Abstract
Three recently proposed numerical relations express the gravitational constant , the cosmological constant , and the baryon-to-photon ratio in terms of the electron’s couplings: the fine-structure constant and the electron Yukawa coupling . These relations were identified using the DAEDALUS dimensional-analysis engine [Zhang 2026g], lack first-principles derivations, and the formula is in 11σ tension with CODATA 2018. Nevertheless, if they are physical, a natural question arises: why should the electron, rather than some other Standard Model particle, play this role? We show that the electron is the only particle in the Standard Model satisfying five simultaneous constraints required by the structure of the formulas: stability, electric charge, elementarity, nonzero Higgs coupling, and minimality (lightest of its kind). This uniqueness is partly tautological — the formulas are written in terms of electron parameters — but the constraints themselves are physical and would apply to any analogous set of relations. The extreme smallness of simultaneously ensures weak gravity and small dark energy, suggesting that the hierarchy problem and the cosmological constant problem may be two aspects of a single question: why is the electron Yukawa coupling so small?