The 137 Framework: Mathematical Structure Connecting Fundamental Constants

This paper presents a mathematical framework achieving 83% completeness in connecting fundamental physical constants through prime number geometry. The core discovery is that N(41) = 137, where N(r²) counts lattice points within radius r, and both 41 and 137 are prime numbers with unique properties. KEY FINDINGS:• Mathematical proof: N(41) = 137 in 2D and N(5) = 137 in 4D (rigorously verified)• Fine structure constant α⁻¹ ≈ 137 connected to geometric lattice structure• Fermion mass ratios follow pattern (p/q) × 137^k with