{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:NUJAVAPDBUWD5O6ENJB76DPPVT","short_pith_number":"pith:NUJAVAPD","canonical_record":{"source":{"id":"1404.2371","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2014-04-09T05:48:36Z","cross_cats_sorted":[],"title_canon_sha256":"e6c59020e6d42d05a153b9959d2fe872abb13787f0713322ca82fda387913768","abstract_canon_sha256":"e55f9ce9da1d85b9b32abf2d89aca3802e73af4b7fb5b95dfa941ef3784c16d6"},"schema_version":"1.0"},"canonical_sha256":"6d120a81e30d2c3ebbc46a43ff0defacc0c7f8ed2947fc7603e1a8f0ef20abb4","source":{"kind":"arxiv","id":"1404.2371","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.2371","created_at":"2026-05-18T02:54:31Z"},{"alias_kind":"arxiv_version","alias_value":"1404.2371v1","created_at":"2026-05-18T02:54:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.2371","created_at":"2026-05-18T02:54:31Z"},{"alias_kind":"pith_short_12","alias_value":"NUJAVAPDBUWD","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"NUJAVAPDBUWD5O6E","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"NUJAVAPD","created_at":"2026-05-18T12:28:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:NUJAVAPDBUWD5O6ENJB76DPPVT","target":"record","payload":{"canonical_record":{"source":{"id":"1404.2371","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2014-04-09T05:48:36Z","cross_cats_sorted":[],"title_canon_sha256":"e6c59020e6d42d05a153b9959d2fe872abb13787f0713322ca82fda387913768","abstract_canon_sha256":"e55f9ce9da1d85b9b32abf2d89aca3802e73af4b7fb5b95dfa941ef3784c16d6"},"schema_version":"1.0"},"canonical_sha256":"6d120a81e30d2c3ebbc46a43ff0defacc0c7f8ed2947fc7603e1a8f0ef20abb4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:31.689778Z","signature_b64":"mO+fR4XsSW3OC8cB/646uVpHeoby89d9ZEGK3jl5rR3TyBeZr+ZkTl8+p4sCjTc+3ggPppEJ7xfw0LQQ1tscDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6d120a81e30d2c3ebbc46a43ff0defacc0c7f8ed2947fc7603e1a8f0ef20abb4","last_reissued_at":"2026-05-18T02:54:31.689098Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:31.689098Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.2371","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":"2026-05-18T02:54:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uB67pUxMKoadFSYq+agY4hstWL1tgh/2OeYaZ3J13FsNTC+cc+SPJjHQDeagQO+vDn4G7OptxNeSMRfujAWiAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T09:00:39.930269Z"},"content_sha256":"b3dae4f3d9175287c1817e46e5cda7853df6a5cf96686066734088cd76700512","schema_version":"1.0","event_id":"sha256:b3dae4f3d9175287c1817e46e5cda7853df6a5cf96686066734088cd76700512"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:NUJAVAPDBUWD5O6ENJB76DPPVT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Secant-Newton Map is Optimal Among Contracting $n^{th}$ Degree Maps for $n^{th}$ Root Computation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.SC","authors_text":"Hoon Hong, Kayla Bishop","submitted_at":"2014-04-09T05:48:36Z","abstract_excerpt":"Consider the problem: given a real number $x$ and an error bound $\\epsilon$, find an interval such that it contains the $\\sqrt[n]{x}$ and its width is less than $\\epsilon$. One way to solve the problem is to start with an initial interval and to repeatedly update it by applying an interval refinement map on it until it becomes narrow enough. In this paper, we prove that the well known Secant-Newton map is optimal among a certain family of natural generalizations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.2371","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":"2026-05-18T02:54:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WLcQadPJDmxeebhKpumaXUcWTRFeajPAZhHopKNtOj1jISzFOfSQ6nfI5BHUC5DW1Vp8IiL0JwlO/ZTjtwX0Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T09:00:39.930637Z"},"content_sha256":"ac27552667797ad76aa7768bbd608320ef8f8abc71ea1f68a424f63732be54ea","schema_version":"1.0","event_id":"sha256:ac27552667797ad76aa7768bbd608320ef8f8abc71ea1f68a424f63732be54ea"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NUJAVAPDBUWD5O6ENJB76DPPVT/bundle.json","state_url