Geometric Origin of the Fine-Structure Constant From the Law of Existential Self-Consistency and Two Geometric Axioms

The fine-structure constant α=e2/(4πε0ℏc)≈1/137remains a poorly understood parameter within the Standard Model. This paper attempts to explore a possible geometric origin of αbased on a first principle—the Law of Existential Self-Consistency—and two geometric axioms. This principle requires physical structures to simultaneously satisfy a non-self-intersection constraint and energy minimization. Within this framework, we demonstrate the Hierarchical Nesting Theorem and the Intrinsic Geometric Spherical Symmetry Theorem. We suggest that when a closed band twists into a Möbius configuration, its geometric offset satisfies a self-consistent equation αln(1/α)=π. The analytical solution, expressed via the Lambert Wfunction as α−1=π−1W−1(−π), yields the numerical value 137.0359990958297…, which appears to agree with the CODATA 2022 recommended value within current experimental uncertainty. The core proposition is that the numerical value of αmay not be accidental, but rather a necessary outcome arising from the interplay of geometric constraints and energy minimization. If this geometric picture holds, every high-precision measurement of αwould constitute a test of this proposal. The author is fully aware of the limitations inherent in this attempt and welcomes critical scrutiny from readers.