Quadratic Bias after Random Reshuffling and Richardson Extrapolation: An Exact Counterexample and Cancellation Criterion

We give an exact two-component, one-dimensional strongly convex quadratic example in which random reshuffling followed by two-level Richardson-Romberg extrapolation has stationary mean bias of order h^2, rather than h^3. The epoch-boundary mean is m(h) = h/[2(3-2h)], and 2m(h)-m(2h) = -2h^2/[(3-2h)(3-4h)]. Independent centered Gaussian perturbations, shared randomness across the two step sizes, and temporal averaging do not alter this conclusion. The example satisfies the stated assumptions of Lemma 4.5 and Theorem 4.6 of Emmanouilidis, Vlatakis-Gkaragkounis, and Vidal (ICLR 2026), contradicting those assertions as written in the inspected versions. For scalar quadratic finite sums, we also derive an explicit necessary and sufficient condition for cancellation of the quadratic bias term, and give a nontrivial example satisfying it. All example identities are checked by an accompanying exact-arithmetic script.