The definition of productive efficiency is that any given output is produced for the lowest possible cost.
In the short run, only the minimum point on the SRAC curve is productively efficient - this makes sense because at any other output, the firm could move to a different SRAC curve that would give a lower cost for that output.
However, the LRAC is, by definition, the envelope of all SRAC curve - it shows the cheapest way to produce any given output.
Agree / disagree?
If true, why is it that so many economics sources claim that "productive efficiency is achieved when the firm produces at the lowest point of its AC curve"? Is it simply that firm decisions are perpetually taken in the short run?