Precision Dominoes: From an Algebraic Fine Structure Constant to the Gravitational Constant

An algebraic equation with zero empirical inputs produces α⁻¹ = 137.035999177, indistinguishable from the most precise measurement in physics (Fan et al., 2023; 0.3σ, 11 ppb). This paper traces a five-link chain of consequences from that value to the gravitational constant G — the worst-known constant in physics, measured only to 2.2 × 10⁻⁵ relative uncertainty. Link 1: α from SECS (11 ppb). Link 2: m_p/m_e = 6π⁵(1 + α²/(2√2)), accurate to 2.3 ppb — an 8,154-fold improvement over the Lenz formula. Link 3: electron mass improves 161-fold with exact α. Link 4: proton mass follows. Link 5: G lies one equation away. The α² correction coefficient 1/(2√2) is shown to beat all alternative expressions by at least 14×. Newton published the inverse-square law in 1687. In 339 years, G has never been derived from first principles. Four of the five links are now closed.