Thanks Afmob and Ed for correcting some minor errors.
Prelims
a) 7(2) cage at R1C9 = {16/25/34}, no 7,8,9
b) R5C89 = {39/48/57}, no 1,2,6
c) R67C2 = {59/68}
d) R67C5 = {18/27/36/45}, no 9
e) R6C78 = {17/26/35}, no 4,8,9
f) R78C6 = {16/25/34}, no 7,8,9
g) R9C56 = {49/58/67}, no 1,2,3
h) 21(3) cage at R1C1 = {489/579/678}, no 1,2,3
i) 11(3) cage at R1C2 = {128/137/146/236/245}, no 9
j) 7(3) cage at R2C3 = {124}
k) 20(3) cage at R2C5 = {389/479/569/578}, no 1,2
l) 22(3) cage at R2C6 = {589/679}
m) 10(3) cage at R2C9 = {127/136/145/235}, no 8,9
n) 10(3) cage at R8C1 = {127/136/145/235}, no 8,9
o) And, of course, 45(9) cage at R5C2 = {123456789}
Steps resulting from Prelims
1a. Naked triple {124} in 7(3) cage at R2C3, CPE no 4 in R2C5
1b. 22(3) cage at R2C6 = {589/679}, CPE no 9 in R2C5
2. 45 rule on R1 2 innies R1C19 = 12 = [75/84/93], clean-up: no 1,5,6 in R2C8
3. 45 rule on N9 2 outies R6C69 = 11 = {29/38/47/56}, no 1
4. 45 rule on N1 4 outies R1234C4 = 19 = {1279/1459/1468/2458/2467} (cannot be {1369/1378/1567/2359/2368/3457} because R23C4 must contain two of 1,2,4), no 3
4a. R1234 only contains two of 1,2,4 -> no 1,2,4 in R14C4
4b. 11(3) cage at R1C2 = {128/137/146/236/245}
4c. R1C4 = {5678} -> no 5,6,7,8 in R1C23
5. 45 rule on C1234 1 innie R6C4 = 1 outie R8C5 + 3, no 1,2,3 in R6C4, no 7,8,9 in R8C5
6. 45 rule on D\ 2 innies R1C1 + R5C5 = 1 outie R3C2 + 5, IOU no 5 in R5C5
6a. Min R1C1 + R5C5 = 8 -> min R3C2 = 3
6b. Max R1C1 + R5C5 = 14, min R1C1 = 7 -> max R5C5 = 6 (R1C1 + R5C5 cannot be [77])
7. 45 rule on D/ 3 innies R7C3 + R8C2 + R9C1 = 18 = {189/279/369/378/468/567} (cannot be {459} which clashes with 7(2) cage at R1C9)
7a. The value in R7C3 must be in two different combinations for 18 because R7C3 + R8C2 + R9C1 = 18 and 18(3) cage at R7C3 and R8C34 “see” R8C2 -> no 1,2 in R7C3 (CCC)
7b. 1 of {189} must be in R9C1 -> no 1 in R8C2
[Note that step 7a doesn’t eliminate 4 from R7C3 because 18(3) cage at R7C3 can still be 4{59}.]
8. 25(4) cage at R2C2 = {1789/2689/3589/3679/4579/4678}
8a. Killer quad 1,2,3,4 in R1C23, R2C3 and 25(4) cage, locked for N1
8b. 21(3) cage at R1C1 = {579/678}, 7 locked for C1 and N1
9. 45 rule on R6789 1 outie R5C2 = 1 innie R6C4, R6C4 = {456789} -> R5C2 = {456789}
[I was a bit slow to spot …]
10. 45 rule on N1 1 outie R4C4 = 3 innies R1C23 + R2C3 + 1
10a. Min R1C23 + R2C3 = 6 -> min R4C4 = 7
10b. Max R1C23 + R2C3 = 8 must contain 1, locked for N1
10c. R1234C4 (step 4) = {1279/1459/1468/2458/2467}
10d. 8 of {1468/2458} must be in R4C4 -> no 8 in R1C4
[Taking step 8 a bit further …]
11. 25(4) cage at R2C2 = {2689/3589/4579/4678} (cannot be {3679} which clashes with 21(3) cage at R1C1)
[This would also have eliminated {1789} if I hadn’t spotted step 10 first.]
