Equivariant multiplicities and torsion at attractive fixed points

Let $X$ be a rationally smooth complex affine variety with a torus action and an attractive fixed point $x$. Suppose that $X\setminus \{x\}$ is $p$-smooth and that its integral equivariant cohomology has no $p$-torsion. We prove that the order of its total $p$-primary cohomology torsion is the $p$-part of the reduced numerator of the equivariant multiplicity at $x$. In particular, this resolves the torsion-order conjecture of Juteau–Williamson and its local version for normal slices in Schubert varieties, using the equivariant torsion-freeness result of Fiebig–Williamson.