Prelims
a) R1C56 = {19/28/37/46}, no 5
b) R12C7 = {39/48/57}, no 1,2,6
c) R23C4 = {59/68}
d) R34C5 = {69/78}
e) R3C89 = {19/28/37/46}, no 5
f) R45C1 = {49/58/67}, no 1,2,3
g) R45C8 = {49/58/67}, no 1,2,3
h) R45C9 = {19/28/37/46}, no 5
i) R5C23 = {49/58/67}, no 1,2,3
j) R6C78 = {69/78}
k) R9C56 = {69/78}
l) 21(3) cage at R1C3 = {489/579/678}, no 1,2,3
1. 45 rule on N3 1 innie R3C7 = 3, placed for D/, clean-up: no 9 in R12C7, no 7 in R3C89
2. R45C8 = {49/58} (cannot be {67} which clashes with R6C78), no 6,7 in R45C8
2a. Killer pair 8,9 in R45C8 and R6C78, locked for N6, clean-up: no 1,2 in R45C9
2b. Killer pair 6,7 in R45C9 and R6C78, locked for N6
2c. 3 in N6 only in R456C9, locked for C9
3. 45 rule on N1 1 outie R1C4 = 1 innie R3C3 + 2, no 1,8,9 in R3C3, no 5 in R1C4
4. 45 rule on N7 2 innies R7C1 + R9C3 = 7 = {16/25/34}, no 7,8,9
5. 45 rule on N1 3 innies R123C3 = 19 = {289/469/478/568}
5a. 5 of {568} must be in R3C3 (R12C3 cannot be {58} because 21(3) cage cannot contain both of 5,8) -> no 5 in R12C3
5b. 21(3) cage at R1C3 = {489/678}, CPE no 8 in R1C12
6. 6 in N6 only in R45C9 = {46}
or R6C78 = {69} -> R45C8 = {58} (cannot be {49}, locking-out cages), locked for C8 and N6, clean-up: no 2 in R3C9, no 7 in R6C78
6a. Naked pair {69} in R6C78, locked for R6 and N6, clean-up: no 4 in R45C9
6b. Naked pair {37} in R45C9, locked for C9 and N6
[I missed 45 rule on N6 3 innies R45C7 + R6C9 = 7 = {124}, locked for N6, which would have simplified this step and given the three combinations directly in step 2.]7. R5C23 = {49/67} (cannot be {58} which clashes with R5C8), no 5,8 in R5C23
8. 45 rule on N14 3 innies R6C123 = 1 outie R1C4 + 3
8a. R6C123 cannot be {124} = 7 which clashes with R6C9 -> no 4 in R1C4, clean-up: no 2 in R3C3 (step 3)
9. Hidden killer quad 1,2,3,4 in R1C56 + R2C56 + R3C6 for N2, R1C56 contains one of 1,2,3,4 -> R2C56 = {1234}, R3C6 = {124}
10. 5 in N2 only in R23C4 = {59}, locked for C4 and N2, clean-up: no 1 in R1C56, no 7 in R3C3 (step 3), no 6 in R4C5
11. 45 rule on N5 3 innies R4C56 + R5C6 = 16
11a. Min R4C5 = 7 -> max R45C6 = 9, no 9 in R45C6
11b. 9 in N5 only in R45C5, locked for C5, clean-up: no 6 in R9C6
11c. R34C5 = [69]{78}, R9C56 = [69]/{78} -> combined half cage R349C5 = [69]{78}/{78}6, 6 locked for C5, clean-up: no 4 in R1C6
12. R123C3 (step 5) = {469/478/568} = {49}6/{68}5/{78}4 (cannot be {69}4 because 21(3) cage at R1C3 cannot contain both of 6,9)
12a. 12(3) cage at R2C1 cannot be {138} = 3{18} which clashes with R123C3 = {478/568} and with R3C389 = 6{19/28} -> no 8 in 12(3) cage
13. Consider placement for 9 in C5
R4C5 = 9
or R5C5 = 9 => R5C23 = {67}, locked for R5 => R45C9 = [73] => R4C5 = 8
-> R4C5 = {89}, clean-up: no 8 in R3C5
