Here it is!
I post the sum up I tried to make last time (most ideas aren't mine!)
=====> 30...Ra4 31.Kb2 Ne4+
I copy here alternatives to Ne4+, but they don't seem so convincing... but maybe someone wants to have a look at the position! we didn't go in depth with these lines, which keep from general exchange.
"31 (A) ... Nxa2+ 32. Be4 and our situation is pretty bad.
31 (B). ... Rxa2+ 32. Kc1
and then, I see then four average possible moves.
32. the expected 32. ... Bf5 threatening c2.
and the two other possible moves (since we have to move our white bishop): 32. ...Be6 attacking the Knight,
32. ... Ba4 attacking the Knight, but also threatening the c2 pawn, whenever he moves the Knight.
what maybe expected is B d4 to exchange our dear black bishop. and going to soso ending.
32. Bc5, preparing Ne2+. at least, he cannot play Bd4 anymore..."
But let's go on with the Ne4 hypothesis.
=====> 32. Rd4 Nxf2 33. R8xd7 Nd1+ 34. Kc1 Bxd4 35. Nxd4
- here White can take with the Rook, but this is not very convincing: after something like :
35. Rxd4 Rxd4 36. Nxd4 Ne3
White cannot prevent the loss of a pawn:
- 37. f4 (to avoid Ng2 threatening h3). 37. ... Ng2 and f4 cannot be defended.
- or 37 Kd2 Ng2 and h4 cannot be defended.
so Nxd4 seems better.
====> then 35. ... Ne3 the best move no doubt... actually, Nf2 wouldn't make any sense, since the objective was precisely to bring the Knight on e3...
=====> 36. c3 here, I think there might be a better move than c3. c3 is OK, but with 36. Kb2 I think white gain one tempo (due to the fact that then he will not play c3 and then c4, but c4 straight.
that would be:
36. after for instance: 36. Kb2 Nf5 37. Nxf5 gxf5 38. Rxe7 Kg6 39. Kb3 Rxh4, white can play c4 at the 40th move... instead of the 41st.
EDIT: I just read my previous post, and after Kb2, I had suggested we blacks could play Ng2, but this is finally not very good for us I think. But still I mention it to make thinks clear.
36. Kb2 Ng2 37. Kb3 Ra6 (and here we find back what I suggested in one of my posts) 38. Rxe7 Kg7 and here white can play 39. Re4 (there is no f5 pawn...) protecting h4.
in anycase, this will be our choice, so it does not invalidate the whole line. 36. Kb2 Nf5 still holds!
the other alternative to c3 is 36. Rxe7 Rxd4 37. Rxe3 Rxh4. and the situation is between draw and win for us, I would say. our pawn will promote faster, and our rook can go quickly on the c file.
So i would expect Kb2 from Whites (of course to the condition that he considers seriously the following Nf5! because if he misses that, the most likely is c3... and then we are better. actually, in that situation, a5 wouldn't be so obvious, we may just give it up to gain one tempo..., since he will not bring his a pawn anywhere).
36. ... Nf5 still seems the best move. I tried everything else I think in my previous posts, without results...
=====> 37. Nxf5
Tomtom suggested Kb2 here (after 36. c3),
I copy his words here: "We would have to eliminate 37...Nxh4 38.Rxe7 Kg7? Since that is a dead draw instead 38...Kg8! And if 39.Kb3? (obvious looking move but a grave mistake.) we have 39...Ra5! 40.a4 Ng2! Which looks very good for us... Now that leaves 39.Re2 and 39.Re4 both of which look like they can probably draw...unless I have missed something these lines are still much better for white than the 37.Nxf5 lines."
=====> 37. gxf5 necessary.
=====> 38. Rxe7
is the more logical move. Actually, the only other thing I can think of is Kb3, to increase c4 speed. but it doesn't so much, since Rxe7 also win one tempo, by threatening f7.
so Kb3 would be a mere transposition I think.
(38. Kb3 Rxh4 39. Rxe7 Kg6. 40. c4 ... )
=====> 38. ... Kg6
pretty necessary.
=====> 39. Kb3 here, in RS line, here we should play 39. Kb2 a5. but if we go on supposing 36. Kb2 instead of 36. c3 (as I think is slightly better for white), white has some new opportunity: 39. Kb3. the most logical move... that mean we cannot save the a pawn anymore...
=====> 39. ... Rxh4 40. c4 Rook xh4 is logical, and then two possibilities for white: either Rx a7, or c4. c4 would be more powerful I guess.
to ease the comparison with RS, I make this hypothesis.
and then we come back to RS line, one move earlier... the difference are: White didn't do c3 and c4 but c4 straight, and black didn't move a7 to a5. So a bit better than expected for white, but not even sure, since it is not obvious that Rxa7 is good move. in which case, it's back to our situation.
then, might follow RS line, one move earlier :
=====> 40. ... Rh1 41. f4 h4 42.c5 Rc1
pretty logical. at any time, Rxa7 should be considered though.
=====> and here, instead of Re8, maybe Rxa7...
44. Rxa7 h3... but white is pretty bad. so Re8? but not so convincing. It seems pretty good to us.