A Geometric Basis for Fundamental Physical Constants and a Diagnosis of Systemic Errors in Earth Laboratories

This paper proposes that fundamental physical constants, such as the fine-structure constant α and nucleon masses, possess an absolute geometric basis defined by the mathematical constant π. We find that current measurements from Earth-based laboratories exhibit definitive systemic deviations relative to these geometric benchmarks. Specifically, the measured value of the fine-structure constant α_exp deviates by -2.22 ppm (parts per million) from its geometric basis α_geo. By treating this benchmark deviation as a "calibration error" caused by local gravitational potential, we develop four independent geometric algorithms—including benchmark correction, vacuum geometric precession, and atomic spectral analogies—to re-evaluate the muon anomalous magnetic moment (g-2). These algorithms unify to resolve the tension between theory and experiment, reducing the discrepancy from 4.2σ to 0.6σ. Furthermore, the framework predicts and validates a -4.44 ppm systemic shift in the hydrogen 1S-2S transition frequency and provides a natural solution to the "Proton Radius Puzzle," deriving an analytical radius r_p ≈ 0.841857 fm, which is in striking agreement with the latest muonic hydrogen experiments. Crucially, the nucleon mass formulas derived from this framework exhibit remarkable intrinsic stability, suppressing the ppm-level input deviation into ppb (parts per billion) or ppt precision in the output masses. This work offers a unified explanation for multiple empirical anomalies and provides decisive space-based experimental proposals.