Quibbling about what is and is not state isn't particularly productive. There is intrinsic and unavoidable subjectivity in the definition of state. The common pattern is to ignore out-of-memory errors, completely ignore the fact that in the real world time-of-execution is irreducibly an observable side effect, and that whether or not a given computation completes may even depend on whether or not an entirely separate OS process has or has not consumed the memory on the system. There's already non-zero pragmatism in the definition of "statefulness", and adding "whether or not the state of the disk has changed as a result of this 'pure computation'" isn't exactly an impossible stretch. It isn't a binary characteristic; when you really get into the nitty-gritty it is unavoidably a continuum. All real systems have state of some kind.