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An explicit computable transcendental counterexample for Erdős Problem #206

Yuhang Shi

Palomar Registrypalomar/PALOMAR-2026-10-11-000014Oct 11, 2026math.NTscore 0

A Lean formalization of a deterministic rational nested-interval construction defining a particular transcendental real x in (1/4,1/3). For this x, no strictly increasing infinite sequence of positive integer denominators is optimal among all distinct-denominator strict Egyptian underapproximations at every order from any finite starting order onward. The formalization includes the fully specified terminating construction, all prefix and polynomial enumerations, a total executable rational approximation function, and the error bound |x-q_n| = 0. It also proves attainment of the best finite…

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