The Fine-Structure Constant as a Renormalized Lattice Stiffness

The fine-structure constant measures how strongly electric charges interact. Recognition Physics gives a lattice of compact phases whose stiffness is φ⁵, the golden ratio to the fifth power, under one adopted convention: a loop of unit cost carries one native unit of action. Before fluctuations the inverse coupling is 4πφ⁵ = 139.3632. Periodic phases soften the response. In four dimensions the one-loop correction is exactly −π, giving 136.2216; two loops give 136.1626; a direct simulation at this stiffness gives 136.22 ± 0.06 (statistical, with fit dependence of order 0.2). The measured value is 137.036, 0.6 percent above. The cosine cost and the isotropic geometry are forced by the framework’s composition and calibration premises; the stiffness rests on the adopted convention. The remainder can sit in three places, each stated here as a requirement: the conversion of a loop’s cost into action, the carrier of a link, or the momentum at which the lattice charge is read. The first is the one with a definite object behind it.