  Let X and Y be finite-type CW-complexes (X connected, Y simply connected),
such that the rational cohomology ring of Y is a k-rescaling of the rational
cohomology ring of X. Assume H^*(X,Q) is a Koszul algebra. Then, the homotopy
Lie algebra pi_*(Omega Y) tensor Q equals, up to k-rescaling, the graded
rational Lie algebra associated to the lower central series of pi_1(X). If Y is
a formal space, this equality is actually equivalent to the Koszulness of
H^*(X,Q). If X is formal (and only then), the equality lifts to a filtered
isomorphism between the Malcev completion of pi_1(X) and the completion of
[Omega S^{2k+1}, Omega Y]. Among spaces that admit naturally defined
homological rescalings are complements of complex hyperplane arrangements, and
complements of classical links. The Rescaling Formula holds for supersolvable
arrangements, as well as for links with connected linking graph.
