Diophantine Structure of a Pool of Numbers
$ 70
Description
Where does the boundary lie between the spectral structure of a physical theory and the universal properties of rational approximation? In this monograph, theoretical physicist Robert Dosseh-Kpotogbey offers an in-depth analysis of the mathematical mechanisms arising from the characteristic equation of the Dimensional Metric Theory (DMT). For every integer t ≥ 1, this equation defines a unique real root s₂(t) ∈ (−1, 0), giving rise to a remarkable family of values b(t, k, σ). Through a rigorous theoretical and algorithmic journey, the book explores: • The geometry of the generated numbers: The emergence of band structures and "gaps" within the spectral pool. • Weighted pairings: The possibility of representing a target as an exact weighted average using strictly bounded weights. • Chaining algorithmics: The sequential dynamics along an ordered sequence of targets. • Critical Diophantine analysis: The use of Dirichlet's approximation theorem as a control test to isolate the spectral structure specific to the theory from the universal biases of arithmetic. This book offers essential insight to researchers and enthusiasts of theoretical physics and spectral analysis who wish to assess the geometric scope of metric models.