Thanks Afmob and Ed for correcting my typos
Prelims
a) R12C1 = {49/58/67}, no 1,2,3
b) R1C89 = {69/78}
c) R2C45 = {18/27/36/45}, no 9
d) R34C1 = {49/58/67}, no 1,2,3
e) R4C67 = {19/28/37/46}, no 5
f) R5C12 = {18/27/36/45}, no 9
g) R67C1 = {15/24}
h) R7C67 = {59/68}
i) R89C1 = {14/23}
j) R9C89 = {19/28/37/46}, no 5
k) 11(3) cage at R1C6 = {128/137/146/236/245}, no 9
l) 19(3) cage at R8C5 = {289/379/469/478/568}, no 1
m) 26(4) cage at R5C5 = {2789/3689/4589/4679/5678}, no 1
1. 45 rule on C1 1 innie R5C1 = 8, R5C2 = 1, clean-up: no 5 in R12C1, no 5 in R34C1, no 5 in R7C1
2. R6C1 = 5 (hidden single in C1), R7C1 = 1, clean-up: no 4 in R89C1
2a. Naked pair {23} in R89C1, locked for N7
3. 45 rule on R789 1 remaining innie R7C2 = 1 outie R6C9 + 4 -> R6C9 = {1234}, R7C2 = {5678}
4. 45 rule on R1234 2 innies R4C48 = 11 = {29/38/47/56}, no 1
5. 45 rule on N9 2 innies R79C7 = 1 outie R6C9 + 10
5a. Min R79C7 = 11, no 1 in R9C7
6. 45 rule on R9 3 outies R8C126 = 14
6a. Max R8C12 = 12 -> min R8C6 = 2
6b. 1 in N8 only in R9C456, locked for R9, clean-up: no 9 in R9C89
7. 1 in N9 only in R8C789, locked for 25(6) cage at R6C9, no 1 in R6C9, clean-up: no 5 in R7C2 (step 3)
7a. Min R6C9 = 2 -> min R79C7 (step 5) = 12, no 2 in R9C7
8. 45 rule on R789 3 remaining outies R6C239 = 13 = {247/346}, no 9, 4 locked for R6
9. 13(3) cage at R7C3 = {247/256/346} (cannot be {238} because 2,3 only in R7C4), no 8,9
9a. 2,3 only in R7C4 -> R7C4 = {23}
9b. 9 in N7 only in R8C2 + R9C23, locked for 31(5) cage at R8C2, no 9 in R9C45
10. Hidden killer pair 4,5 in 13(3) cage at R7C3 and 31(5) cage at R8C2 for N7, 13(3) cage contains one of 4,5 -> 31(5) cage must contain one of 4,5 in N7 (it may also contain 4 or 5 in N8) -> 31(5) cage = {25789/34789/35689/45679} (cannot be {16789} which doesn’t contain 4 or 5), no 1
11. R9C6 = 1 (hidden single in R9), clean-up: no 9 in R4C7
11a. R9C6 = 1 -> R8C6 + R9C7 = 12 = {39/48/57}, no 2,6
11b. R8C126 = 14 (step 6), min R8C12 = 6 -> max R8C6 = 8, clean-up: no 3 in R9C7
11c. Min R12C6 = 5 -> max R1C7 = 6
12. 45 rule on N6 2 innies R46C9 = 1 outie R4C6 + 2, IOU no 2 in R6C9, clean-up: no 6 in R7C2 (step 3)
13. 45 rule on N6 3 innies R4C79 + R6C9 = 12 = {138/147/237/246/345} (cannot be {129/156} because R6C9 only contains 3 and 4), no 9
13a. 5 of {345} must be in R4C9, 3 or 4 of other combinations must be in R6C9 -> no 3,4 in R4C9
14. 25(6) cage at R6C9 = {123469/123478/123568/124567}, 2 locked for N9, clean-up: no 8 in R9C89
14a. 25(6) cage = {123469/123478/123568} (cannot be {124567} which clashes with R9C89)
14b. 25(6) cage = {123469/123478/123568}, CPE no 3 in R9C9, clean-up: no 7 in R9C8
14c. Killer pair 6,7 in 25(6) cage and R9C89, locked for N9, clean-up: no 8 in R7C6, no 5 in R8C6 (step 11a)
15. 15(4) cage at R4C4 = {1239/1248/1257/1347/1356/2346}
15a. 9 of {1239} must be in R45C4 (R456C4 cannot be {23}1 which clashes with R7C4), no 9 in R5C3
15b. 1 in R6C4 or 15(4) cage = {2346} -> R6C4 = {1236}
15c. 9 in N4 only in R4C123, locked for R4, clean-up: no 2 in R4C48 (step 4), no 1 in R4C7
[I don’t know whether this counts as a “serendipity” step.]
