Prelims
a) R5C12 = {39/48/57}, no 1,2,6
b) R5C89 = {17/26/35}, no 4,8,9
c) R89C5 = {29/38/47/56}, no 1
d) 22(3) cage at R1C1 = {589/679}
e) 8(3) cage at R3C1 = {125/134}
f) 21(3) cage at R3C3 = {489/579/678}, no 1,2,3
g) 19(3) cage at R6C1 = {289/379/469/478/568}, no 1
h) 21(3) cage at R6C7 = {489/579/678}, no 1,2,3
i) 9(3) cage at R7C2 = {126/135/234}, no 7,8,9
j) 6(3) cage at R7C8 = {123}
k) 19(3) cage at R8C4 = {289/379/469/478/568}, no 1
l) 19(3) cage at R8C9 = {289/379/469/478/568}, no 1
1a. 22(3) cage at R1C1 = {589/679}, 9 locked for N1
1b. Naked triple {123} in 6(3) cage at R7C8, locked for N9
1c. 45 rule on N1 3 innies R1C3 + R3C13 = 8 = {125/134} -> R3C3 = {45}, R1C3 + R3C1 = {12/13}, 1 locked for N1
1d. 21(3) cage at R3C3 = {489/579} (cannot be {678} because R3C3 only contains 4,5) -> R3C4 + R4C3 = {79/89}
1e. 45 rule on N7 3 innies R7C13 + R9C3 = 22 = {589/679}, 9 locked for N7
1f. Min R7C3 = 5 -> max R6C3 + R7C4 = 7, no 7,8,9 in R6C3 + R7C4
1g. 45 rule on R89 4 innies R8C2378 = 10 = {1234}, locked for R8, 4 locked for N7, clean-up: no 7,8,9 in R9C5
1h. 45 rule on R89 2 outies R8C28 = 5 = {23}
1i. 9(3) cage at R7C2 = {234} (only remaining combination), locked for N7
1j. 45 rule on C12 4 innies R2378C2 = 15 = {2346}, locked for C2, 6 locked for N1, clean-up: no 7 in 22(3) cage at R1C1, no 8,9 in R5C1
1k. R2C3 = 7 (hidden single in N1) -> R23C2 = 8 = {26}, 2 locked for C2 and N1
1l. R78C2 = [34] -> R8C3 = 2, R7C8 = 2, clean-up: no 6 in R5C9
1m. R3C3 = 4 (hidden single in N1) -> R3C4 + R4C3 = {89}, CPE no 8,9 in R4C4
1n. 45 rule on C89 2 outies R28C7 = 7 = [43/61]
1o. Max R2C7 = 6 -> min R23C8 = 12, no 1 in R23C8
1p. 45 rule on C89 3 remaining innies R238C8 = 15 = {159/168/348/357} (cannot be {456} because R8C8 only contains 1,3
1q. R8C8 = {13} -> no 3 in R23C8
1r. 1 in N7 only in R9C12, locked for R9
1s. 45 rule on C1234 1 outie R5C5 = 1 innie R6C4 + 3, no 1,2,3 in R5C5, no 7,8,9 in R6C4
1t. 45 rule on C6789 1 outie R4C5 = 1 innie R6C6, no 1,2,3,4 in R4C5, no 6,7,8,9 in R6C6
1u. 45 rule on R12 3 outies R3C258 = 17 = {269/278/368} (cannot be {cannot be {179/359} because R3C2 only contains 2,6), no 1,5
1v. Killer pair 8,9 in R3C258 and R3C4, locked for R3
2a. Consider permutations for 8(3) cage at R3C1 = [125/341] -> R4C2 = {24}
8(3) cage = [125]
or 8(3) cage = [341] => R5C12 = {57}
-> 5 in R4C2 + R5C12, locked for N4
2b. 5 in C3 only in R79C3, locked for N7
2c. R7C13 + R9C3 (step 1e) = {589}, 8 locked for N7
2d. 14(3) cage at R8C1 = {167}, 6 locked for C1
2e. Naked triple {589} in R127C1, 5 locked for C1 and N1, clean-up: no 7 in R5C2
