Prelims

a) R1C56 = {14/23}
b) R34C4 = {15/24}
c) R34C8 = {49/58/67}, no 1,2,3
d) R5C45 = {19/28/37/46}, no 5
e) R89C2 = {39/48/57}, no 1,2,6
f) R8C34 = {12}
g) 11(3) cage at R1C1 = {128/137/146/236/245}, no 9
h) 11(3) cage at R6C6 = {128/137/146/236/245}, no 9
i) 22(3) cage at R8C6 = {589/679}
j) 27(4) cage at R1C3 = {3789/4689/5679}, no 1,2
k) 28(4) cage at R6C2 = {4789/5689}, no 1,2,3
l) 36(8) cage at R4C2 = {12345678}, no 9

Steps resulting from Prelims
1a. Naked pair {12} in R8C34, locked for R8
1b. Killer pair 1,2 in R34C4 and R8C4, locked for C4, clean-up: no 8,9 in R5C5
1c. 22(3) cage at R8C6 = {589/679}, CPE no 9 in R8C89

2. 36(8) cage at R4C2 = {12345678}, CPE no 1…8 in R4C1 -> R4C1 = 9, clean-up: no 4 in R3C8
2a. 45 rule on N1 2 remaining innies R12C3 = 16 = {79}, locked for C3, N1 and 27(4) cage at R1C3, no 7,9 in R12C4
2b. R12C3 = 16 -> R12C4 = 11 = {38/56}, no 4 in R12C4
2c. 7 in C1 only in R56789C1, locked for 36(8) cage at R4C2, no 7 in R45C2

3. 28(4) cage at R6C2 = {4789/5689}, 9 locked for R7
3a. 34(6) cage at R6C5 must contain 9, locked for C5
3b. 9 in N2 only in R23C6, locked for C6
3c. 22(3) cage at R8C6 = {589/679}, 9 locked for C7 and N9

4. 9 in N6 only in 30(7) cage at R4C6 = {1234569} (only possible combination), no 7,8

5. 45 rule on R1 4 outies R2C2348 = 16 = {1267/1357/2347} (cannot be {1249} because R2C4 only contains 3,5,6,8, cannot be {1258/1348/1456/2356} because R2C3 only contains 7,9), no 8,9 -> R2C3 = 7, R1C3 = 9, clean-up: no 3 in R1C4 (step 2b)
5a. 6 of {1267} must be in R2C4 -> no 6 in R2C28
5b. 7 in N2 only in R3C56, locked for R3, clean-up: no 6 in R4C8

6. 45 rule on C1234 3(1+2) outies R5C5 + R9C56 = 9
6a. Min R9C56 = 3 -> max R5C5 = 6, clean-up: no 3 in R5C4
6b. Min R59C5 = 3 -> max R9C6 = 6
6c. Min R5C5 + R9C6 = 2 -> max R9C7 = 7

7. 12(3) cage at R5C3 cannot be {129}, which clashes with R8C3, no 9 in R6C4

8. 45 rule on R1234 3 innies R4C236 = 10 = {136/145/235}, no 8

9. 28(4) cage at R6C2 = {4789/5689}
9a. Hidden killer pair 7,9 in 28(4) cage and R89C2 for C2, 28(4) cage cannot contain both of 7,9 (because [79]{48} clashes with R89C2 = {48}) -> 28(4) cage and R89C2 must each contain one of 7,9 in C2 -> R89C2 = {39/57}, no 4,8
9b. 7 in C2 only in 28(4) cage = {4789} or R89C2 = {57} -> no 5 in R6C2 + R7C23 (locking-out cages)
9c. {5689} can only be [6985/8965] -> no 6 in R7C24

10. 17(3) cage at R2C9 = {179/269/278/359/368/458/467}
10a. 7 of {179} must be in R4C9 -> no 1 in R4C9
10b. 9 in N3 only in 17(3) cage = {179/269/359} or R34C8 = [94] (locking cages) -> no 4 in R4C9

11. 11(3) cage at R1C1 = {128/146/236/245}
11a. 5 of {245} must be in R1C12 (R1C12 cannot be {24} which clashes with R1C56), no 5 in R2C2

12. 7 in N3 only in 18(4) cage at R1C7 = {1278/1467/2367/2457}
12a. Hidden killer triple 5,6,8 in 11(3) cage at R1C1, R1C4 and 18(4) cage for R1, 11(3) cage contains one of 5,6,8, R1C4 = {568} -> 18(4) cage must contain one of 5,6,8 in R1
12b. 18(4) cage only contains one of 5,6,8 -> no 5 in R2C8

