  In a recent paper, the second author and Joana Cirici proved a theorem that
says that given appropriate hypotheses, $n$-formality of a differential graded
algebraic structure is equivalent to the existence of a chain-level lift of a
homology-level degree twisting automorphism using a unit of multiplicative
order at least $n$.
  Here we give another proof of this result of independent interest and under
slightly different hypotheses. We use the homotopy transfer theorem and an
explicit inductive procedure in order to kill the higher operations. As an
application of our result, we prove formality with coefficients in the $p$-adic
integers of certain dg-algebras coming from hyperplane and toric arrangements
and configuration spaces.