2f. Naked triple {589} in R479C3, 8,9 locked for C3
2g. 19(3) cage at R6C1 = {289/379/478} -> R6C1 = {234}
2h. 12(3) cage at R6C3 = {138/156/345}, no 9
2i. R7C3 = {58} -> no 5 in R7C4
3a. 18(3) cage at R2C7 = {459/468/567} = [459/468/486/648/657], no 9 in R2C8
3b. R3C258 (step 1u) = {269/368} (cannot be [278] because R2C2 = 6 clashes with R2C7 = {46}cannot be [287] because R2C2 = 6 clashes with R2C78 = [65]), no 7, 6 locked for R3
3c. 3 of {368} must be in R3C5 -> no 8 in R3C5
3d. 18(3) cage at R2C7 = {459/468}, 4 locked for R2 and N3
3e. Hidden killer pair 5,7 in R3C67 and R3C9 for R3, R3C67 cannot contain both of 5,7 -> 12(3) cage at R3C6 must contain one of 5,7, R3C9 = {57}
3f. 12(3) cage at R3C6 = {147/156/237/345} -> R4C7 = {2346}
3g. 45 rule on N3 3 innies R1C7 + R3C79 = 14 = {158/167/257} (cannot be {239} because R3C9 only contains 5,7, cannot be {356} which clashes with 18(3) cage), no 3,9
3h. 6,8 of {158/167} only in R1C7 -> no 1 in R1C7
3i. Killer pair 5,6 in R1C7 + R3C79 and 18(3) cage, locked for N3
3j. 13(3) cage at R1C8 = {139/238}, no 7
3k. 7 in N3 only in R1C7 + R3C79 = {167/257}, no 8
3l. 12(3) cage = {147} can only be [174] (cannot be [714] which clashes with R28C7), 12(3) cage = {156} can only be [156] (cannot be [516] which clashes with R1C7 + R3C79 = [617] -> no 1 in R3C7
3m. R1C7 + R3C79 = {257} (only remaining combination), 2,5 locked for N3, 2 locked for C7
3n. 18(3) cage = {468} (only remaining combination), 8 locked for C8 and N3
3o. 12(3) cage = {156/345} must be [156/354] -> no 5 in R3C6
3p. 5 in R3 only in R3C79, locked for N3
3q. 9 in R3 only in R3C45, locked for N2
3r. R3C258 = {269/368} must be [296/638], no 2,6 in R3C5
3s. R3C5 = {39} -> no 6 in 12(3) cage at R1C5
3t. 6 in R1 only in R1C46, locked for N2
3u. R1C3 = {13} -> 13(3) cage at R1C3 cannot contain 6 (because no 4 in R2C4)
3v. R1C6 = 6 (hidden single in R1) -> R1C7 + R2C6 = 8 = [71], R3C79 = [25], R3C28 = [68] -> R3C1456 = [1937], R4C7 = 3 (cage sum), R4C2 = 5 -> R4C1 = 2 (cage sum), R8C7 = 1 -> R2C7 = 6 (step 1n), R2C8 = 4
[Cracked; clean-ups omitted from here.]
4a. R3C5 = 3 -> R12C5 = 9 = [45]
4b. R2C2 = 2 -> R12C4 = [28], R2C1 = 9, R1C12 = [58], R5C2 = 9 -> R5C1 = 3, R6C12 = [47], R7C1 = 8 -> R79C3 = [59]
4c. R89C5 = [92] (only remaining permutation) -> 21(3) cage at R6C7 = [849] (only remaining permutation)
4d. R9C3 = 9 -> R89C4 = 10 = [73], R89C1 = [67]
4e. R8C9 = 8 -> R9C89 = 11 = [56]
4f. R7C9 = 7 -> R6C89 = 11 = [92], R5C9 = 1 -> R5C8 = 7
and the rest is naked singles.