Spectral Determination of Fundamental Constants in Grand Consistency Theory

This paper develops a quantitative framework for the spectral determination of fundamental physical constants within Grand Consistency Theory (GCT). Starting from the converged positive spectrum of the unified Constraint Laplacian, the analysis constructs a controlled mapping from dimensionless spectral data to the Planck constant, gravitational constant, cosmological constant, and fine-structure constant. A dimensional consistency scale is introduced through an explicit calibration prescription, with a strict distinction maintained between calibration inputs, conditional predictions, and independent predictions. The framework propagates spectral and calibration uncertainties through a joint covariance structure and quantifies correlations among the resulting constants. Numerical robustness is assessed through refinement stability, spectral-truncation sensitivity, scale dependence, and a resolved uncertainty budget. A covariance-aware statistical procedure is then established for comparison with measured and observationally inferred values. The independent predictive content is characterized by the local rank of the spectral prediction map after calibration. The resulting construction provides a traceable computational pathway from the microscopic GCT spectrum to empirically testable fundamental constants and specifies the numerical information required for a direct quantitative assessment of the theory.