What hard evidence—exactly—do you expect Carlsen to be able to produce? Alternatively, imagine anyone in a similar position. What hard evidence can anyone produce in situations such as this?
I don't expect him to produce evidence, but I expect him to say more than "I suspect he cheated"
If he saw something unusual, like "Hans was messing with his shoe" or "I heard several vibrations coming from Hans during the game" etc.. that would be at least something.
Magnus has produced what he can given the situation and has staked something of extreme personal value—his legendary near-2900 ELO—on it with his move-1 resignation.
If he'd heard the guy's damn shoe buzzing he would have insisted on a search.
I believe you could have an engine look at the historical games of a player and identify the "strength" of each move. How strong (in terms of elo) does a player have to be before they find a certain move? How often do the top players find moves that greatly exceed their own elo? Does Hans find top moves more frequently than his opponents?
The challenge with this appoach of course is identifying a players strengths and adjusting for their preparation. Making 20 top engine moves in a row is not odd if both players studied that exact line before the match.
What's odd is making 20 top moves in a row on a bizzare line that nobody has ever played before that Magnus specifically prepared because he knew it was unusual (and engine disadvantaged) and unlikely to be in anyone's prep.
Niemann have admitted cheating before when playing online, so Carlsen is just not making this up about any random player. There is a history of cheating.
There is no smoking gun, but there is a lot of smoke. The ease with which Niemann pulled out of the hand a couple of brilliant moves, without spending too much time thinking about it, on an unusual line, is highly suspicious.
That probably would have been even worse of a shit-storm. You think you are rational and will ask good questions, but if you are not a trained journalist, and you haven’t prepared, you will most likely only ask really dumb question that do nothing except cause more drama.
I expect people to hold off the public allegations if they can't prove anything.
I could name specific players who I'm pretty sure were cheating in my own game. I've sometimes had a quiet word with a ref and asked them to watch a particular player closely. I've occasionally had a louder word with a ref and asked them to enforce the rules that are in place to make cheating harder. But you can't pull something like this based off of nothing but your own feelings.
If he saw something unusual, like "Hans was messing with his shoe" or "I heard several vibrations coming from Hans during the game" etc.. that would be at least something.
It would be something. Magnus has given nothing.