If you count the filesystem stats on a file as part of the system state, it is certainly not idempotent. You need to be aware of that effect on system state bef

If you count the filesystem stats on a file as part of the system state, it is certainly not idempotent. You need to be aware of that effect on system state before you can decide whether to ignore it. Idempotency requires that the function map from a space back onto itself. Touch is only roughly idempotent in that you can define a statistic S on the overall system state discarding filesystem stats such that S(f(f(x))) = S(f(x)).