I still think we should give him the time he needs, seeing as we've gone into 3+ days for the last couple of moves.
Martin vs the world analysis thread #4

I'm glad Martin is taking his time. It does show that he's taking the game seriously, and it certainly hints that he's not got an obvious refutation. He could just be busy and this game is low priority, but I'd like to think the defeat he had against the world hurt him enough to want revenge, which incidentally is probably why he was unsatisfied with his good luck last game.
11. Nh3 feels like the obvious move here. Now that black has a hole on g5, 12. Ng5+ becomes a dangerous threat that he has to deal with. But we also have a hole on g4, and we can't play f3 right away (because of ...Bg3+), so we have to watch out for ...Ng4 ideas. I'm pretty sure black has to move his king after 11. Nh3 (or he would just give us a free check).
One possible line is 11. Nh3 Kg8 12. Bh6 (we offer an exchange of bishops) 12...Bb4 (black can decline the trade of bishops, since bishops are probably worth more than rooks) 13. Ng5.
We can of course also play 10. Nf3 instead of 10. Nh3. I'm not sure which move is better. It doesn't feel like a knight on f3 would do much that a knight on h3 wouldn't do (protecting d4 and e5 with a knight on f3 doesn't seem that important to me and the knight can't easily go to d2 from f3). With the knight on h3 we still have the option of playing f3 later on (not right away, because of ...Bg3+) if we move our king or trade dark squared bishops.
I can't really see any other candidate moves besides 10. Nh3 and 10. Nf3, but I'm open to suggestions. We should consider alternatives, if there are any.
I've barely looked at the position and I don't claim to have found the best moves. These are just my initial thoughts on the position.

I won't lie, I didn't analyse 10... h5 at all. But I feel like this is good news.
He didn't want to go for the complications after 10... Bb4 or 10... Ng4. He skipped two moves that were the most concerning to me personally and went for ...h5.
Objectively and psychologically speaking I think we're better.

I can't see anything wrong with Nf3 here, I expect he immediately moves his king, and then Ng5 is an excellent move for us. There's no immediate threat, but it's a great square for the knight, and if he wants to eliminate or move it he either has to allow hxg5, or weaken his position with f6, which allows Ne6. I think we're fine castling queenside, our attack is happening faster than his. f3/g4 seems the way forwards, but f4 might be an option too. This after 0-0-0 of course.
Nh3 is an option too, I don't think there's any difference because he won't play Bxh3, and if he does that's great for us. Nh3 might be more flexible, actually. From there we can have f4 and Nf2 to support g4.

After castling we should probably play Kb1 fairly quickly to avoid any complications. With our bishop also along that diagonal, it's not so pressing, but it's a move we'll have to play eventually, so I'd say Kb1 when we don't have any good attacking move.

Our knight on g5 will do an excellent job of stopping him from playing Bh7, which would be a good defensive resource for him, as well as a potential attacking threat. We want to already be on b1 when for when he plays Bh7, so we can immediately play Ka1.

I also think f3 is a better move than f4, we don't want this knight on f2 when it can be on g5. f3 will support g4.

11. Nh3 feels like the obvious move here. Now that black has a hole on g5, 12. Ng5+ becomes a dangerous threat that he has to deal with. But we also have a hole on g4, and we can't play f3 right away (because of ...Bg3+), so we have to watch out for ...Ng4 ideas. I'm pretty sure black has to move his king after 11. Nh3 (or he would just give us a free check).
One possible line is 11. Nh3 Kg8 12. Bh6 (we offer an exchange of bishops) 12...Bb4 (black can decline the trade of bishops, since bishops are probably worth more than rooks) 13. Ng5.
We can of course also play 10. Nf3 instead of 10. Nh3. I'm not sure which move is better. It doesn't feel like a knight on f3 would do much that a knight on h3 wouldn't do (protecting d4 and e5 with a knight on f3 doesn't seem that important to me and the knight can't easily go to d2 from f3). With the knight on h3 we still have the option of playing f3 later on (not right away, because of ...Bg3+) if we move our king or trade dark squared bishops.
I can't really see any other candidate moves besides 10. Nh3 and 10. Nf3, but I'm open to suggestions. We should consider alternatives, if there are any.
I've barely looked at the position and I don't claim to have found the best moves. These are just my initial thoughts on the position.
I hadn't read this before I posted.
I don't think there's any difference really, I think we immediately play Ng5 either way, so it's not like the knight on f3 is blocking us.

If everyone believes we will be playing Ng5 immediately, then Nf3 makes better sense: don't even give him the chance to play Bxh3. By allowing Bxh3, Martin might like the idea of ruining our O-O, and he may have seen something he liked about our O-O-O.
I found Rxh3 to be an ugly move. The position doesn't have too much maneuverability.
It's unclear to me if we should play 12. Ng5 immediately after 11. Nh3/Nf3 or delay it a bit. For example, after 11. Nh3 Kg8, we could consider playing 12. Bh6 before Ng5 (12. 0-0-0 is maybe also an option).
After 11. Nh3 Kg8 12. Ng5, black could maybe play 12...Nh7, but that might just be bad for him, since ...Nxg5 would allow hxg5 and we've opened up the h-file (partially).
I think I like 11. Nh3 slightly more than 11. Nf3. If we were completely sure that we're going to play 12. Ng5 on the next move then I agree it doesn't matter if we play 11. Nf3 or 11. Nh3. But it's unclear if we should play Ng5 immediately after or delay it a bit.
I don't think we should be afraid of 11. Nh3 Bxh3. I would much prefer Martin playing 11...Bxh3 instead of allowing our knight to go to g5. Our knight might be strong on g5, but I'm pretty sure it's not worth giving up a bishop for a knight to prevent it from coming to g5. I think playing 11...Bxh3 would be like giving us a 2-3 point advantage in material. Martin is not going to play 11...Bxh3 unless he thinks his position is REALLY bad, and if he does then he'd be defending a losing position.

I agree, Nh3 is more flexible. We can play f3 before Ng5 if it suits us. I don't imagine it will end up making a difference, but it means we don't have to play Ng5 straight away. There's no reason to commit yet, He isn't going to play Bxh3, and if he does I'm happy about it.

Just a cursory review… not willing to look too deep.
Nh3.
Martin has to either take the Knight or move his King.
If he takes the Knight, we capture back with our pawn. Good bye teleporting Bishop. (and I've found from moving the pieces around, two of them make the difference… one, not so much)
Who cares about those two doubled pawns, one of which keeps his Knight from feeling frisky.
And we will then be bringing our Rooks to bear on the g file.
Once we castle long, Martin's head will spin. A lot of firepower will be aimed his way in no time… and he knows it.
I vote Nh3.
P.S. Martin will respond quickly, moving his King.
Not exactly sure, but I think Ry played h4 two days ago. Martin would have flagged us for the 4 day time limit by now, had the move not been entered into acceptance by Martin.
So, Martin has been struggling with what will be his next move for 2 days now. Good. Let him see how difficult it is for a change.
I think he'll go all the way up to the brink of his time limit.