Is there a counterexample to this claim https://arxiv.org/abs/1610.00353? They claim a $O(n^6)$ LP model with simulations to support. I think asking validity is not a reasonable problem. However asking for counter examples here might be a reasonable extended formulations problem.
Predecessor versions of this paper have been around for more than 15 years. I remember that there were counter-examples to the first versions, then first revisions, counter-examples to the first revisions, second revisions, new counter-examples, further revisions, further counter-examples, and so on.
It would be much better, if the authors were able to provide a mathematical proof that the given LP formulation indeed yields a full description of the TSP.
From the scientific point of view, it is certainly not enough to just state an LP formulation and to claim that it is correct, as long as nobody is able to explicitly construct a counter-example.
All in all, I would say that it is safe to ignore this paper as long as the authors do not provide supporting arguments for their claims.