Prelims
a) R1C34 = {16/25/34}, no 7,8,9
b) R1C67 = {16/25/34}, no 7,8,9
c) R2C34 = {19/28/37/46}, no 5
d) R2C67 = {49/58/67}, no 1,2,3
e) R8C34 = {15/24}
f) R8C67 = {69/78}
g) R9C34 = {19/28/37/46}, no 5
h) R9C67 = {18/27/36/45}, no 9
i) 8(3) cage at R1C8 = {125/134}
j) 11(3) cage at R3C6 = {128/137/146/236/245}, no 9
k) 21(3) cage at R4C2 = {489/579/678}, no 1,2,3
l) 20(3) cage at R4C8 = {389/479/569/578}, no 1,2
m) 10(3) cage at R8C2 = {127/136/145/235}, no 8,9
n) 26(4) at R2C9 = {2789/3689/4589/4679/5678}, no 1
1a. 45 rule on C5 1 innie R5C5 = 1
1b. 45 rule on C1234 2 innies R5C34 = 15 = {69/78}
1c. 45 rule on C6789 2 innies R5C67 = 7 = {25/34}
2a. Hidden triple {789} in R1C125
2b. Killer triple 7,8,9 in R1C2 and 21(3) cage at R4C2, locked for C2
2c. 6 in R1 only in R1C34 = {16} or R1C67 = {16} (locking cages), 1 locked for R1
2d. 8(3) cage at R1C8 = {125/134} -> R2C8 = 1, clean-up: no 6 in R1C6, no 9 in R2C34
2e. 18(3) cage at R1C1 = {279/378}, 7 locked for R1 and N1, clean-up: no 3 in R2C4
2f. 18(3) cage = {279/378} -> R2C2 = {23}
2g. 45 rule on R9 1 innie R9C5 = 2 outies R8C28 + 1
2h. Min R8C28 = 3 -> min R9C5 = 4
2i. Max R8C28 = 8 -> no 8,9 in R8C8
3a. 45 rule on N1 2 outies R12C4 = 8 = [17]/{26}, clean-up: no 2,3,4 in R1C3, no 2,6 in R2C3
3b. 45 rule on N3 2 outies R12C6 = 9 = [18/27/36]/{45}, no 9, clean-up: no 4 in R2C7
3c. 45 rule on N7 2 outies R89C4 = 5 = [14/23/41] -> R9C3 = {679}, clean-up: no 1 in R8C3
3d. 45 rule on N9 2 outies R89C6 = 13 = {67}/[85/94] -> R9C7 = {2345}
3e. 45 rule on C12 2 outies R37C3 = 13 = {49/58}/[67]
3f. 45 rule on C89 2 outies R37C7 = 10 = [28]/{37/46}/[91], no 5, no 9 in R7C7
3g. Killer pair 1,2 in R12C4 and R89C4, locked for C4
3h. Max R67C4 = 11 -> no 9 in R67C4
3i. Min R67C4 = 8 (cannot be {34} which clashes with R89C4) -> max R6C3 = 4
4a. 45 rule on N4 3 innies R456C3 = 12 = {129/138/147/237} (cannot be {156} which clashes with R1C3, cannot be {246} which clashes with R89C3, cannot be {345} because no 3,4,5 in R5C3), no 6, clean-up: no 9 in R5C4 (step 1b)
4b. R5C3 = {789} -> no 7,8,9 in R4C3
4c. Killer triple 7,8,9 in 21(3) cage at R4C2 and R5C3, locked for N4
4d. 9 in C4 only in 17(3) cage at R3C4 = {179/269/359}, no 4,8
4e. 12(3) cage at R4C1 = {156/246/345}
4f. Killer triple 4,5,6 in 12(3) cage and 21(3) cage, locked for N4
4g. Max R4C3 = 3 -> min R34C4 = 14, no 3
[I spent time looking at other interactions in C34 before finding a relatively simple forcing chain …]
4h. R5C34 = 15 (step 1b), R12C4 (step 3a) = 8 = [17]/{26}, R89C4 (step 3c) = 5 = [14/23/41]
4i. Consider placement for 8 in C4
R5C4 = 8 => R5C3 = 7 => R46C3 = {23} => R1C3 = 1 (hidden single in C3) => R12C4 = [62]
or 8 in 12(3) cage at R6C3 = 1{38}, 3 locked for C4
-> R89C4 = {14}, locked for C4 and N8, R12C4 = {26}, locked for C4 and N2, clean-up: no 6 in R1C3, no 3 in R1C6 (step 3b), no 4,5 in R1C7, no 3 in R2C3, no 7 in R2C6 (step 3b), no 6,7 in R2C7, no 9 in R5C3 (step 1b), no 4 in R8C4, no 9 in R8C6 (step 3d), no 6 in R8C7, no 7 in R9C4, no 5 in R9C7
4j. Naked pair {78} in R5C34, locked for R5
4k. Killer pair 4,8 in R2C3 and R2C67, locked for R2
4l. 21(3) cage at R4C2 = {489/579} (cannot be {678} which clashes with R5C3), no 6, 9 locked for C2
4m. 6 in N4 only in 12(3) cage at R4C1, locked for N1
4n. 3 in C3 only in R46C3, locked for N4
4o. 6 in N1 only in R3C23, locked for R3
4p. R37C3 (step 3e) = {49}/[67] (cannot be {58} which clashes with R12C3), no 5,8
4q. R89C6 (step 3d) = {67} (cannot be [85] which clashes with R12C6), locked for C6 and N8, clean-up: no 7 in R8C7, no 4 in R9C7
4r. Hidden killer triple 4,6,7 in 23(4) cage at R1C5 and R6C5 for C5, 23(4) cage cannot contain all of 4,6,7 -> R6C5 = {467}
4s. 12(3) cage at R6C3 = 1{38}/[273], no 5
4t. R34C4 = {59} (hidden pair in C4) -> R4C3 = 3 (cage sum)
[I was then doing the more routine steps after the key step 4i before I spotted this final breakthrough.]
5a. 18(3) cage at R1C1 (step 2e) = {279/378}
5b. R2C34 = [46] (cannot be [82] which clashes with 18(3) cage), R1C4 = 2 -> R1C3 = 5, R8C3 = 2 -> R8C4 = 4, R9C4 = 1 -> R9C3 = 9, R367C3 = [617] -> R5C34 = [87]
5c. Naked pair {34} in R1C89, locked for R1 and N3 -> R1C67 = [16], R2C6 = 8 (step 3b) -> R2C7 = 5, R1C5 = 9, R34C4 = [59]
5d. 21(3) cage at R4C2 = {579} (last remaining combination), 5,7 locked for C2, 5 locked for N4, R1C12 = [78] -> R2C2 = 3 (cage sum)
5e. R12C5 = [97] = 16 -> R34C5 = 7 = [34]
5f. R3C6 = 4 -> R4C67 = 7 = [52], R9C7 = 3 -> R9C6 = 6, R8C6 = 7 -> R8C7 = 8
5g. R5C67 (step 1c) = 7 = [34]
5h. R37C7 (step 3f) = 10 = [91]
5i. R8C58 = [56], R6C7 = 7
5j. R4C8 = 8 -> R56C8 = 12 = [93]
and the rest is naked singles.