Rational Approximation of 2π via Hexadecimal Truncation for High-Precision Computing

This document presents an exceptional rational fraction, 884279719003555 / 140737488355328, derived from truncating the first 14 hexadecimal digits of 2π. The fraction achieves the maximum observable numerical precision in double-precision floating point (~10⁻¹⁶) and satisfies a theoretical Diophantine approximation bound (~10⁻²⁹), demonstrating its mathematical optimality for its denominator. Its denominator being a power of two (2⁴⁷) makes it particularly suited to modern binary-based computing architectures, enhancing numerical stability in applications such as fast Fourier transforms, physical simulations, and harmonic arithmetic. This contribution provides a rigorous rational basis for representing and computing 2π in high-precision numerical systems.