Every sound that actually propagates in air (or water or any other medium) and we can hear, is bandwidth limited. And these bandwidth limited waves can be digitally encoded and reconstructed with mathematical perfection, so long as we sample them at more than twice the highest frequency we want to capture.
Digital audio isn't perfect, but its limitations are not theoretical. They are about the bit rates used, and the algorithms used. We're not using quite high enough bit rate to be fully transparent to all humans, and we're not using the mathematically perfect reconstruction algorithm. However, using higher bit rates and depths can account for both of these limitations.
Proofs of such ... Please?