Experimental Geometry of a Three-Way Reciprocal Construct: Numerical Evidence for Structural Stability

This repository contains a numerical study of a minimal reciprocal rational family exhibiting intrinsic three-way intersection points defined by the condition f(x)=±1f(x)=\pm1f(x)=±1. The work investigates whether these intersections behave as fragile algebraic coincidences or as structurally stable geometric features under perturbation. The study introduces a controlled experimental pipeline combining deterministic perturbation scans across more than one thousand orders of magnitude, Monte Carlo ensemble sampling with paired contrasts, robustness testing under injected noise, and dual-backend computation using both double precision and arbitrary precision arithmetic. Diagnostic observables are defined to probe the sensitivity of the lock geometry under small parameter perturbations. Across all tested regimes, the three-way structure exhibits smooth power-law sensitivity scaling, reproducible detectability thresholds (around δ≈10−12\delta \approx 10^{-12}δ≈10−12–10−1310^{-13}10−13), and strong robustness under perturbation. These findings suggest that the observed behavior reflects intrinsic structural properties of the construct rather than numerical artifacts. This work is exploratory and does not claim an analytical proof. Instead, it establishes a reproducible numerical foundation and provides code, data, and figures to support further investigation. The repository includes the full manuscript, source code for all experiments, and generated datasets and plots.