(This question is probably hard to engage with without rep privileges to see deleted answers or mod privileges to see deleted comments - sorry about that!)
A while ago, I posted this question, which got a fair bit of attention. Over the past two years, one user has kept posting answers to this problem, and the following exchange reliably occurs:
They post an answer that claims to exhibit a counterexample to the OP.
I, or another user, observe that this doesn't seem quite right, or has misunderstood the question, or suggests false conclusions if its methods were generalizable (e.g. it would suggest unboundedly large solutions, when explicit upper bounds have been proven).
Some back-and-forth ensues, in which they post dismissive comments suggesting I have misunderstood their answer, and I end up putting some time into carefully explaining exactly where their error lies / which calculations went amiss / where the correctly-evaluated optimum for their family of shapes would be, and why it doesn't improve on the OP.
They recognize the error, delete all their comments on the answer (and sometimes ask the other users to do the same), and either edit the answer to a slightly modified version or delete it.
This process repeats every few months, with a new answer appearing or an old answer getting a makeover until it presents some completely new approach to the problem. As of this writing, I think it's occurred 5 times.
I have no objections to people making attempts at hard problems and sometimes getting them wrong. But the problem is quite hard (57 upvotes and no solutions after most of 2 years, and a commenter observes that it appears equivalent to a little-known conjecture in the literature), and it seems to me that the user really ought to update about the difficulty of finding a counterexample after considering how many other people have failed to solve the problem, including their past self five times in a row.
At this point I don't really want to keep sinking time into evaluating and responding to their future answers, though I feel a duty as the question-asker to perform this evaluation each time they post a new attempt.
Is there a good approach here? I don't want the user banned or anything, they seem to have a bunch of worthwhile contributions elsewhere on the site and clearly have good intentions. But I've tried gently giving dissuading them already:
As a meta remark, this is now your fourth incorrect answer to this problem. I would suggest updating on the difficulty of this question, and considering this state of affairs as some evidence that the strategy of looking for counterexamples is not likely to be very effective, especially as I would guess that there are no such counterexamples to be found. – RavenclawPrefect Oct 29 at 16:15
and this has not seemed to work. I'd appreciate thoughts on the right course of action here.