":"https://pith.science/pith/NUJAVAPDBUWD5O6ENJB76DPPVT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NUJAVAPDBUWD5O6ENJB76DPPVT/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":"2026-05-19T09:00:39Z","links":{"resolver":"https://pith.science/pith/NUJAVAPDBUWD5O6ENJB76DPPVT","bundle":"https://pith.science/pith/NUJAVAPDBUWD5O6ENJB76DPPVT/bundle.json","state":"https://pith.science/pith/NUJAVAPDBUWD5O6ENJB76DPPVT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NUJAVAPDBUWD5O6ENJB76DPPVT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:NUJAVAPDBUWD5O6ENJB76DPPVT","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":"e55f9ce9da1d85b9b32abf2d89aca3802e73af4b7fb5b95dfa941ef3784c16d6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2014-04-09T05:48:36Z","title_canon_sha256":"e6c59020e6d42d05a153b9959d2fe872abb13787f0713322ca82fda387913768"},"schema_version":"1.0","source":{"id":"1404.2371","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.2371","created_at":"2026-05-18T02:54:31Z"},{"alias_kind":"arxiv_version","alias_value":"1404.2371v1","created_at":"2026-05-18T02:54:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.2371","created_at":"2026-05-18T02:54:31Z"},{"alias_kind":"pith_short_12","alias_value":"NUJAVAPDBUWD","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"NUJAVAPDBUWD5O6E","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"NUJAVAPD","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:ac27552667797ad76aa7768bbd608320ef8f8abc71ea1f68a424f63732be54ea","target":"graph","created_at":"2026-05-18T02:54:31Z","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":"Consider the problem: given a real number $x$ and an error bound $\\epsilon$, find an interval such that it contains the $\\sqrt[n]{x}$ and its width is less than $\\epsilon$. One way to solve the problem is to start with an initial interval and to repeatedly update it by applying an interval refinement map on it until it becomes narrow enough. In this paper, we prove that the well known Secant-Newton map is optimal among a certain family of natural generalizations.","authors_text":"Hoon Hong, Kayla Bishop","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2014-04-09T05:48:36Z","title":"The Secant-Newton Map is Optimal Among Contracting $n^{th}$ Degree Maps for $n^{th}$ Root Computation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.2371","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:b3dae4f3d9175287c1817e46e5cda7853df6a5cf96686066734088cd76700512","target":"record","created_at":"2026-05-18T02:54:31Z","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":"e55f9ce9da1d85b9b32abf2d89aca3802e73af4b7fb5b95dfa941ef3784c16d6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2014-04-09T05:48:36Z","title_canon_sha256":"e6c59020e6d42d05a153b9959d2fe872abb13787f0713322ca82fda387913768"},"schema_version":"1.0","source":{"id":"1404.2371","kind":"arxiv","version":1}},"canonical_sha256":"6d120a81e30d2c3ebbc46a43ff0defacc0c7f8ed2947fc7603e1a8f0ef20abb4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6d120a81e30d2c3ebbc46a43ff0defacc0c7f8ed2947fc7603e1a8f0ef20abb4","first_computed_at":"2026-05-18T02:54:31.689098Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:31.689098Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mO+fR4XsSW3OC8cB/646uVpHeoby89d9ZEGK3jl5rR3TyBeZr+ZkTl8+p4sCjTc+3ggPppEJ7xfw0LQQ1tscDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:31.689778Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.2371","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b3dae4f3d9175287c1817e46e5cda7853df6a5cf96686066734088cd76700512","sha256:ac27552667797ad76aa7768bbd608320ef8f8abc71ea1f68a424f63732be54ea"],"state_sha256":"5b130907745ec1b419d7735a97980e5c8f54db668177c3b1f808c2b0b4ba40c0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QY43V1vmk2TWSaUY/OI6F9s/6PRvXw5Zb0MuU+rZ8x82+I1zOj1anDyr9ISA6K8bHxNMZIUjK7Dh9CJbVKQqCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-19T09:00:39.932269Z","bundle_sha256":"61caa8f3647b8b2233b1a3c193546afe0cc8d481994bc1fbb3ac48876ed1a276"}}