Theoretical endgame position?

Hi,

Is the position with black to move a theoretical one? It seems there are many ways to win, but I'm looking for somekind of book response:

Assuming the black pawn is going up, that's pretty typical position leading to Lucena. Müller and Lamprecht give the following example in their "Fundamental Chess Endings".

If the pawn is going other way, then black should probably win by cutting off the white king along a rank. For example

Thanks for the response

I came across the problem on chesstempo:

http://chesstempo.com/chess-problems/84145

Here is the fastesed replay, with funny rook manouvre:

there is indeed no lucena needed, but I might go for it for safety puropose

Post 3 left out a critical step. 

9.Ra4 should be replaced with 9.Ra1, and then followed by a Check on d1, getting the King 3 files away from the pawn, and only then build the bridge with Rd4.

And in Post 4, 5.Rc4 is a mistake.  5...Rb7 puts up more resistence.  White is still lost, but why make it easy for Black?

In that position, you don't have to go for a Lucena.  There are some thematic tactics the pawn plus side uses to force through the queening.

The smell of tablebases is strong in that one. It's indeed arithmetically perfect play by both sides but why Ra1+Rb1 is better than direct Rb1 is mystery to me and some of white's moves also look very strange. The solution I gave is much more human imo. Also, it's about as close to a book response as you can hope for. Before Dvoretsky's (R.I.P.) Endgame Manual came out Fundamental Chess Endings was the bible and it's modern enough to be checked against tablebases.

Sure, if you want to spend an extra tempo you can play Ra1+Rd1+Rd4. Müller and Lamprecht prefer to build the bridge directly with Ra4+Rd4.

post #4/#8: after 5.Rc4 the rook on a1 is misplaced, but I dont know why indeed