In this work, we present a theory to link the fine structure constant
α to the Pythagorean prime 137. This model is based on quantized
lattice spacetime and gauge symmetry of electromagnetism. Unlike
the conventional Dirac equation which assumes an electron as a
point-like particle without an internal structure. However, such a
concept would lead to a divergence in self-energy. Instead, we treat
an electron as a charged particle with an internal structure and a
finite size due to the self’s electrostatic interaction. We propose a
modified equation using Cayley-Dickson’s octonion operators of the
Clifford geometric algebra formalism. We elucidate the number
theory of the magic 137 as a Pythagorean prime triple with
