Hardest Mate in 4 of All Time

But in this case the composer clearly did analyze all the histories, since in order for the solution to be complete, he had to confirm that either side could castle but not both in the starting position. 

I think the composer missed the ressource ...Rf7.

Black can and should castle no matter what, which forces white to use his queen to deliver the final blow (otherwise he needs 2 pieces to covers g8 and h8, and it is much slower).

To help the queen mating, the most accurate first move is 1.Nf5 (or Qe2)

If Black moves his king other than O-O, then b7 b8(=R) is mate in 2 (3 overall). If Black does not move his King, he loses to Qe2+ followed by b7 b8(=R) (mate in 4 overall).

After Black castles, 1...O-O 2. Qe2 anyway.

And it seems Black cannot stop mate in 2 via Qe7, Qxg7# which would give mate in 4 overall.

But black can actually play Rf7 right away or after Qe7. For example :

1.Nf5 O-O 2.Qe2 Rf7 3.Qe8+ Rf8 4.Ne7+ Kh8 5.Qxf8#

So mate in 5 with correct defense from black.

I think you forgot that after 1. Qc4, castling by Black is illegal.

That is actually a very good point, Polar_Bear! To a real retro FAN, FEN = NO FUN! The disadvantage of an image is that you can't fuse it with a solution line. The situation is unresolvable as there is no axiomatic way to determine what the rights are; it all depends on the choices and goals of the players during the solution.

In my view, the communication on some retro problem types will therefore remain in the domain of text exchanges between humans, for many years to come - even though work is being done to formally manage some of it.

b7 b4 b8=Q and black cannot castle I checked with analysis after i finished solving it.

I'd be interested to see that analysis. The point of the composition is that black can castle in the diagram though there are some ifs and buts about it.