Prelims
a) R12C5 = {69/78}
b) R2C34 = {19/28/37/46}, no 5
c) R34C8 = {69/78}
d) R34C9 = {19/28/37/46}, no 5
e) R5C12 = {39/48/57}, no 1,2,6
f) R5C89 = {16/25/34}, no 7,8,9
g) R67C1 = {19/28/37/46}, no 5
h) R67C2 = {17/26/35}, no 4,8,9
i) R89C5 = {18/27/36/45}, no 9
j) R8C67 = {15/24}
k) 21(3) cage at R2C1 = {489/579/678}, no 1,2,3
l) 19(3) cage at R6C9 = {289/379/469/478/568}, no 1
m) 10(4) cage at R1C1 = {1234}
n) 11(4) cage at R1C8 = {1235}
o) 27(4) cage at R6C8 = {3789/4689/5679}, no 1,2
Steps resulting from Prelims
1a. 10(4) cage at R1C1 = {1234}, CPE no 1,2,3,4 in R1C2
1b. 11(4) cage at R1C8 = {1235}, locked for N3, clean-up: no 7,8,9 in R4C9
1c. 27(4) cage at R6C8 = {3789/4689/5679}, CPE no 9 in R9C8
2. 45 rule on C12 1 innie R1C2 = 8, clean-up: no 2 in R2C4, no 7 in R2C5, no 4 in R5C1
2a. R1C34 = 9 = {27/36/45}, no 1,9
3. 45 rule on C89 1 innie R9C8 = 1, clean-up: no 6 in R5C9, no 8 in R8C5, no 5 in R8C6
3a. R9C67 = 11 = {29/38/47/56}
3b. 11(4) cage at R1C8 = {1235}, 1 locked for C9, clean-up: no 9 in R3C9, no 6 in R5C8
4. 45 rule on R89 3 innies R8C89 + R9C9 = 24 = {789}, locked for N9, clean-up: no 2,3,4 in R9C6 (step 3a)
4a. 27(4) cage at R6C8 = {3789/4689/5679}
4b. 3 of {3789} must be in R7C8 -> no 3 in R6C8
4c. 19(3) cage at R6C9 = {289/379/469/568} (cannot be {478} which clashes with R34C9)
4d. 2,3 of {289/379} must be in R7C9 -> no 2,3 in R6C9
5. 45 rule on R12 3 innies R1C1 + R2C12 = 13
5a. Max R1C1 + R2C2 = 7 -> min R2C1 = 6
6. Consider combinations for R5C89 = {25/34}
R5C89 = {25} => naked triple {235} in R125C8, locked for C8
or R5C89 = {34} => caged X-wing for 3 in 11(4) cage at R1C8 and R5C89, no other 3 in C89
-> no 3 in R7C8
[Alternatively this could be done by combined cages 11(4) cage at R1C8 and R5C89, the two-dimensional combined cage locking 3 for C8. I prefer the more elegant short forcing chain.]
6a. 27(4) cage at R6C8 = {4689/5679} -> R67C8 = {46/56}, 6 locked for C8, clean-up: no 9 in R34C8
6b. Naked pair {78} in R34C8, locked for C8 -> R8C8 = 9
6c. Naked pair {78} in R89C9, locked for C9, clean-up: no 2,3 in R4C9
6d. Naked pair {46} in R34C9, locked for C9, clean-up: no 3 in R5C8
6e. Killer triple 4,5,6 in R4C9, R5C89 and R6C8, locked for N6 -> R6C9 = 9, clean-up: no 1 in R7C1
6f. R6C9 = 9 -> R78C9 = 10 = [28/37]
6g. 3 in C8 only in R12C8, locked for N3
[After the key step 6, things are a lot easier.]
