Benchmarking Code for: Closed-Loop Parameter Selection and Gaussian-Tail Certification for a Theta–Carlson Formula for π

This repository contains the benchmarking and closed-loop parameterselection code accompanying the paper: "Closed-Loop Parameter Selection and Gaussian-Tail Certificationfor a Theta–Carlson Formula for π" The script reproduces: • Fixed-m runtime sweeps• Closed-loop parameter selection experiments• Gaussian tail verification plots• Runtime scaling with target precision• Certification against independent high-precision references The implementation uses a theta–elliptic formulationwith AGM-based evaluation of the complete elliptic integralfor numerical stability at high precision. Author: Lâu Thiat-uíYear: 2026