Now it suddenly makes sense to me, I "get it". Infinite samples of a repeating function will create a unique pattern.
You're getting closer.
You seem to be forgetting that the signal is bandpassed before encoding. Thus any frequency below the Nyquest limit maps to a unique pattern.
A sound recording of duration 1/R second will generate one sample. The value of that single sample tells us virtually nothing about the sound.
For that signal has a period twice the lowpass frequency.
Since real-life sounds are not infinitely long repetitions, samples of real sounds can be pretty good approximations, only.
But you know what? The ear can't distinguish those either. What does a sub-cycle-length 21 Khz tone sound like?
It doesn't sounds like a continuous 21 Khz tone.
Such signals, in the context of hearing exist only in theory.