Chess Fortress?!

While watching my husband's game in Bundesliga this weekend, I was stunned by another encounter, between Anish Giri and Markus Ragger. The game went on for 113 moves and I was shocked to see that Black was not able to make any progress from a position which looked to me, at the first glance, completely winning!

White to move
Is this a fortress or not?!

I haven't seen for some time such an unusual position and I became interested to find out the truth: is this drawish or not? Unfortunately there are 8 pieces on the board so we cannot ask the endgame tablebases for the ultimate answer:(
What I could do was to ask the engine (which shouts a decisive advantage for Black, thus clearly showing us he understands nothing) and to move the pieces on the board, together with Erwin.


After some time, I came to the conclusion that what Anish played in the game:
58.Rd7+ Ke4 59.Ra7 was maybe not the most precise way to hold a draw. Black had a better try to look for a win, by placing his rook on h8, forcing the White king to come out with the unpleasant checks on h2 and h1, which he cannot avoid due to the mating threat on g1. (Just in between, Black cannot try to give mate by placing his rook on the first rank because of the stalemate trick; white will just give checks forever, the so called "crazy" rook:) 
Back to our ideas, the White king will be eventually kicked out from g2, all the way to the d3 square, when to me it looks like an improvement from what actually appeared in the game. And yet...I think it still is quite difficult to win. But my husband says it is winning, so I should believe him:)


[update: Anish just told me he intended to meet Rh8 with rook to the first rank. Than Rh1+ Kg2 Rxa1 would be again stalemate! So tricky this guy:) He also mentioned the recent game Wang Hao-Le Quang Liem, mindgames China 2011, where exactly the same endgame occured - "That's why I went for it in the game so readily!" says Anish]


The 'easiest' way for White to hold is to place his rook on h7, thus blocking Black's idea written above and to annoy his opponent with checks or attacking the g4 pawn, while keeping the king safe on g2.
I tried several ideas for Black to make progress but I just couldn't make them work! White always has checks and the exchange of rooks or pawns in a favorable position...the best I could come up with was the plan to attack the f2 pawn twice, with the rook and the knight, after that to sacrifice a piece and thus moving into a pawn endgame. Unfortunately, the Black king should be able to reach the d4 square in time, immediately after the White king captures back on f2. And I couldn't make this happen.


Right now I believe it is a draw but I could also be mistaken, so please correct me if I am wrong! And if it is a draw, it should definetely be included in a future endgame manual!