Fingerprints, and especially the data captured by fingerprint sensors, is not unique, but it is so unlikely that two people will be recognized as the same one, that they are good enough.

There are no proofs of any kind about the natural world. However, it could be shown with a small population sample that fingerprint and dna signatures from the respective technologies are statistically unique.

So, for fingerprints, have actual similarity studied been performed on a sample size large enough to draw conclusions about the test of the population?

There’s a long history of fingerprint identification in law enforcement. That’s a far bigger sample size than any academic study could hope for.

On the other hand, the issue here seems to be less about how unique fingerprints are, and more about how unique the machine’s reading of a fingerprint is. That has more to do with the machine than the biology.

It is all based on the way the machines read our fingerprints. Only a very few specific data points are stored by the machines and not the entire fingerprint itself(guess it is called minutiae). This loss of information increases the probability for false positives.

How could DNA be non-unique, except for identical twins or clones?

Chance?

Hashes are not unique by definition, though we can treat them as such in many practical situations. The same is true for anything with a fixed number of variables with finite states, e.g. DNA.

The DNA usually isn’t completely sequenced. Instead, they look at specific regions of the genome called short tandem repeats, or STRs. Each STR consists of a short pattern of a few bases that repeats over and over. The theory is that individuals have different numbers of repeats—you might have ten repeats of AATG at the TPOX locus, while I only have nine. Individually, this doesn’t tell you much, but if you combine information from multiple loci—six repeats there, seven here, and four there-you can rapidly find profiles that are unlikely to belong to more than one person. This works best if the set are statistically independent.

Still, one can be (un)lucky, or the statistical models could be wrong—maybe the number of repeats is different in a sub population or the STRs aren’tstatistically independent.

There's a 1 in 2^46 chance that siblings born separately will have mostly identical DNA, minus a few random mutations.

Even born separately from the same parents, or from different parents with the same available genes to generate the same haploids?

Yeah, plus some infinitesimal chance your aunt marries your uncle and your cousin comes out just like you, etc.

Does that qualify as significant in any practical implementation for identity?

If ID was based on a full sequence, probably not, but it rarely is. But if you ask how can it be not unique, that's an answer.