Yes, I meant the latter, the actual execution. Kevlin Henney puts it well in his talks (paraphrase):
"Functional programming is great! You don't need to worry about the outside environment, it just works! Why, even if you unplug the computer, it just works—no, wait. These are all abstractions."
The execution environment is the invariant the webpage starts out with. The programming environment, and its relation to state, can be changed.
if i enter (+ 1 2) which is a lisp program, where is the state? in the context of lisp.
but of course, everything is stateful at the end of the day - that's what your cpu is up to.