Hadronic τ decays present an opportunity to determine the isovector part of the hadronic-vacuum-polarization contribution to the anomalous magnetic moment of the muon in a way complementary to e+e−→hadrons cross sections. However, the required isospin rotation is only exact in the isospin limit, and corrections need to be under control to draw robust conclusions, most notably for τ→ππν_τ  decays to determine the two-pion contribution to a_μ^{HVP, LO}. I will present a novel analysis [arXiv:2511.07507] of the required radiative corrections using dispersion relations, thereby extending in a model-independent way the previous analysis in chiral perturbation theory (ChPT) beyond the threshold region.