If I have made any errors, including typos, or anything needs clarification, please contact me by PM. I hope that my explanations for step 9a and step 24 are clear enough.
Prelims
a) R45C1 = {39/48/57}, no 1,2,6
b) R45C9 = {29/38/47/56}, no 1
c) R89C5 = {16/25/34}, no 7,8,9
d) 11(3) cage at R1C1 = {128/137/146/236/245}, no 9
e) 9(3) cage at R6C1 = {126/135/234}, no 7,8,9
f) 7(3) cage at R6C2 = {124}
g) 20(3) cage at R6C6 = {389/479/569/578}, no 1,2
h) 23(3) cage at R7C4 = {689}
i) 41(8) cage at R1C3 = {12356789}, no 4
j) 44(8) cage at R2C2 = {23456789}, no 1
k) 37(8) cage at R2C7 = {12345679}, no 8
Steps resulting from Prelims
1a. Naked triple {124} in 7(3) cage at R6C2, locked for R6
1b. Naked triple {689} in 23(3) cage at R7C4, locked for R7 and N8, clean-up: no 1 in R89C5
1c. 4 in N2 only in R3C456, locked for R3 and 36(7) cage at R3C4, no 4 in R4C3467
2. 45 rule on R6789 1 innie R6C5 = 7
2a. 45 rule on R6 2 remaining innies R6C19 = 11 = [38/56/65]
2b. 9(3) cage at R6C1 = {126/135/234}
2c. 6 of {126} must be in R6C1 -> no 6 in R8C1
2d. Min R6C9 = 5 -> max R78C9 = 8, no 8,9 in R8C9
3. 23(5) cage at R7C2 cannot be formed from five of {123457} (because {23457} = 21) -> cage must contain one of 6,8,9 -> R8C3 = {689}
3a. 25(4) cage at R8C2 = {1789/3589/3679/4579/4678} (cannot be {2689} which clashes with R8C3), no 2
3b. Hidden killer triple 6,8,9 in 25(4) cage and R8C3 for N7, R8C3 = {689} -> 25(4) cage must contain two of 6,8,9 -> 25(4) cage = {1789/3589/3679/4678} (cannot be {4579} which only contains one of 6,8,9)
4. 26(5) cage at R7C7 cannot be formed from five of {123457} (because {23457} = 21) -> cage must contain one of 6,8,9, {3457} = 19 -> no 6 in cage -> R8C7 = {89}
5. 45 rule on N5 4 innies R46C46 = 23 = {1589/2489/4568} (cannot be {3569} because R6C4 only contains 1,2,4), no 3, 8 locked for N5
5a. 1 of {1589} must be in R6C4 -> no 1 in R4C46
5b. 1,4 only in R6C4 -> R6C4 = {14}
6. 2 in R6 only in R6C23, locked for N4
6a. 44(8) cage at R2C2 = {23456789}, 2 locked for N1
6b. 11(3) cage at R1C1 = {137/146}, no 5,8, 1 locked for N1
6c. X-Wing for 1 in 11(3) cage at R1C1 and 41(8) cage at R1C3, no other 1 in R12
7. 45 rule on N9 3(1+2) outies R6C9 + R89C6 = 14
7a. R6C9 = {568} -> R89C6 = 6,8,9 = {15/17/27} (cannot be {24/35/45} which clash with R89C5), no 3,4 in R89C6
7b. 26(5) cage at R7C7 cannot contain both of 1,2 (because remaining three cells cannot total 23), R89C6 = {15/17/27} -> no 1,2 in R7C78
8. 45 rule on N8 6(3+3) outies R7C2378 + R8C37 = 34
8a. Max R7C2378 = {3457} = 19 -> min R8C37 = 15 -> R8C37 = {69/89}, 9 locked for R8
8b. R8C37 = {69/89} = 15,17 -> R7C2378 = 17,19 = {1457/2357/3457}, 5,7 locked for R7
9. 7 in R3 only in R7C2378, 7 in N8 only in R89C46 -> 23(5) cage at R7C2 and 26(5) cage at R7C7 must both contain 7 -> 23(5) cage = {12479/12578/13478/14567/23567}, 26(5) cage = {14579/23579/24578}
