{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:CKZKXJYDO6HEX7I7PR5KN2IEMT","short_pith_number":"pith:CKZKXJYD","schema_version":"1.0","canonical_sha256":"12b2aba703778e4bfd1f7c7aa6e90464e3f37e470a4232e914cf5796d55e4b0b","source":{"kind":"arxiv","id":"1211.6403","version":1},"attestation_state":"computed","paper":{"title":"Practical Explicitly Invertible Approximation to 4 Decimals of Normal Cumulative Distribution Function Modifying Winitzki's Approximation of erf","license":"http://creativecommons.org/licenses/publicdomain/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Alessandro Soranzo, Emanuela Epure","submitted_at":"2012-11-27T19:53:21Z","abstract_excerpt":"We give a new explicitly invertible approximation of the normal cumulative distribution function: $\\Phi(x) \\simeq 1/2 + 1/2 \\sqrt{1-{e}^{-x^2\\frac{17+{x}^{2}}{26.694+2x^2}}}$, $\\forall x \\ge 0$, with absolute error $<4.00\\cdot 10^{-5}$, absolute value of the relative error $<4.53\\cdot 10^{-5}$, which, beeing designed essentially for practical use, is much simpler than a previously published formula and, though less precise, still reaches 4 decimals of precision, and has a complexity essentially comparable with that of the approximation of the normal cumulative distribution function $\\Phi(x)$ i"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1211.6403","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.ST","submitted_at":"2012-11-27T19:53:21Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"15b6cb217861d030c43f592ad1b71779bda3381300c96869d366dffea10913ae","abstract_canon_sha256":"4a504581513e1ad8a94c5d8ebda27a7c9e85e733b79293625cd291fda370a535"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:39:51.896161Z","signature_b64":"sf0zqLTSuD0LvPbdCnIdyxk+0N48rqC9h5oaQJq5BcJZQtkHT4O/MdpSObh1o0w0H4TQOwVOvBo+iYN/v8bLDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"12b2aba703778e4bfd1f7c7aa6e90464e3f37e470a4232e914cf5796d55e4b0b","last_reissued_at":"2026-05-18T03:39:51.895758Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:39:51.895758Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Practical Explicitly Invertible Approximation to 4 Decimals of Normal Cumulative Distribution Function Modifying Winitzki's Approximation of erf","license":"http://creativecommons.org/licenses/publicdomain/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Alessandro Soranzo, Emanuela Epure","submitted_at":"2012-11-27T19:53:21Z","abstract_excerpt":"We give a new explicitly invertible approximation of the normal cumulative distribution function: $\\Phi(x) \\simeq 1/2 + 1/2 \\sqrt{1-{e}^{-x^2\\frac{17+{x}^{2}}{26.694+2x^2}}}$, $\\forall x \\ge 0$, with absolute error $<4.00\\cdot 10^{-5}$, absolute value of the relative error $<4.53\\cdot 10^{-5}$, which, beeing designed essentially for practical use, is much simpler than a previously published formula and, though less precise, still reaches 4 decimals of precision, and has a complexity essentially comparable with that of the approximation of the normal cumulative distribution function $\\Phi(x)$ i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.6403","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1211.6403","created_at":"2026-05-18T03:39:51.895820+00:00"},{"alias_kind":"arxiv_version","alias_value":"1211.6403v1","created_at":"2026-05-18T03:39:51.895820+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.6403","created_at":"2026-05-18T03:39:51.895820+00:00"},{"alias_kind":"pith_short_12","alias_value":"CKZKXJYDO6HE","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_16","alias_value":"CKZKXJYDO6HEX7I7","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_8","alias_value":"CKZKXJYD","created_at":"2026-05-18T12:27:01.376967+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CKZKXJYDO6HEX7I7PR5KN2IEMT","json":"https://pith.science/pith/CKZKXJYDO6HEX7I7PR5KN2IEMT.json","graph_json":"https://pith.science/api/pith-number/CKZKXJYDO6HEX7I7PR5KN2IEMT/graph.json","events_json":"https://pith.science/api/pith-number/CKZKXJYDO6HEX7I7PR5KN2IEMT/events.json","paper":"https://pith.science/paper/CKZKXJYD"},"agent_actions":{"view_html":"https://pith.science/pith/CKZKXJYDO6HEX7I7PR5KN2IEMT","download_json":"https://pith.science/pith/CKZKXJYDO6HEX7I7PR5KN2IEMT.json","view_paper":"https://pith.science/paper/CKZKXJYD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1211.6403&json=true","fetch_graph":"https://pith.science/api/pith-number/CKZKXJYDO6HEX7I7PR5KN2IEMT/graph.json","fetch_events":"https://pith.science/api/pith-number/CKZKXJYDO6HEX7I7PR5KN2IEMT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CKZKXJYDO6HEX7I7PR5KN2IEMT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CKZKXJYDO6HEX7I7PR5KN2IEMT/action/storage_attestation","attest_author":"https://pith.science/pith/CKZKXJYDO6HEX7I7PR5KN2IEMT/action/author_attestation","sign_citation":"https://pith.science/pith/CKZKXJYDO6HEX7I7PR5KN2IEMT/action/citation_signature","submit_replication":"https://pith.science/pith/CKZKXJYDO6HEX7I7PR5KN2IEMT/action/replication_record"}},"created_at":"2026-05-18T03:39:51.895820+00:00","updated_at":"2026-05-18T03:39:51.895820+00:00"}