12. 25(4) cage at R2C2 (step 11) = {2689/3589/4579/4678}, R1C19 (step 2) = [75/84/93]
12a. R4C4 = R1C23 + R2C3 + 1 (step 10)
Consider combinations for R1C23 + R2C3
R1C23 + R2C3 = {123} = 6, 3 locked for R1 (no 9 in R1C1, step 2) => R4C4 = 7 => R1C1 = 8 => 25(4) cage = {4579}
or R1C23 + R2C3 = {124/134} = 7,8 => R4C4 = {89} => 25(4) cage = {2689/3589}
-> 25(4) cage = {2689/3589/4579}, CPE no 9 in R1C1, clean-up: no 3 in R1C9 (step 2), no 4 in R2C8
13. 11(3) cage at R1C2 = {137/146/236} (cannot be {245} which clashes with R1C9), no 5
14. 25(4) cage (step 12a) = {2689/3589/4579}, R1C19 (step 2) = [75/84]
14a. Consider combinations for 7(2) cage at R1C9
7(2) cage = [43] => R1C1 = 8 => 25(4) cage = {4579}
or 7(2) cage = [52] => 7(3) cage at R2C3 = {14}2 => 25(4) cage = {3589/4579}
-> 25(4) cage = {3589/4579}, no 2,6
14b. 6,7 in N1 only in 21(3) cage at R1C1 (step 8b) = {678} (only remaining combination), locked for C1 and N1
14c. 25(4) cage = {3589/4579}, 7,8 only in R4C4 -> R4C4 = {78}
14d. Naked pair {78} in R1C1 + R4C4, locked for D\, clean-up: no 3,4 in R6C9 (step 3)
14e. Naked pair {78} in R1C1 + R4C4, CPE no 7 in R1C4 -> R1C4 = 6, clean-up: no 6 in R5C2 (step 9), no 3 in R8C5 (step 2)
15. R1234C4 (step 4) = {1468/2467} -> R23C4 = {14/24}, 4 locked for C4, N2 and 7(3) cage at R2C3, no 4 in R2C3, clean-up: no 4 in R5C2 (step 9), no 1 in R8C5 (step 5)
15a. 22(3) cage at R2C6 = {589/679}
15b. 6 of {679} must be in R2C7 -> no 7 in R2C7
15c. 20(3) cage at R2C5 = {389/479/578} (cannot be {569} = [596] which clashes with 22(3) cage), no 6
16. 11(3) cage at R1C2 (step 13) = {146/236}, R1C19 (step 2) = [75/84]
16a. Again consider combinations for 7(2) cage at R1C9
7(2) cage = [43] => R1C1 = 8 => R4C4 = 7
or 7(2) cage = [52] => R2C3 = 1 => R23C4 = {24} => R4C4 = 7 (step 15)
-> R4C4 = 7, placed for D\, R1C1 = 8, R1C9 = 4 -> R2C8 = 3, both placed for D/, clean-up: no 7 in R5C2 (step 9), no 8 in R5C8, no 9 in R5C9, no 5 in R6C7, no 2 in R7C5, no 4 in R8C5 (step 5)
[Cracked. The rest is fairly straightforward.]
16b. R1234C4 (step 15) = {2467} (only remaining combination) -> R23C4 = {24}, 2 locked for C4, N2 and 7(3) cage at R2C3 -> R2C3 = 1
16c. Naked pair {23} in R1C23, locked for R1 and N1
16d. R7C3 + R8C2 + R9C1 (step 7) = {189/279/567}
16e. R9C1 = {125} -> no 2,5 in R7C3 + R8C2
17. R3C5 = 3 (hidden single in N2) -> R24C5 = 17 = [89], clean-up: no 9 in R5C2 (step 9), no 1,6 in R67C5, no 6 in R8C5 (step 5), no 4,5 in R9C6
17a. 22(3) cage at R2C6 = {679} (only remaining combination) -> R2C7 = 6, R23C1 = [76], R23C6 = [97], clean-up: no 2 in R6C8, no 4,6 in R9C5
17b. Naked pair {15} in R1C56, locked for R1
18. Killer pair 5,8 in R5C2 and R67C2, locked for C2 -> R2C2 = 4, placed for D\, R3C2 = 9, R3C3 = 5, placed for D\, R2C4 = 2, clean-up: no 5 in R67C2
18a. Naked pair {68} in R67C2, locked for C2 -> R5C2 = 5, R6C4 = 5 (step 9), placed for D/, R8C2 = 7, R8C5 = 2, R6C5 = 4 -> R7C5 = 5, R9C5 = 7 -> R9C6 = 6, clean-up: no 7 in R5C89, no 3 in R6C7, no 1 in R78C6
19. Naked pair {34} in R78C6, locked for C6 and N8 -> R6C6 = 2
19a. Naked pair {18} in R56C6, locked for N5 -> R5C4 = 3, R5C5 = 6, placed for both diagonals, R5C9 = 8 -> R5C8 = 4, R5C6 = 1, R4C6 = 8, R3C7 = 1 (cage sum), 1,8 placed for D/, R6C7 = 7 -> R6C8 = 1
19b. R7C3 = 9 -> R8C34 = 9 = [81]
[I'd originally included step 19b, then mistakenly persuaded myself that it wasn't necessary.]
and the rest is naked singles.