Cool puzzle! Though I think the line that follows after 2. Ke2? Is pretty cool: 2. Ke2 Rxb5 3. c7 Rb2+ 4. Kd3 Rc2!! when 5. Kxc2 is stalemate.
Is this the best Endgame Miniature ever?
Yep! It's essentially the same line as given after 2. Kc2! Rc5+ 3. Kd2? Rxb5! 4. c7 Rb2+! 5. Kd3 Rc2!! I tried to cut down on duplicate lines!
Addendum: In fact, black does not need the stalemate trick after 2. Ke2? Rxb5 3. c7 Re5+. Which means that it is only relevant in the variation given in my previous comment and the solution text!
Great problem, but how can an endgame be a miniature?
In composition chess anything of up to 7 chess units (kings, pieces and pawns) counts as a miniature. Up to 12 units, it's called a Meredith. Since it is harder to show content with fewer units, you definitely earn bonus points for a miniature!
Obviously, with only 6 units Liburkins creation is a giant in artistic chess. Two underpromotions and three stalemate positions plus several sacrifices! That it "only" scored 2nd prize in a composition tournament may be due to the fact that it includes the Saavedra theme which was already known. That however deducts not one iota from the accumulated virtues of the total composition.

Case 1:
1. Nc1 Rxb5 2. c7
If 2... Rc5 3. Nb3+ (+- Fork: Knight takes rook).
If 2... Rb7 3. c8=Q +-
If 2... Rd5+ 3. Ke2 (and the king goes up unstoppable to support the pawn promotion).
Case 2:
1. Nc1 Kb2 2. Nd3+ (fork +-)
Ok, problem solved. Next!
Case 1:
1. Nc1 Rxb5 2. c7
If 2... Rd5+ 3. Ke2 (and the king goes up unstoppable to support the pawn promotion).
edited:
ad Case1:
if 2... Rd5+ 3. Ke2 Re5+ 4. K~ Re8! draws
Case 3:
1. ... Rd5+ and what next?

1. ... Rd5+ and what next?
I already said:
If 2... Rd5+ 3. Ke2 (and the king goes up unstoppable to support the pawn promotion). I don't think it's necessary to explain all the following moves, because they are obvious, but it's ok, I'll do it:
1. Nc1 Rxb5 2. c7 Rd5+ 3. Ke2 Re5+ ( 3... Rc5 4. Nb3+ +- it's a fork and white wins ) 4. Kd3 Rd5+ 5. Ke4 Rb5 (5... Rc5 6. Nb3+ would be the same fork and white wins) 6. c8=Q
Any other option instead of 2... Rd5+ the pawn promotes.
Problem is solved. It was a pretty problem, but a problem solved is not a problem anymore. So I hope I made your life easier from now on
@p8Q: All you write is to no avail when you don't read. But I am surely not the 1st person to tell you that.

Llegue tarde, con mi jugada Nd3 no me daban los tiempos justos, aisi que empeze a mirar Ke2, bueno ya esta la solucion! pero gane! la Solucion era 1.Nc1!
No te des por vencida, no he dedicado mucho tiempo a pensar y alguna variación me he podido saltar. No voy a decir todas las posibilidades y dejo libre la oportunidad de que alguien venga con un contra-ejemplo que demuestre que me equivoco.

@p8Q: All you write is to no avail when you don't read. But I am surely not the 1st person to tell you that.
Sorry, you are right, I read too fast and skipped what you said. I include your two variations in the previous pgn file. Maybe there is still something missing, I didn't think too much.
Sorry, you are right, I read too fast and skipped what you said. I include your two variations in the previous pgn file. Maybe there is still something missing, I didn't think too much.
You missed the white win, mainly played weak defensive moves for black and ignored a black draw which you yourself pointed out! In this composition the black options are as critical as the white moves.
Here is the correct solution with all the best black defenses and the white tries.

Wooow! that's cool
mainly played weak defensive moves for black and ignored a black draw which you yourself pointed out
Yes, I didn't feel like thinking much. It took more time creating the pgn than thinking
It's a cool endgame, now I realize. It deserved to pay more attention.
There is an endless stream of topics on chess.com forums claiming to present the best of the best of the best on some subject. Most of these are complete trash, some have justifiable claims to fame. Considering that chess compositions are 50% science and 50% art, it is clear that objective verdicts are an illusion. Tastes come into play besides expertise. It is however noticeable that some posters mistake compositions for games. To be rated a top game, most of us agree that the win should not be "easy" and we are impressed by the intricate analysis demonstrating the deep reading of a World Champion. OK, but that is not how chess problemists look at compositions. They look at content - which is the sum of all ideas and themes in all of the tries and variations. For instance, a failed attempt may be more important to the content than the main solution line. And especially, it doesn't matter how hard it is to solve the problem. Well, it is probably hard for a game player but experienced solvers are accustomed to solutions which turn the normal game logics upside down. Great endgame studies are therefore often (relatively) easy to solve for them!
By these standards, the next endgame created by Mark Liburkin in 1931 is definitely a hit! It involves some technical skill, but most lines are short, clear and artistic just like the best music video clips. You are not required to sit through the 4 hrs of the "Sound of Music" to get to the finished product. If solving is not your cup of tea, then simply click through the main solution moves and review the solution text with all the variations on the right side of the diagram!