16. 31(5) cage at R8C2 (step 10) = {25789/34789/35689/45679}
16a. Consider permutations for R6C9 + R7C2 (step 3) = [37/48]
R6C9 + R7C2 = [37] => 8 in N7 only in 31(5) cage
or R6C9 + R7C2 = [48] => 4 in N9 only in R9C78, locked for R9 => 31(5) cage cannot be 4{5679} which clashes with R9C89
-> 31(5) cage = {25789/34789/35689}
16b. 31(5) cage must contain one of 4,5 in N7 (step 10) -> no 4,5 in R9C45
16c. Killer pair 2,3 in R7C4 and 31(5) cage, locked for N8, clean-up: no 9 in R9C7 (step 11a)
16d. Killer pair 2,3 in R9C1 and 31(5) cage, locked for R9, clean-up: no 7 in R9C9
16e. Naked pair {46} in R9C89, locked for R9 and N9, clean-up: no 8 in R8C6 (step 11a)
16f. 7,9 in R9 only in R9C2345, locked for 31(5) cage, no 7,9 in R8C2
17. R79C7 = R6C9 + 10 (step 5)
17a. R6C9 = {34} -> R79C7 = 13,14 = {58}/[95], 5 locked for C7 and N9
18. 31(5) cage at R8C2 (step 16a) = {25789/34789} (cannot be {35689} which clashes with R9C7), no 6
[Ed pointed out Ed that 31(5) cage contains both of 7,9 (step 16f) is simpler.]
18a. 6 in N7 only in R78C3, locked for C3
18b. 13(3) cage at R7C3 (step 9) = {256/346}, no 7
19. R6C239 (step 8) = {247/346}
19a. 6 of {346} must be in R6C2, 4 of {247} must be in R6C9 -> no 3,4 in R6C2
20. 19(3) cage at R7C5 = {469/568} (cannot be {478} which clashes with R8C6), no 7, 6 locked for N8, clean-up: no 8 in R7C7
20a. Naked pair {59} in R7C67, locked for R7
20b. R7C35 = {46} (hidden pair in R7)
21. 25(6) cage at R6C9 (step 14a) = {123478} (only remaining combination), 8 locked for N9 -> R9C7 = 5, R8C6 = 7 (step 11a), R7C67 = [59], clean-up: no 3 in R4C7
21a. 25(6) cage = {123478} -> R6C9 = 4, R7C2 = 8 (step 3), R9C89 = [46], clean-up: no 9 in R1C8, no 6 in R4C6
21b. R6C9 = 4 -> R4C79 (step 13) = 8 = [62/71], R4C6 = {34}
21c. Naked triple {238} in R7C4 + R9C45, 8 locked for R9 and N8
22. 45 rule on N3 2 innies R13C7 = 1 outie R4C9 + 4
22a. R4C9 = {12} -> R13C7 = 5,6 = {14/24} (cannot be {23} because whichever value is in R4C9 must also be in one of R13C7), 4 locked for N3
23. 11(3) cage at R1C6 = {128/146/236}
23a. 1 of {146} must be in R1C7 -> no 4 in R1C7
24. R3C7 = 4 (hidden single in N3), clean-up: no 9 in R4C1
25. 9 in R4 only in 14(3) cage at R3C2 = {239}, R3C2 = {23}
25a. Killer pair 2,3 in 14(3) cage and 17(3) cage at R6C2, locked for N4
26. 45 rule on N5 2 innies R4C56 = 1 outie R5C3 + 4
26a. R5C3 = {47} -> R4C56 = 8,11 = [53/74/83]
26b. R4C9 = 1 (hidden single in R4), R4C7 = 7 (step 21b), R4C6 = 3, clean-up: no 6 in R3C1
[I forgot about clean-up for R4C48 (step 4) but this isn’t important, so I haven’t re-worked.]
27. Naked pair {29} in R4C23, locked for N4 and 14(3) cage at R3C2 -> R3C2 = 3, R6C3 = 3 (hidden single in N4), R6C2 = 6 (cage sum), R4C1 = 4, R3C1 = 9
28. R5C4 = 7 -> R456C4 = 8 = {125} (only remaining combination) = [521], R4C5 = 8, R4C8 = 6, clean-up: no 9 in R1C9, no 4,7 in R2C5
29. Naked pair {78} in R1C89, locked for R1 and N3
30. R2C6 = 8 (hidden single in C6) -> R1C67 = 3 = [21], R3C6 = 6, R3C5 = 1 (cage sum)
30a. R2C45 = {45} (only remaining combination) = [45]
31. R7C4 = 3 -> R78C3 = 10 = {46}, locked for C3 and N7
and the rest is naked singles.