The first thing I tried was "Lipschitz selection", a somewhat overloaded phrase that I encountered a lot in graduate school. I guess I had in mind a summary of this paper:
The page I got stated the following, obviously false, "theorem": let M be a metric space, and let S be a subset of M such that inf_{y in S} d(x, y) < infinity for all x in M. Then there exists a map f: M to S such that f(x) = x for all x in S. As far as I can tell, this isn't a garbling of something which is true, it's just nonsense.
It suggested that I look up "Whitney extension" which is indeed related to the first paper I posted, so I did that. The opening summary, if you squint hard enough, could arguably be interpreted as true:
> The theorems state that any sufficiently smooth function on a closed subset of Rn can be extended to a function on all of Rn with the same level of smoothness.
This is really vague though. Like if someone didn't know the actual statement of Whitney's theorem, they would not be able to intuit it from this sentence. You have to be really, really charitable to describe it as true. I'm not being nitpicky here, Whitney produced a pretty non-trivial definition of the notion of a C^m function on an arbitrary closed set (basically you have to specify the entire mth order Taylor polynomial at each point, or a section of the jet bundle if you're fancy). You can check out the actual wikipedia if you're interested:
The body of the generated article goes into more detail, and again produces something which is completely false, and not particularly close to anything that is true:
> Whitney's extension theorem states that any continuous function on a closed subset of Rn can be extended to a C∞ function on Rn.
Finally, I should just say that this is all still really impressive. The sentences are grammatical, and use words somewhat related to the subject at hand. I could imagine a student who hadn't studied the material and was totally in over his head in the class writing things like this on an exam! But I would never use this as a research tool.
https://arxiv.org/abs/1801.00325
but would have been happy with a description of work related to this paper:
https://arxiv.org/abs/1905.11968
or any number of other things.
The page I got stated the following, obviously false, "theorem": let M be a metric space, and let S be a subset of M such that inf_{y in S} d(x, y) < infinity for all x in M. Then there exists a map f: M to S such that f(x) = x for all x in S. As far as I can tell, this isn't a garbling of something which is true, it's just nonsense.
It suggested that I look up "Whitney extension" which is indeed related to the first paper I posted, so I did that. The opening summary, if you squint hard enough, could arguably be interpreted as true:
> The theorems state that any sufficiently smooth function on a closed subset of Rn can be extended to a function on all of Rn with the same level of smoothness.
This is really vague though. Like if someone didn't know the actual statement of Whitney's theorem, they would not be able to intuit it from this sentence. You have to be really, really charitable to describe it as true. I'm not being nitpicky here, Whitney produced a pretty non-trivial definition of the notion of a C^m function on an arbitrary closed set (basically you have to specify the entire mth order Taylor polynomial at each point, or a section of the jet bundle if you're fancy). You can check out the actual wikipedia if you're interested:
https://en.wikipedia.org/wiki/Whitney_extension_theorem
The body of the generated article goes into more detail, and again produces something which is completely false, and not particularly close to anything that is true:
> Whitney's extension theorem states that any continuous function on a closed subset of Rn can be extended to a C∞ function on Rn.
Finally, I should just say that this is all still really impressive. The sentences are grammatical, and use words somewhat related to the subject at hand. I could imagine a student who hadn't studied the material and was totally in over his head in the class writing things like this on an exam! But I would never use this as a research tool.