I don't think he was cheating, if just because he was playing a series of players far, far lower than his standard level, and he proves that level in tournament

I don't think he was cheating, if just because he was playing a series of players far, far lower than his standard level, and he proves that level in tournaments that have far superior anti-cheating requirements. However, could he be cheating, if he wanted to, in ways undetectable by the livestreaming? Absolutely! At the GM level, just having the evaluation visible somewhere is more than sufficient to gain 100 points of ELO: You know when your opponent blunders, and if you are winning. That can be setup trivially somewhere out of view. He doesn't need to be told one move, ever. See, for instance, Carlsen-Caruana WCC, game 6. Ended in a draw. But there was a mate in 30 once, that neither player saw. The moment Fabiano was told of the mate in 30, after the game, he started blurting out the right line... because if there's mate in 30, there was only one way it could possibly go, but it was too hard to calculate. Mate in 30 says 'yes, the really crazy line that you saw works out!' The same can happen in blitz. As for Hikaru being faster than the engine... it's a crazy claim that he wouldn't believe himself. At any and all time controls, the engine wins, all the time. The calculations from the previous move already included every move your opponent does... It's just that the lame browser engines aren't set up to remember the line from move to move, so they recompute. See what happens with any engine in the cloud, using aggressive parallelism, the kind a super GM uses to study. There's minimal cheat prevention in titled Tuesday. Even when streaming, cheating is trivially easy to do, by anyone. But this is a place where Kramnik is overplaying his hand. There's probably many players making money in titled tuesday by cheating, as their performance is so very far from over-the-board performance, it's highly suspicious. But the top dozen super-GMs, for which Titled Tuesday money is unimportant? The statistical differences vs their regular play would have to be far bigger than what Kramnik shows for them.