13. 45 rule on N4789 2 outies R6C45 = 1 innie R7C9 + 13
13a. Max R6C45 = 17 -> max R7C9 = 4
13b. Min R6C45 = 14, R6C4 = {5678}, R6C5 = {6789}
13c. Min R6C4 = 5 -> max R56C3 = 7, no 8 in R56C3

14. 28(4) cage at R6C2 = {4789/5689}
14a. 7 or 9 of {4789} must be in R7C4 (R6C2 + R7C23 cannot be {479/789} which clash with R89C2), 5 of {5689} must be in R7C4
-> R7C4 = {579}

15. 1,2,6 in N7 only in R789C1 + R79C3, CPE no 1,2,6 in R4C3

16. 45 rule on N47 2 outies R67C4 = 2 remaining innies R89C3 + 7
16a. Min R67C4 = 11 -> min R89C3 = 4 -> no 1,2 in R9C3
16b. Hidden killer pair 1,2 in R789C1 and R8C3 for N7, R8C3 = {12} -> R789C1 must contain one of 1,2,3
16c. 36(8) cage at R4C2 contains both of 1,2 -> R4C2 + R5C12 + R6C1 must contain one of 1,2
16d. Hidden killer pair 1,2 in R4C2 + R5C12 + R6C1 and R56C3 for N4, R4C2 + R5C12 + R6C1 contains one of 1,2 -> R56C3 must contain one of 1,2
16e. Killer pair 1,2 in R56C3 and R8C3, locked for C3
16f. 12(3) cage at R5C3 = {138/147/156/237/246} (cannot be {345} because R56C3 must contain one of 1,2)

17. Consider combinations for R34C4 = {15/24}
R34C4 = {15}, locked for C4 => R12C4 = [83] => R1C56 = {14}, locked for N2
or R34C4 = {24}, killer pair 2,4 in R1C56 and R3C4 for N2
-> no 4 in R23C56, no 1 in R3C3, clean-up: no 5 in R3C4

18. 17(4) cage at R9C3 = {1349/1358/1367/1457/2348/2357/2456} (cannot be {1259/1268}which clash with R8C4)
18a. Killer pair 1,2 in R8C4 and 17(4) cage, locked for N8

19. Consider combinations for R12C4 (step 2b) = {56}/[83]
R12C4 = {56}, locked for C4 => R34C4 = {24}, locked for C4 => no 4,6 in R5C4
or R12C4 = [83] => max R6C45 = [79] = 16 => max R7C9 (step 13) = 3 => R5C45 cannot be {46} (because R5C45 “see” all cells of 30(7) cage at R4C6 except for R67C9)
-> no 4,6 in R5C45

20. 34(6) cage at R6C5 = {136789/245689} (cannot be {145789/235789/345679} which clash with R7C4 because R6C5 is the only cell of the 34(6) cage which doesn’t “see” R7C4)
[I then had an incorrect sub-step, so I’ve had to re-work from here.]

21. R6C45 = R7C9 + 13 (step 13)
21a. R7C9 = {1234} -> R6C45 + R7C9 = [591/692/793/894]/{68}1 (cannot be {78}2 because R5C45 = [91] which clashes [91] of 30(7) cage at R4C6 in R67C9), no 7 in R6C5

22. Caged X-Wing for 8 in 36(8) cage at R4C2 and 28(4) cage at R6C2 for N47, no other 8 in N47

23. Consider combinations for R12C4 (step 2b) = {56}/[83]
R12C4 = {56}, locked for C4 => R567C4 = {789} with 8 in R56C4
or R12C4 = [83]
-> 8 in R156C4, locked for C4

24. 17(4) cage at R9C3 (step 18) = {1349/1367/1457/2357/2456}
24a. Consider combinations for R34C4 = {24}/[51]
R34C4 = {24}, locked for C4 => R8C4 = 1 => 17(4) cage = {2357/2456}
or R34C4 = [51], no 9 in R5C4, R12C4 (step 2b) = [83] => R5C4 = 7 => R7C4 = 9
-> 17(4) cage = {1367/1457/2357/2456}, no 9