9a. 25(4) cage at R8C2 (step 3b) = {1789/3589/3679} (cannot be {4678} because 23(5) cage cannot be {12}9{47} since R7C2378, step 8b, cannot contain both of 1,2), no 4, 9 locked for R9 and N7
[This is the simplest way I could find to do this step; I’d originally been looking at interactions between the 23(5) and 26(5) cages and R89C5]
9b. R8C7 = 9 (hidden single in R8)
10. 45 rule on N9 2 remaining innies R7C78 = 1 outie R6C9 + 3
10a. R6C9 = {568} -> R7C78 = 8,9,11 = {35/45/47}
10b. 45 rule on N9 4 remaining innies R7C789 + R8C9 = 16 = {1357/1456/2347/2356} (cannot be {1267} because 1,2,6 only in R78C9)
10c. 1 of {1357/1456} must be in R7C9 (because {35/45} are needed for R7C78), no 1 in R8C9
10d. 4 of {1456/2347} must be in R7C78 (because {45/47} are needed for R7C78), no 4 in R78C9
[I ought to have spotted this step earlier …]
11. 45 rule on C1 2 innies R39C1 = 1 outie R1C2 + 13
11a. Min R39C1 = 14, no 1,2,3
11b. Max R39C1 = 17 -> max R1C2 = 4
12. 2 in C1 only in R78C1, locked for N7
12a. 9(3) cage at R6C1 contains 2 = {126/234}, no 5, clean-up: no 6 in R6C9 (step 2a)
12b. R6C1 = {36} -> no 3 in R78C1
[The next 45 was spotted a long time ago, but is only useful after the previous step.]
13. 45 rule on N7 3(1+2) outies R6C1 + R89C4 = 12
13a, R6C1 = {36} -> R89C4 = 6,9 = {15/27} (cannot be {24/45} which clash with R89C5), no 3,4
14. R89C5 = {34} (hidden pair in N8), locked for C5
14a. 3 in N5 only in R5C46, locked for R5, clean-up: no 9 in R4C1, no 8 in R4C9
15. 45 rule on C1 4 innies R1239C1 = 24 = {1689/3579} (cannot be {3489} because 11(3) cage at R1C1 cannot contain both of 3,4, cannot be {3678/4569} which clash with R45C1, cannot be {4578} because 11(3) cage at R1C1 cannot contain both of 4,7), no 4, 9 locked for C1, clean-up: no 3 in R4C1
15a. 5,8,9 must be in R39C1 -> no 6,7 in R39C1
15b. R12C1 = {16/37} -> R1C2 = {14} (step 6b)
16. 45 rule on R7, R7C2378 = 17,19 (step 8b) -> 2 remaining innies R7C19 = 3,5 contains 2 = [12/21/23], no 4
17. R6C9 = {58} -> R7C78 = 8,11 (step 10) = {35/47}
17a. 20(4) cage at R8C8 = {1478/1568/2468} (cannot be {2378/2567/3458/3467} which clash with R7C78), no 3
17b. Killer pair 4,5 in R7C78 and 20(4) cage, locked for N9
18. 3 in C1 only in R126C1
18a. Grouped X-Wing for 3 in R126C1 and 44(8) cage at R2C2, no other 3 in N14
19. 45 rule on N14 3(1+2) innies R1C3 + R4C3 + R6C1 = 1 outie R6C4 + 16
19a. R6C4 = {14} -> R1C3 + R4C3 + R6C1 = 17,20, max R1C3 + R6C1 = 15 -> no 1 in R4C3
19b. R6C23 = {12} (hidden pair in N4), locked for R6 -> R6C4 = 4
19c. R14C3 + R6C1 = 20 = {89}3/{59}6 (cannot be {68}6 which clashes with R8C3), no 6,7 in R14C3, 9 locked for C3
19d. R3C6 = 4 (hidden single in R3)
20. 45 rule on R89 4 outies R7C2378 = 2 innies R8C19 + 11
20a. R7C2378 = 17,19 (step 8b) -> R8C19 = 6,8 = [42/17/26], no 3
20b. 3 in N9 only in R7C789, locked for R7
21. 3 in N7 only in 25(4) cage at R8C2 (step 9a) = {3589/3679}, no 1
