The Nature of Constants: Derivations from First Principles

This paper presents a comprehensive mathematical derivation of fundamental physical constants using the Pan framework. We demonstrate that these constants, traditionally determined through empirical measurement as documented in the CODATA evaluations by Mohr et al. [1] and Tiesinga et al. [2], can be derived with extraordinary precision from first principles through structured resonance mechanics. By applying the universal weighting function established in the Pan framework, we derive fundamental constants spanning quantum, electromagnetic, gravitational, and thermodynamic domains with precision matching experimental values to multiple decimal places. Our derivations reveal previously unrecognized connections between seemingly unrelated constants and provide compelling evidence that the fine-structure constant, recently measured with unprecedented precision by Parker et al. [3] and Gabrielse et al. [4], gravitational constant, carefully determined through lunar laser ranging by Müller and Biskupek [5], and Planck's constant are not arbitrary values but emerge naturally from the underlying mathematical structure of spacetime. Furthermore, we demonstrate that quantum chromodynamics can be reinterpreted as an entropy-driven phenomenon, connecting with Kharzeev's [6] perspective on deconfinement as entropic self-destruction, rather than a force law, and we resolve the cosmological constant problem identified by Weinberg [7] and further explored by Carroll [8] without fine-tuning. These results strongly suggest that the Pan framework offers a mathematically consistent path toward a unified theory of physics that bridges quantum and classical domains through a single coherent structure.