These appear to be write-only. Where have they documented the method of scanning and conversion? Is it patented?

The publication on arxiv only mentions visual inspection, in the context of being a bad idea.

Hexagonal, with shaded colors? QR Codes are, by definition, square and binary and traditionally use black and white. They're also used for a different purpose typically. They could easily have made them look more like QR Codes if they had wanted to, but they made their own artistic choices. Which I love btw, but they could have maybe chosen better wording. Something like 'fingerprint' or 'mugshot' would have conveyed the idea of it being useful for identification, if not perfect, much better.

It is strong, but not 1 to 1:

> Tubbenhauer computed, for instance, that the invariant uniquely identifies more than 97% of the knots with 18 crossings.

Which I not only mentioned in my comment, it is not even slightly unique to QR codes.

> they look kinda like QR codes

In what way? QR Codes are black and white, square, and asymmetrical. These are colourful, hexagonal, and symmetrical. By that token, a 16th century tile also “looks kinda like a QR Code”.

I very much doubt you could show one of these to someone, ask them what they are, and that they would answer “QR Code”. They don’t look alike at all.

Yes.