= Solution
The exact mode functions satisfy the Wronskian normalization
$$
f_kf_k^{*\prime}-f_k^*f_k'=i.
$$
Using the <Dirac delta function> generated by the ladder-operator commutator therefore gives the exact <canonical commutation relation>
$$
\boxed{[\hat f(\tau,\mathbf x),\hat\pi(\tau,\mathbf y)]
=i\delta^{(3)}(\mathbf x-\mathbf y)}.
$$
This remains true on <superhorizon scales>, so the exact operators do not literally commute. A claim of classical behavior must instead compare this fixed commutator with the growing statistical fluctuations, or appeal to <quantum decoherence>.
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