I agree that "metaphysical" and "unverifiable" are traits of spirituality, as i understand the word. I consider theorem and animism to be categories of spirituality, but not the totality of it.

I describe myself as a humanist, and to me that approximately means a spiritual existentialist with no belief in spirits. From existentialism you can, of course, reach nihilism, a philosophy that is not so much wrong as unhelpful. But existentialism doesn't teach that there is no meaning; it teaches us that meaning is whatever we want, and it's important because we say it is important. From there you can end up back in any school of philosophy you want, but with a grounding that's compatible with living on a ball of rock hurtling through space.