22. R1C3 “sees” all of 44(8) cage at R2C2 except for R45C2, R1C3 = {589} and 44(8) cage contains all of 5,8,9 -> the value in R1C3 must be in one of R45C2
22a. 45 rule on N1 3 outies R45C2 + R5C3 = 1 innie R1C3 + 10
22b. R1C3 = {589} -> R45C2 + R5C3 = 15,18,19 = {357/378/468/379/469} (cannot be {456} which clashes with R45C1)
22c. 5 of {357} must be in R5C2 -> no 5 in R4C2 + R5C3
22d. 3,9 of {379} must be in R45C2 -> no 7 in R45C2
22e. 8 of {378/468} must be in R45C2 -> no 8 in R5C3
23. Consider placement for 1 in 37(8) cage at R2C7
1 in R3C789, locked for R3 and 37(8) cage, no 1 in R4C8 + R5C78 => R4C7 = 1 (hidden single in N6)
or 1 in R4C8 +R5C78, locked for 37(8) cage, no 1 in R3C789 => R1C7 = 1 (hidden single in N3), 1 in R3 only in R3C45
-> 1 in R14C7, locked for C7
and 1 must be in R3C45 + R4C7 -> 36(7) cage at R3C4 = {1245789/1345689}
24. 1 in C7 only in R14C7
24a. 45 rule on N36 3(2+1) innies R14C7 + R6C9 = 1 outie R6C6 + 4, IOU R14C7 cannot be {13} -> no 3 in R14C7
24b. R14C7 cannot be {12} = 3 (because R6C9 cannot be 1 more than R6C6) -> no 2 in R14C7
24c. R14C7 cannot be {15} = 6 (because R6C6 cannot be 2 more than R6C9) -> no 5 in R14C7
24d. R14C7 cannot be {18} = 9 (because R6C6 cannot be 5 more than R6C9) -> no 8 in R14C7
24e. R14C7 = {16/17} = 7,8 -> R6C6 must be 3 or 4 more than R6C9 -> R6C69 = [85/95] -> R6C9 = 5, R6C1 = 6 (step 2a), clean-up: no 5 in R45C9
25. R6C1 = 6 -> R78C1 = 3 = {12}, locked for C1 and N7
25a. R1C2 = 1 (hidden single in N1), R6C23 = [21], R4C7 = 1 (hidden single in C7)
25b. Naked pair {37} in R12C1, locked for C1 and N1, clean-up: no 5 in R45C1
25c. Naked pair {48} in R45C1, locked for C1 and N4 -> R5C3 = 7, clean-up: no 4 in R4C9
25d. R4C2 = 3 (hidden single in N4), R9C3 = 3 (hidden single in C3), R89C5 = [34], clean-up: no 8 in R5C9
26. R6C9 = 5 -> R78C9 = 8 = [17/26]
27. R6C9 = 5 -> R7C78 = 8 (step 10) = {35}, locked for R7 and N9 -> R7C23 = [74]
27a. R7C78 = {35} = 8, R8C7 = 9 -> R89C6 = 9 = {27}, locked for C6 and N8
27b. Naked pair {15} in R89C4, locked for C4, R8C3 = 6 (cage sum)
27c. Naked triple {589} in R8C2 + R9C12, 8 locked for C2
28. Naked pair {59} in R3C1 + R5C2, locked for 44(8) cage at R2C2 -> R23C2 = [46], R23C3 = {28}, locked for C3
29. 8 in N6 only in R6C78, locked for R6 -> R6C6 = 9
29a. R46C46 (step 5) = {2489} (only remaining combination) -> R4C46 = [28], R45C1 = [48], R7C6 = 6, clean-up: no 9 in R5C9
30. Naked pair {59} in R3C5 + R4C3, CPE no 5 in R4C5 -> R4C5 = 6, R5C4 = 3
30a. Naked pair {15} in R5C56, locked for R5 -> R5C2 = 9, R39C1 = [59], R14C3 = [95], R3C45 = [79], R7C45 = [98]
30b. Naked triple {123} in R3C789, locked for R3, N3 and 37(8) cage at R2C7 -> R23C3 = [28]
30c. Naked pair {46} in R5C78, locked for R5 and 37(8) cage at R2C7 -> R5C9 = 2, R4C9 = 9, R4C8 = 7, R2C78 = [59]
and the rest is naked singles.
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