Integers exist in quantum physics (e.g. electron charge, spin), which is why I think quantum gravity is important to this argument. Spacetime ends up being discretizable and we can end up having rational valued physical phenomena.
Mostly as an abstraction on top of a continuous wavefunction/quantum field
> Spacetime ends up being discretizable
As far as I know this is speculative and usually assumed by physicists to be false; it's definitely not a required feature of quantum mechanics per se, and as far as I know not of any other well-accepted theory.
> Integers are fundamental in quantum mechanics, particularly as quantum numbers that define the discrete properties of particles, such as energy levels, angular momentum, and spin.
> Quantum mechanics dictates that certain properties, like energy and angular momentum, are quantized, meaning they can only exist in discrete packets or "quanta".
