[egdod]

From Tao’s blog post, it sounds like the result is more in terms of things like: for almost all n<N, the maximum value of n’s Collatz orbit is bounded by extremely slow-growing functions of N (e.g. log log log log N).

[AstralStorm]

Nice. This means that any resulting limit cycle will be tiny, thus hard to hit. So he actually proved that it's hard to disprove the conjecture.