{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:UILP7MOIGMSJD4NSFK4AG4LFHF","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":"52f0808f2caa4fcfdd32d1ef4c66009587ab5a1b71d60ec56fccc3c50dc200e7","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GM","submitted_at":"2020-12-07T09:52:35Z","title_canon_sha256":"fb635aa0d4317459a9ca0d4f7ff96e5ccabc0fae9efbdc4c94bc860ce3f7d2e7"},"schema_version":"1.0","source":{"id":"2012.04466","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2012.04466","created_at":"2026-07-05T04:43:17Z"},{"alias_kind":"arxiv_version","alias_value":"2012.04466v2","created_at":"2026-07-05T04:43:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2012.04466","created_at":"2026-07-05T04:43:17Z"},{"alias_kind":"pith_short_12","alias_value":"UILP7MOIGMSJ","created_at":"2026-07-05T04:43:17Z"},{"alias_kind":"pith_short_16","alias_value":"UILP7MOIGMSJD4NS","created_at":"2026-07-05T04:43:17Z"},{"alias_kind":"pith_short_8","alias_value":"UILP7MOI","created_at":"2026-07-05T04:43:17Z"}],"graph_snapshots":[{"event_id":"sha256:3cfd028b687d3cd557449d059b540adde1afa804cc92f67405936ad1d8fca8de","target":"graph","created_at":"2026-07-05T04:43:17Z","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/2012.04466/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper a spline based integral approximation is utilized to propose a sequence of approximations to the error function that converge at a significantly faster manner than the default Taylor series. The approximations can be improved by utilizing the approximation erf(x) approximately equal to one for x>>1. Two generalizations are possible, the first is based on demarcating the integration interval into m equally spaced sub-intervals. The second, it based on utilizing a larger fixed sub-interval, with a known integral, and a smaller sub-interval whose integral is to be approximated. Both","authors_text":"Roy M. Howard","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GM","submitted_at":"2020-12-07T09:52:35Z","title":"Arbitrarily Accurate Analytical Approximations for the Error Function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.04466","kind":"arxiv","version":2},"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":"sha256:792c61e7b0ab4b7aa87e7215da74de4e45217a66dc7d2c668582f3352c7a2eeb","target":"record","created_at":"2026-07-05T04:43:17Z","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":"52f0808f2caa4fcfdd32d1ef4c66009587ab5a1b71d60ec56fccc3c50dc200e7","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GM","submitted_at":"2020-12-07T09:52:35Z","title_canon_sha256":"fb635aa0d4317459a9ca0d4f7ff96e5ccabc0fae9efbdc4c94bc860ce3f7d2e7"},"schema_version":"1.0","source":{"id":"2012.04466","kind":"arxiv","version":2}},"canonical_sha256":"a216ffb1c8332491f1b22ab80371653958d33db9a96a0d15a9acecb658928635","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a216ffb1c8332491f1b22ab80371653958d33db9a96a0d15a9acecb658928635","first_computed_at":"2026-07-05T04:43:17.614322Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:43:17.614322Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8AEMnCoF6+gQBj2osXiPAcJaJvftA9ui6G8wP5Vf2bEeTMzLFtbbwyeH9oceG8StRCDsLWfYqsAk8A0rTZ/ZBw==","signature_status":"signed_v1","signed_at":"2026-07-05T04:43:17.614704Z","signed_message":"canonical_sha256_bytes"},"source_id":"2012.04466","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:792c61e7b0ab4b7aa87e7215da74de4e45217a66dc7d2c668582f3352c7a2eeb","sha256:3cfd028b687d3cd557449d059b540adde1afa804cc92f67405936ad1d8fca8de"],"state_sha256":"0df8e29d62e93aecc1aed68d9ee55eb0666dd1a8e4059ff34ac5475588f73e1f"}