Tatenda submitted a preprint on ArXiV of his disproof: https://arxiv.org/abs/2006.12546v20.
What does the proof say about a counterexample? I mean, if it actually had a specific one, this question wouldn't be here, all you'd need is the value of the number that disproves the hypothesis and there would be no argument. So it can't have that. Does it give a lower bound like "we don't know any counterexamples yet, but the imaginary part of the smallest one must be > 10^^^^^100" or something like that? Or some constraint like "it's the 137th root of an integer with 82 distinct prime factors"? Does it make any claim about how frequent counterexamples are? Like, is it unique? Are there finitely many? They at least obey the things we've already proven, that all zeros lie on a really narrow band around 1/2, right?
Edit: oh gosh, the author claims there's a counterexample with real part 3/4. (And in more recent versions he thinks he's extended this to 1.)