Fundamental Constants from the Microscopic Spectrum

This paper develops the fundamental-constant sector of Grand Consistency Theory (GCT) by establishing a spectral connection between the microscopic Constraint Laplacian and measurable physical constants. Planck’s constant, Newton’s gravitational constant, the cosmological curvature scale, and the fine-structure constant are represented as infrared quantities arising from a common microscopic spectrum through sector-specific spectral susceptibilities. The framework introduces normalized spectral measures, spectral moments, response coefficients, and a microscopic consistency scale that together determine the physical normalization of the quantum, gravitational, vacuum, and electromagnetic sectors. It further develops dimensionless relations and correlations among the resulting constants and formulates a numerical procedure based on finite spectral realizations, positive-spectrum eigenvalue densities, susceptibility extraction, and refinement convergence. A joint precision-testing and falsification framework is presented for comparing refinement-stable predictions with experimental measurements. The resulting construction provides a quantitative route for testing whether multiple fundamental constants can emerge from a single microscopic consistency structure and identifies numerical evaluation of the Constraint Laplacian as the decisive step toward parameter-reduced predictions.