What better way to start out than with a Loyd miniature. The excellent flight-giving, sacrificial key puts Black in Zugzwang: 1.Re!! If the bB is lifted off of the board then White can mate with Qg1. The bB can correct by moving to g2 and prevent this mate. However this move self-blocks and allows 2.Qh4.
Here is a textbook example that Mansfield used to demonstrate Black correction in his classic book Adventures in Composition. The key 1.Re8! threatens 2.Qxd5. Movement of the d5 knight obviously defeats the threat. However, it also makes the error of opening the wQ's guard to c4 thus freeing the wSa3 and allowing 2.Sxc2. The d5 knight can correct this error by landing on b4 and guarding c2, but this interferes with the bRb3 yielding 2.Sb5. The d5 knight has a second correction 1...Se3, this time self-blocking and succumbing to 2.Be5. There is a more parallel correction play by the bSe4. 1...Se~ 2.Sxb3, 1...Sd2 2.Se2.
Here is a problem that I was recently made aware of in David Shire's article on Tikkanen in the September 2017 issue of The Problemist. Notice there are several ambushed white pieces aimed at the bK's flights. This one, with its waiting key, would be very difficult for me to solve. The three mobile black pieces each open guard and correct by self-blocking.
Outstanding use of the bK flights and self-blocks.
Another Mansfield classic with an outstanding key and subtle threat. This time correction play is seen from both the bSg4 and bBg6. The idea is that these two pieces clear the way for the double check from the R+B battery. However, they can play onto the battery lines to correct this, only to interfere with other pieces.
Here is an excellent work showing a bS with 3 correction moves full of interference. The general error places guard on c5 allowing 2.Rd6.
Another classic from a French expert on correction play. The problem shows three changed mates after correction moves. The problem is an excellent light-weight.
Wonderful changes and some beautiful by-play:
Here is one of my earlier compositions showing the four-way formula where the key move sets up the following effects: 1. the opening of a Black line defeating the threat, 2. the opening of a White line creating a new contingent threat 3. the closing of a White line defeating the contingent threat 4. the closing of a Black line allowing mate.
1...Sh4 (Sh~) 2.Qg4
Looking back on the problem I wish I would have moved wSd7 to g8 and the wK to a8. Giving the extra variation 1...gxf6 2.Sgf7.
Here is an example of quaternary black correction. The key 1.Qf8 threatens 2.Se7. From here the idea is that a black piece on d5 will self-block and allow additional threats. 1...Bd5 does just that allowing 2.Qc8. 1...Scd5 defeats the original threat and the contingent threat but allows 2.Rxc4. 1...Sbd5 defeats the original threat 2.Se7, the first contingent threat 2.Qc8, the second contingent threat 2.Rxc4, but allows 2.Sb8. Finally, 1...d5 defeats all of the above threats but now allows 2.Qc5.
1...Scd5 2.Rxc4 (2.Qc8?)
1...Sbd5 2.Sb8 (2.Rxc4? Qc8?)
1...d5 2.Qc5 (2.Sb8? Rxc4? Qc8?)
Here is the record for most correction moves in a wonderfully constructed open problem.
We end with a couple of my compositions. In this problem I manage to obtain three corrections moves by the bS.
Here is what one of the solvers called a superb example of a dying breed: an incomplete waiter. In the diagram White must do something about 1...Sc~ and 1...Rxc6. Placing guard on d6 will help.
Three black pieces with two correction moves each.