Uniform Weak Robin Comparisons on Triangles and a Cubic Moment Formula

We give a quantitative comparison for the first Robin eigenvalue among triangles of fixed area. There exists an absolute positive constant epsilon such that, whenever \(0 < |\alpha|\sqrt A < \varepsilon\), the eigenvalue difference from the equilateral triangle, divided by alpha, is at least one twenty-fourth of the perimeter deficit divided by A. The parameter interval is common to all triangle shapes, including degenerating families. The proof combines analytic perturbation near the equilateral triangle, compactness on bounded-perimeter families, and a one-dimensional estimate on thin triangles. Earlier attractive-Robin comparisons and width estimates are explicitly credited. Separately, for each fixed domain satisfying \((x-I)\cdot\nu=r\) almost everywhere on its boundary, the cubic Robin coefficient equals \(\operatorname{Var}(|X-I|^2)/r^3\) for X uniform in the domain. Neither result settles the triangle optimization problem at arbitrary nonzero Robin parameter; frozen AIM-ANALYSIS-0019 remains partial. This is an unrefereed preprint with no absolute-priority claim.