25. 28(4) cage at R6C2 = {4789/5689}
25a. Consider combinations for R6C45 (step 21a) = [59/69/79/89]/{68}
R6C45 = [59/69/79/89] => R7C4 = 9 (hidden single in N8) => 28(4) cage = {4789}
or R6C45 = {68}, locked for R6 => R6C2 = {47} => 28(4) cage = {4789}
-> 28(4) cage = {4789}, no 5,6
25b. 6 in N47 and C3 only in R569C3 (the other 6s in N47 are in 36(8) cage at R4C2), locked for C3

26. Consider combinations for R12C4 (step 2b) = {56}/[83]
R12C4 = {56}, locked for C4 => R567C4 = {789}, locked for C4
or R12C4 = [83] => R57C4 = {79}, locked for C4
-> no 7 in R9C4

27. 17(4) cage at R9C3 (step 24a) = {1367/1457/2357/2456}
27a. 7 of {1367/1457/2357} must be in R9C5 -> no 1,3 in R9C5
27b. 1,2 of {1367/1457/2357} must be in R9C6 -> no 3 in R9C6

28. 8 in C3 only in R37C3
28a. 45 rule on C12 4(3+1) outies R347C3 + R7C4 = 24
28b. R7C4 = {79} -> R347C3 = 15,17 = {348/458}, 4 locked for C3

29. R67C4 = R89C3 + 7 (step 16)
29a. Max R89C3 = 8 -> max R67C4 = 15, no 7 in R6C4, clean-up: no 3 in R7C9 (step 21a)
[Cracked at last, the rest is fairly straightforward.]

30. 12(3) cage at R5C3 (step 16f) = {138/156}, 1 locked for C3 and N4 -> R8C34 = [21], clean-up: no 5 in R3C4
30a. Naked pair {24} in R34C4, locked for C4
30b. Killer pair 2,4 in R1C56 and R3C4, locked for N2
30c. Naked quad {3568} in R1269C4, locked for C4, clean-up: no 2 in R5C5
30d. 1 in N7 only in R79C1, locked for C1

31. R347C3 (step 28b) = {348/458}, 12(3) cage at R5C3 (step 30) = {138/156}
31a. Killer pair 3,5 in R347C3 and 12(3) cage, locked for C3 -> R9C3 = 6
31b. 17(4) cage at R9C3 (step 24a) = {2456} (only remaining combination) -> R9C4 = 5, R9C56 = {24}, locked for R9, clean-up: no 7 in R8C2

32. R2C4 = 3 (hidden single in C4), R1C4 = 8 (step 2b), clean-up: no 2 in R1C56
32a. Naked pair {14} in R1C56, locked for R1 and N2 -> R34C4 = [24], clean-up: no 9 in R3C8

33. 9 in N3 only in 17(3) cage at R2C9, locked for C9
33a. R5C8 = 9 (hidden single in N6), R5C4 = 7, R5C5 = 3, R7C4 = 9

34. R7C6 = 3 (hidden single in N8) -> 34(6) cage at R6C5 (step 20) = {136789} (only remaining combination) -> R6C5 = 9, 1 locked for R7 and N9
34a. R7C9 = 2 (hidden single in N9)

35. R6C4 = 6 -> R56C3 = 6 = {15}, locked for C3 and N4 -> R4C3 = 3

36. R7C1 = 5 (hidden single in R7), clean-up: no 7 in R9C2

37. R2C2348 (step 5) = {2347} (only remaining combination) -> R2C28 = {24}, locked for R2

38. Naked pair {15} in R45C6, locked for C6, N5 and 30(7) cage at R4C6 -> R1C56 = [14], R9C56 = [42]
38a. Naked pair {46} in R5C79, locked for R5 and N6 -> R6C9 = 3
38b. Naked pair {28} in R5C12, locked for N4 and 36(8) cage at R4C2 -> R4C2 = 6

39. R6C6 = 8 -> R6C78 = 3 = {12}, locked for R6 and N6

40. R4C5 = 2 -> 30(5) cage at R2C5 = {25689} (only remaining combination) -> R2C67 = [98], R23C5 = {56}, locked for C5 and N2
40a. R3C6 = 7, R4C7 = 5, R3C7 = 4 (cage sum)

41. R2C8 = 2
41a. R2C2 = 4 -> R1C12 = 7 = [25]

and the rest is naked singles.

I'll rate my walkthrough for Pinata #48 at least Hard 1.5. I used several short forcing chains.