Prelims
a) R56C4 = {29/38/47/56}, no 1
b) R5C89 = {18/27/36/45}, no 9
c) 20(3) cage at R1C4 = {389/479/569/578}, no 1,2
d) 23(3) cage at R3C5 = {689}
e) 20(3) cage at R3C8 = {389/479/569/578}, no 1,2
f) 21(3) cage at R6C8 = {489/579/678}, no 1,2,3
g) 20(3) cage at R8C3 = {389/479/569/578}, no 1,2
h) 12(4) cage in N1 = {1236/1245}, no 7,8,9
i) 13(4) cage in N3 = {1237/1246/1345}, no 8,9
j) 13(4) cage in N7 = {1237/1246/1345}, no 8,9
k) 12(4) cage in N9 = {1236/1245}, no 7,8,9
Steps resulting from Prelims
1a. 12(4) cage in N1 = {1236/1245}, 1,2 locked for N1
1b. 13(4) cage in N3 = {1237/1246/1345}, 1 locked for N3
1c. 23(3) cage at R3C5 = {689}, CPE no 6,8,9 in R3C3 (using D\) + R5C5
1d. 13(4) cage in N7 = {1237/1246/1345}, 1 locked for N7
1e. 12(4) cage in N9 = {1236/1245}, 1,2 locked for N9
2. R5C5 + R6C6 = {12} (hidden pair on D\), locked for N5, clean-up: no 9 in R56C4
2a. R5C5 = 1 (hidden single on D/), R6C6 = 2, clean-up: no 8 in R5C89
3. R5C5 = 1 -> 17(3) cage at R4C5 = {179}, locked for C5 and N5, clean-up: no 4 in R56C4
3a. Killer pair 6,8 in R4C4 and R56C4, locked for C4 and N5
4. 4 in N5 only in R45C6, locked for C6
4a. 15(3) cage at R4C6 = {348/456} -> R5C7 = {68}
5. R5C3 = 9 (hidden single in 23(3) cage at R3C5
6. R37C4 = {12} (hidden pair in C4)
6a. 1 in N6 only in R46C7, locked for C7
7. 20(3) cage at R1C4 and 20(3) cage at R8C3 can only contain one 8 in C3 and one 9 in C4 -> both 20(3) cages = {479/569/578}, no 3, 8 locked in R28C3 for C3
8. 3 in C4 only in R56C4 = {38}, locked for C4 and N5 -> R4C4 = 6, placed for D\, R3C5 = 8
9. Naked pair {45} in R45C6, locked for C6, R5C7 = 6 (step 4a), clean-up: no 3 in R5C89
10. R5C89 = {27} (cannot be {45} which clashes with R5C6), locked for R5 and N6
[Returning to the 20(3) cages at R1C4 and R8C3.]
11. One of the 20(3) cages must contain 4 for C4 and the other must contain 8 for C3 -> 20(3) cages at R1C4 and R8C3 (step 7) = {479/578}, no 6 in R28C3, CPE no 7 in R2C6, no 7 in R8C6
11a. 4 of the cage containing {479} must be in C4 -> no 4 in R28C3
11b. 8 of the cage containing {578} must be in C3 -> no 5 in R28C3
11c. Naked pair {78} in R28C3, locked for C3
12. 21(3) cage at R6C8 = {489/579} (cannot be {678} because 6,7 only in R7C8), no 6, CPE no 9 in R4C8
12a. 7 of {579} must be in R7C8 -> no 5 in R7C8
13. 6 in N9 only in 12(4) cage = {1236}, locked for N9
14. 3 on D\ only in R1C1 + R2C2 + R3C3, locked for N1
14a. 12(4) cage in N1 = {1245} (only remaining combination), locked for N1 -> R3C3 = 3
15. R3C2 = 6 (hidden single in N1)
15a. 9 in N1 only in R1C1 + R2C2, locked for D\
15b. 4,5 on D\ only in R7C7 + R8C8 + R9C9, locked for N9
16. 20(3) cage at R3C8 = {389/578} (cannot be {479} = [749] which clashes with 21(3) cage at R6C8), no 4, 8 locked for R4 and N6
16a. 9 of {389} must be in R3C8, 7 of {578} must be in R3C8 -> R3C8 = {79}
17. 21(3) cage at R6C8 (step 12) = {489/579}
17a. 7,8 only in R7C8 -> R7C8 = {78}
17b. 9 locked for R6 and N6 -> R6C5 = 7, R4C5 = 9
18. R8C7 = 9 (hidden single in N9)
19. 9 in R3 only in R3C68, CPE no 9 in R1C9 + R2C8
20. R3C8 = 9 (hidden single in N3)
20a. 20(3) cage at R3C8 (step 16) = {389} (only remaining combination), 3,8 locked for R4 and N6
21. R6C9 = 9 (hidden single in N6)
21a. R9C1 = 9 (hidden single on D/)
22. 20(3) cage at R8C3 (step 11) = {578} (only remaining combination) -> R8C3 = 8, R89C4 = {57}, locked for C4 and N8, R2C3 = 7, R1C1 = 8, placed for D\, R2C2 = 9, R2C4 = 4, R1C4 = 9
23. R7C8 = 8 (hidden single in N9), R6C8 = 4 (step 12), R4C89 = [38]
24. Naked triple {457} in R7C7 + R8C8 + R9C9, locked for cage at R6C7 -> R6C7 = 1, R4C7 = 5, R4C6 = 4, placed for D/, R5C6 = 5
25. 5 in N3 only in 13(4) cage = {1345} (only remaining combination), locked for N3
26. Naked triple {267} in R1C9 + R2C8 + R3C7, locked for D/, N3 and cage at R1C9 -> R2C7 = 8, R3C6 = 1
and the rest is naked singles, without needing to use diagonals.