= Formal rigidity from vanishing second Hochschild cohomology
If $HH^2(A,A)=0$, every <formal associative deformation> on the <adic completion of a module> $A[[t]]$ is trivial. After killing lower coefficients, <associativity> makes the order-$r$ coefficient a <Hochschild cocycle> $\mu_r=\delta g_r$. Transport by $\operatorname{id}+t^rg_r$ subtracts $\delta g_r$ and kills it. The successive transformations stabilize modulo each $t^n$ and converge to an invertible change of coordinates. Completeness, and equivalence congruent to the identity modulo $t$, are essential to this argument.
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