Calm Stiffness Homogenization Newtonian Limit and Microscopic a

S³-field theory with a single constrained field (\Phi:\mathbb{R}^{3,1}\to S^{3}) as the only fundamental object. The paper defines a long-wavelength calm potential (\tau) by coarse-graining a chart gradient and extracting its irrotational component, then formulates a homogenization cell problem that fixes the calm stiffness (K) (yielding (K=F^{2}) under an explicit neutrality condition). Using a weak-field metric normalization, it derives the Newtonian Poisson constraint and the matching relation (G=a^{2}c^{4}/(4\pi K)), clarifying that this does not determine the coupling (a). Two non-circular microscopic routes to (a) are stated—twist defect response (dE_{\rm tw}/d\tau) and ripple normalization (d\ln Z/d\tau)—and the remaining requirements for a parameter-free prediction of (G), including IR masslessness for a (1/r) tail, are identified.