14. R3C9 = 8 (hidden single in R3) -> R3C8 = 2, clean-up: no 4 in R12C7
14a. Naked pair {57} in R12C7, locked for C7 and N3
14b. 8 in N2 only in R1C456, locked for R1
14c. Min R3C12 = {15} = 6 (R3C12 cannot be {14} which clashes with R3C6) -> max R2C1 = 6
15. 12(3) cage at R2C1 = {129/147/156} (cannot be {237} because 2,3 only in R2C1, cannot be {246/345} which clashes with R123C3), no 3, 1 locked for N1
15a. 1 in R1 only in R1C89, locked for N3
16. 3 in N1 only in 14(3) cage at R1C1 = {239/347/356}, no 8
16a. R2C3 = 8 (hidden single in N1) -> R1C34 = 13 = {67}, locked for R1 -> R12C7 = [57]
16b. 8 in N2 only in R1C56 = {28}, locked for R1 and N1
16c. 14(3) cage = {239} (only remaining combination, cannot be {356} because 5,6 only in R2C2) -> R1C12 = {39}, locked for R1 and N1, R2C2 = 2, placed for D\
16d. R2C89 = {69} (hidden pair in N3), locked for R2 -> R23C4 = [59]
16e. Naked pair {69} in R26C8, locked for C8
17. R1C4 = R3C3 + 2 (step 3)
17a. R1C4 = {67} -> R3C3 = {45}
18. R6C123 = R1C4 + 3 (step 8)
18a. Max R1C4 = 7 -> max R6C123 = 10, no 8 in R6C12
19. 8 in R6 only in R6C456, locked for N5 -> R4C5 = 9, R3C5 = 6, R1C34 = [67], clean-up: no 4 in R5C1, no 7 in R5C2, no 1 in R7C1 (step 4), no 9 in R9C6
19a. R1C4 = R3C3 + 2 (step 3)
19b. R1C4 = 7 -> R3C3 = 5, placed for D\, clean-up: no 2 in R7C1 (step 4)
19c. Naked pair {78} in R9C56, locked for R9 and N8
19d. R6C4 = 8 (hidden single in C4), placed for D/
20. R7C7 = 8 (hidden single on D\)
20a. 45 rule on N9 2 remaining innies R7C89 = 6 = [15/42]
21. 9 in N4 only in R45C1 = [49] or R5C23 = {49} -> 4 in R4C1 + R5C23, locked for N4 (locking cages)
22. R6C123 = R1C4 + 3 (step 8)
22a. R1C4 = 7 -> R6C123 = 10 = {127/235}, 2 locked for R6 and N4
22b. Naked pair {14} in R16C9, locked for C9
22c. R78C9 = {25} (hidden pair in C9), locked for N9
22d. R3C3 = 5 -> R4C23 = 9 = [63/81]
23. 18(3) cage at R8C8 = {279/459/567} (cannot be {369} because R8C9 only contains 2,5), no 1,3
24. 1 on D\ only in R4C4 + R5C5 + R6C6, locked for N5
24a. R4C56 + R5C6 = 16 (step 11)
24b. R4C5 = 9 -> R45C6 = 7 = {25} (cannot be {34} which clashes with R23C6, ALS block), locked for C6 and N5 -> R1C56 = [28], R9C56 = [87]
24c. R78C6 = {69} (hidden pair in C6), locked for N8
25. Naked pair {14} in R17C8, locked for C8 -> R8C8 = 7, placed for D\, R9C8 = 3, clean-up: no 4 in R7C1 (step 4)
26. 5 in R9 only in R9C12, locked for N7, clean-up: no 2 in R9C3 (step 4)
27. R7C3 = 7 (hidden single on D/) -> R7C2 + R8C3 = 8 = [62], R7C1 = 3, R9C3 = 4 (step 4), R1C1 = 9, placed for D\, R9C9 = 6, placed for D\
28. R8C9 = 5, R7C9 = 2 -> R7C8 = 4 (step 20a), R1C8 = 1, R1C9 = 4, placed for D/, R5C5 = 1, placed for D/
and the rest is naked singles, without using the diagonals.