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This formula is based on the arctangent function identity with argument $x=\\sqrt{2-{{a}_{k-1}}}/{{a}_{k}}$, where \\[ {{a}_{k}}=\\underbrace{\\sqrt{2+\\sqrt{2+\\sqrt{2+\\cdots +\\sqrt{2}}}}}_{k\\,\\,\\text{square}\\,\\,\\text{roots}} \\] is a nested radical consisting of $k$ square roots. The computational test we performed reveals that the proposed formula for pi provides a significant improvement in accuracy as the integer $k$ increases."},"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":"1610.07713","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2016-10-25T02:39:56Z","cross_cats_sorted":[],"title_canon_sha256":"8110256c20ac3fdf3eecb8e2aa85ef72ef8ca085959b0d7368f0f5d4d20fe675","abstract_canon_sha256":"5da24877cc4729be17b54ee031be78eb39e6ab7d723ec5ab579bcc175f75d6e1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:48.022281Z","signature_b64":"8nnOaMa+XBl6XOXNFUKy/peZAPK06M/izoI9a9A2IZBv2kA1XNLhAXWSUDGIkP1SSZfTy1rTSOsP5QDIeq/yDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9e8ff7db391c73a96151ce414919aa28451fb2d070f7098693cbd65ff42c4fe5","last_reissued_at":"2026-05-18T00:10:48.021724Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:48.021724Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A formula for pi involving nested radicals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"B. 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