GP is correct, that’s the definition of “lossy”. We don’t need to invent ever new marketing buzzwords for well-established technical concepts.

GP is incorrect.

There is "Is identical", "looks identical" and "has lost sufficient detail to clearly not be the original." - being able to differentiate between these three states is useful.

Lossless means "is identical".

The other two are variations of lossy.

Calling one of them "perceptually lossless" is cheating, to the disadvantage of algorithms that honestly advertise themselves as lossy while still achieving "looks identical" compression.

It's a well established term, though. It's been used in academic works for a long time (since at least 1970), and it's basically another term for the notion of "transparency" as it relates to data compression.

I honestly don't notice this anymore. Advertisers have been using such language since time immemorial, to the point it's pretty much a rule that an adjective with a qualifier means "not actually ${adjective}, but kind of like it in ${specific circumstances}". So "perceptually lossless" just means "not actually lossless, except you couldn't tell it from truly lossless just by looking".

Importantly the first one is parameterless, but the second and third are parameterized by the audience. For example humans don't see colour very well, some animals have much better colour gamut, while some can't distinguish colour at all.

Perceptually lossless (nature for dogs) video compression at 15bit/s.

But this marketing term has been regularly used in academic papers for nearly 50 years (or probably more), so it seems like it should get a pass IMO.

It's also used in the first paragraph of the Wikipedia article on the term "transparency" as it relates to data compression.

It is in no way the definition of lossy. It is a subset of lossy. Most lossy image/video compression has visible artifacting, putting it outside the subset.

For one, it doesn't obey the transitive property like a truly lossless process should: unless it settles into a fixed point, a perceptually lossless copy of a copy of a copy, etc., will eventually become perceptually different. E.g., screenshot-of-screenshot chains, each of which visually resembles the previous one, but which altogether make the original content unreadable.

Perceptual closure under repeated iterations is just a stronger form of perceptual losslessness, then, after k generations instead of the usual k=1. What you’re describing is called generation loss, and there are in fact perceptually lossy image codecs that have essentially no generation loss; jpeg xl is one https://m.youtube.com/watch?v=FtSWpw7zNkI