92946ebb7bdd9a93f0f64528c008e7f2f87b688f0dce0d171","first_computed_at":"2026-07-05T08:00:28.594430Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:00:28.594430Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MATrVhK79OBBN5U6rFRKGGaHuQLNJ4olMdpVhxwZ22KY5IUoWCqdEQCDGJNem4CW71//iparWrhLOKGe+J8XCA==","signature_status":"signed_v1","signed_at":"2026-07-05T08:00:28.594873Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.08445","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ac31417a36cd94447a3b7b189bcf3e1c86ddfd57dd922867bdf00ef36bbd1533","sha256:0548476a12cf27ace72a8901213662f44005040fffc94b7fc7119c7357c9ef4d"],"state_sha256":"643fbd4e16a576ae0f1ecc8d6492a0383d282bfc8a2acf1938ad4f09e04feca9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"naGJbg/DdYDlq8pYxDPF9tgdAjDkIkFeD/T1gXhNvXeGWrz5cQV4CIILMLNTIWPM6GvUUj7VMR+gtSbZv7b7CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T12:03:35.682695Z","bundle_sha256":"28c897bdd054b5508c9669b66c889abac8df9d605818b3183e314e3117c7b0ad"}}