Integer Physics: Fundamental Constants as Rational Functions of Prime 23

This paper presents a discrete foundation for theoretical physics based on the Structured Vacuum Theory (TVS). We demonstrate that fundamental physical constants—traditionally considered irrational real numbers—are in fact exact rational numbers expressible as fractions with denominators in powers of the prime number 23. Key Results: • α⁻¹ = 1667233/12167 = 137 + 19/23² + 1/23³ (accuracy: 10⁻⁸) • mₚ/mₑ = 84463/46 = 1836 + 7/46 (accuracy: 2.7×10⁻⁵%) • mᵤ/mₑ = 2688/13 = 207 - 3/13 (accuracy: 0.00046%) • sin²θw = 3/13 + 1/(2·23³) (accuracy: 0.18%) These exact rational expressions suggest that physical reality is fundamentally digital, computable, and free from the infinities that plague continuum-based theories. The vacuum is modeled as a 23-channel helical structure (V23) emerging from a generative algorithm Φ(5)=23. This work bridges number theory, discrete geometry, and fundamental physics, offering a solution to the fine-tuning problem and a new paradigm for quantum gravity.