{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:FWY5IJZZ3IL77RUEY2NC53EOOC","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":"fbbcceaeb407cfa33c889dbb8302cfd59db9c6845e48af06198c7a9a8d68ab05","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"stat.CO","submitted_at":"2012-01-05T22:43:16Z","title_canon_sha256":"617afb9b15ff7d20a342d3e9c450bda02f0aa71ee2cb2694bd7cb584282e0957"},"schema_version":"1.0","source":{"id":"1201.1320","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.1320","created_at":"2026-05-18T04:05:04Z"},{"alias_kind":"arxiv_version","alias_value":"1201.1320v1","created_at":"2026-05-18T04:05:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.1320","created_at":"2026-05-18T04:05:04Z"},{"alias_kind":"pith_short_12","alias_value":"FWY5IJZZ3IL7","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"FWY5IJZZ3IL77RUE","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"FWY5IJZZ","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:ebc573e919a7cb9b50124d2a75d99536fbcfc45cdc170650923565f00e241ab9","target":"graph","created_at":"2026-05-18T04:05:04Z","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":"We improve the Modified Winitzki's Approximation of the error function $erf(x)\\cong \\sqrt{1-e^{-x^2\\frac{\\frac{4}{\\pi}+0.147x^2}{1+0.147x^2}}}$ which has error $|\\varepsilon (x)| < 1.25 \\cdot 10^{-4}$ $\\forall x \\ge 0$ till reaching 4 decimals of precision with $|\\varepsilon (x)| < 2.27 \\cdot 10^{-5}$; also reducing slightly the relative error. Old formula and ours are both explicitly invertible, essentially solving a biquadratic equation, after obvious substitutions. Then we derive approximations to 4 decimals of normal cumulative distribution function $\\Phi (x)$, of erfc$(x)$ and of the $Q$ ","authors_text":"A. Soranzo, E. Epure","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"stat.CO","submitted_at":"2012-01-05T22:43:16Z","title":"Simply Explicitly Invertible Approximations to 4 Decimals of Error Function and Normal Cumulative Distribution Function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.1320","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:fd1dd1dcf91a0fc7037fdf8027d4af678bf342a88a0a8be39479ba316d3d560a","target":"record","created_at":"2026-05-18T04:05:04Z","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":"fbbcceaeb407cfa33c889dbb8302cfd59db9c6845e48af06198c7a9a8d68ab05","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"stat.CO","submitted_at":"2012-01-05T22:43:16Z","title_canon_sha256":"617afb9b15ff7d20a342d3e9c450bda02f0aa71ee2cb2694bd7cb584282e0957"},"schema_version":"1.0","source":{"id":"1201.1320","kind":"arxiv","version":1}},"canonical_sha256":"2db1d42739da17ffc684c69a2eec8e70bf895226dbf1d0797d99a7d52f528761","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2db1d42739da17ffc684c69a2eec8e70bf895226dbf1d0797d99a7d52f528761","first_computed_at":"2026-05-18T04:05:04.923570Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:05:04.923570Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6PZ2Kh5FKxStBn6CrVxf5HPdoDSxqnDvSyY8Qr4WwBPXqk6mpUmOQ5q7dF+TvvyqrNJftmBex60N2WR5l8/UAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:05:04.924100Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.1320","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fd1dd1dcf91a0fc7037fdf8027d4af678bf342a88a0a8be39479ba316d3d560a","sha256:ebc573e919a7cb9b50124d2a75d99536fbcfc45cdc170650923565f00e241ab9"],"state_sha256":"696902e73ed5d69e62e14de56966917c069c7f70c6309cbe68451eb0b2868734"}