7. 45 rule on N5 2 outies R5C37 = 9 = {18/27}/[63], no 3,4,5,9 in R5C3
7a. R5C12 = {39/57}/[84], R5C89 = {25}/[43] -> combined cage R5C1289 = {39}{25}/{57}[43]/[84]{25}, 5 locked for R5
7b. R5C37 = {18}/[63] (cannot be {27} which clashes with combined cage R5C1289), no 2,7
8. Killer quad 1,2,3,4 in R234C2 and R67C2, locked for C2, 4 must be in R234C2 -> no 4 in R1C1, clean-up: no 8,9 in R5C1
8a. Killer pair 3,5 in R5C12 and R5C89, locked for R5, clean-up: no 6 in R5C3 (step 7b)
8b. Naked pair {18} in R5C37, locked for R5
8c. 6 in R5 only in R5C456, locked for N5
8d. Killer quad 1,2,3,5 in R1C1, R1C34 and R1C89, locked for R1
9. 24(4) cage at R1C6 = {2679/3489/3678/4569/4578} (cannot be {2589/3579} because 2,3,5 only in R2C6, cannot be {1689} = {69}[18] which clashes with R12C5), no 1
9a. 2,3,5 only in R2C6 -> R2C6 = {235}
9b. Hidden killer quad 6,7,8,9 in R2C1, R2C34, R2C5 and R2C7 for R2, R2C1 = {679}, R2C34 contain one of 6,7,8,9, R2C5 = {689} -> R2C7 must contain one of 6,7,8,9 -> no 4 in R2C7
10. 45 rule on R6789 3 innies R6C456 = 15 = {258/348/357}, no 1
10a. 1 in N5 only in R4C456, locked for R4
10b. 34(7) cage at R3C3 must contain 1, locked for R3
10c. R1C1 + R2C12 = 13 (step 5) must contain 1 for 10(4) cage at R1C1 -> R1C1 + R2C2 = {13}, locked for N1 and 10(4) cage, R2C1 = 9
10d. R2C1 = 9 -> R34C1 = 12 = [48]/{57}
10e. Caged X-Wing for 3 in R1C1 + R2C2 and 11(4) cage at R1C8, no other 3 in R12
10f. 3 in R3 only in R3C456, locked for 34(7) cage, no 3 in R4C37
10g. 34(7) cage contains 3 so must also contain 8 -> caged X-Wing for 8 in 34(7) cage and R34C8, no other 8 in R34
10h. Clean-ups: no 6 in R1C34 (step 2a), no 6 in R1C5, no 7 in R2C3, no 1,7 in R2C4, no 4 in R3C1, no 1 in R6C1
11. R2C7 = 7 (hidden single in R2), R34C8 = [87], R34C1 = [75], R5C1 = 3 -> R5C2 = 9, R1C1 = 1, R2C2 = 3
11a. Naked pair {25} in R2C68, locked for R2, clean-up: no 8 in R2C4
11b. R2C5 = 8 (hidden single in R2) -> R1C5 = 7, clean-up: no 2 in R1C34 (step 2a)
11c. Naked pair {45} in R1C34, locked for R1 -> R1C89 = [32], R2C89 = [51], R5C9 = 5 -> R5C8 = 2, R2C6 = 2
11d. R6C9 = 9, R7C9 = 3 -> R8C9 = 7 (cage sum), R9C9 = 8
11e. Clean-ups: no 5 in R7C2, no 1,2 in R8C5, no 4 in R8C7, no 2 in R9C5
12. Caged X-Wing for 4 in R34C2 and R34C9, no other 4 in R34
12a. R3C9 = 4 (hidden single in N3) -> R4C9 = 6, R34C2 = [24], R67C8 = [46], clean-up: no 6 in R6C2, no 5 in R9C6 (step 3a)
12b. Naked pair {17} in R67C2, locked for C2
12c. Naked pair {56} in R89C2, locked for N7
12d. R89C2 = {56} = 11 -> R89C1 = 10 = [82], R67C1 = [64]
12e. R9C7 = 4 (hidden single in C7), R9C8 = 1 -> R9C6 = 7 (cage sum), clean-up: no 5 in R8C5
13. R5C4 = 7 (hidden single in R5)
13a. R6C456 (step 10) = {258} (only remaining combination), locked for R6 and N5
13b. Naked pair {17} in R6C23, locked for R6 and N4 -> R45C3 = [28], R456C7 = [813]
13c. R4C4 = 1 (hidden single in R4) -> R5C5 + R6C6 = 12 = [48], R5C6 = 6, R1C67 = [96], R4C56 = [93], clean-up: no 5 in R9C5
13d. Naked pair {36} in R89C5, locked for C5 and N5
13e. R8C6 = 4 (hidden single in C6) -> R8C7 = 2
and the rest is naked singles.