Axiom Zero and the Arithmetic Origin of Physical Constants in; A short closure of the Brahim Framework

The provided paper introduces Axiom Zero, a singular arithmetic rule based on a specific Lucas-type linear recurrence that seeks to derive fundamental physical constants without the use of adjustable parameters. By selecting a unique Diophantine seed pair $(3, 4)$, representing color number and spacetime dimension, the author generates a framework of integer primitives and a 840-state manifold tied to the golden ratio. This mathematical structure allows for the creation of a master operator whose eigenvalues and spectral data correspond to seventeen diverse physical observables, including the fine-structure constant, the Yang-Mills mass gap and the Weinberg angle. The text emphasizes a structural shift where constants previously viewed as measured inputs are instead revealed as outputs of elementary arithmetic and Galois theory. Ultimately, the author presents a comprehensive list of falsifiable predictions across particle physics, cosmology, and dynamical systems to test the framework’s validity against experimental reality.