3x3::k:2560:4865:6658:6658:6658:4867:4867:9988:9988:2560:4865:4865:4865:6658:4867:1797:1797:9988:5894:5894:5894:3591:3591:4867:3336:2569:9988:8970:5894:3595:3591:5132:3336:3336:2569:9988:8970:3595:3595:5132:5132:5132:2829:2829:9988:8970:4110:1807:1807:5132:5904:2829:5649:9988:8970:4110:1807:3858:5904:5904:5649:5649:5649:8970:2835:2835:3858:5140:5397:5397:5397:2582:8970:8970:3858:3858:5140:5140:5140:5397:2582:

Preliminaries courtesy of SudokuSolver
Cage 16(2) n47 - cells ={79}
Cage 7(2) n3 - cells do not use 789
Cage 10(2) n1 - cells do not use 5
Cage 10(2) n36 - cells do not use 5
Cage 10(2) n9 - cells do not use 5
Cage 11(2) n7 - cells do not use 1
Cage 7(3) n457 - cells ={124}
Cage 23(3) n58 - cells ={689}
Cage 11(3) n6 - cells do not use 9
Cage 26(4) n12 - cells do not use 1

1. 16(2)r6c2 = {79}: both locked for c2

2. 23(3)r6c6 = {689} -> 9 locked with r67c2 for c67 (caged x-wing)

3. "45" on n5: 4 innies r46c46 = 25 and must have 1,2,4 for r6c4 = {1789/2689/4579/4678}(no 3)
3a. can't have more than one of 1,2,4 -> no 1,2,4 in r4c46

4. "45" on n36: 1 outie r4c6 + 10 = 2 innies r1c7 + r6c8
4a. -> min. 2 innies = 15 (no 1,2,3,4,5; no 6 in r1c7)
4b. max. 2 innies = 17 -> max. r4c6 = 7

5. "45" on n12: 3 outies r1c7 + r4c24 = 21.
5a. max. r1c7 + r4c4 = 18 -> min. r4c2 = 3

6. "45" on n47: 4 innies r4c2 + r679c3 = 14
6a. no 7 in r4c2 -> r679c3 <> 7 -> no 1,2,4 in r9c3

7. "45" on n89: 3 outies r6c68 + r9c3 = 21
7a. max. r6c68 = 17 -> min. r9c3 = 4
7b. r6c68 can't be [97] = 16 because of r6c2 -> no 5 in r9c3

8. "45" on n47: 4 innies r4c2 + r679c3 = 14
8a. min. r679c3 = 9 -> max. r4c2 = 5
8b. min. r4c2 + r9c3 = 9 -> max. r67c3 = 5 = {12/14}: 1 locked for c3 and no 1 in r7c4
8c. min. r4c2 + r67c3 = 6 -> max. r9c3 = 8

9. "45" on n12: 3 outies = 21: max. r1c7 + r4c2 = 14 -> min. r4c4 = 7

The key step
10. h25(4)n5 = {2689/4579/4678}
10a. but [75] blocked from r4c46 by outies n12 can't make 21
10b. -> [7549] blocked
10c. = {2689/4678} (no 5)
10d. must have 6 & 8: both locked for n5 and 6 for c6

Liked this one too.
11. 39(7)r1c8 = {1356789/2346789}: note must have 8
11a. "45" on n36: r4c6 + 10 = r1c7 + r6c8. r4c6 = (67) -> two innies = 16/17
11b. but can't be [88] which would leave no 8 for 39(7)
11c. = [97/98]
11d. r1c7 = 9, no 6 in r6c8

12. 15(4)r7c4 must have 6,7,8 for r9c3
12a. but {24} blocked by r6c4 = (24)
12b. = {1257/1347/1356}(no 8,9)
12c. must have 1: 1 locked for c4 and n8
12d. can't have both 6,7 -> no 6,7 in r789c4

13. outies n89 = 21. r9c3 = (67) -> r6c68 = 14/15 = [68/87]
13a. must have 8: locked for r6

14. 9 must be in 23(3)r6c6: only in r7c56: 9 locked for r7 and n8

15. r67c2 = [97], r9c3 = 6, -> r789c4 = {135} only: 3,5 locked for c4 and n8
15a. r9c3 = 6 -> from outies n89 = 21, r6c68 = 15 = [87] only permutation
15b. r1c7 + r6c8 = 16 -> 1 remaining outie n36, r4c6 = 6
15c. r4c6 = 6 -> r34c7 = 7 = {25/34}(no 1,7,8)
15d. r7c56 = [69]

16. "45" on c9: 1 outie r1c8 - 4 = 1 innie r7c9
16a. = [51/62/84], r1c8 = (568), r7c9 = (124)

17. 5 in c9 only in 39(7) = {1356789}(no 2,4, no 5 in r1c8)
17a. no 5 in r1c8 -> no 1 in r7c9 (IODc9=-4)
17b. must have 1,3,7,9 which are only in c9: locked for c9
17c. 9 locked for n6 also

18. 2 & 4 in c9 only in n9: locked for n9

19. r6c8 = 7 -> r7c789 = 15 = {258/348}(no 1)
19a. must have 8: locked for r7 and n9

20. 10(2)n9 = [64] only permutation

21. r7c9 = 2, -> r1c8 = 6 (IODc9=-4)
21a. r7c78 = 13 = {58} only: 5 locked for r7 and n9

22. "45" on n9: 1 remaining outie r8c6 - 1 = 1 innie r9c7 = [21/43]
22a. r8c7 = 7 (hsingle n9)

23. 10(2)r3c8 = {28} only: both locked for c8
23a. r7c78 = [85]

24. 7(2)n3 = {34} only: both locked for r2 and n3
24a. -> 3 which must be in 37(7) only in n6: 3 locked for n6

25. r34c7 = 7 = {25} only: both locked for c7

26. r34c78 must have two 2's -> 2 locked for r34 (X-wing)

27. outies n12 = 21 -> r4c24 = 12 = [39/57]

28. 14(3)r3c4: must have 7,9 for r4c4 = {149/167/347)(no 5,8)
28a.must have 1,3 which are only in r3c5 -> r3c5 = (13)
28b. must have 4,6 -> r3c4 = (46)

29. "45" on c1: 1 innie r3c1 = 1 outie r9c2
29a. both = (1358)

Realise now I could have done this next step (and the previous couple to get it ready) after step 11, so could have made the rest of this WT better optimised
30. r3c3 = 9 (hsingle r3)

31. 11(2)n7 = {38} only permutation: both locked for r8 and n7

32. naked pair {24} in r8c56: both locked for r8 and n8

33. naked triple {135} in r9c247: all locked for r9

Much easier now.

1. 16(2)r6c2 = {79}
23(3)r6c6 = {689}
-> No 9 anywhere else in r67

2. 39(7)r1c8 = {36789(15|24)}
-> Either (24) or (15) in r789c9
-> r789c9 from [2{46}], [4{28}], or [5{19}]
-> whichever of (689) is in r89c9 goes in 39(7) in r1c8 and in n6 in r456c7

3. 7(3)r6c3 = {124}
Innies n5 = r46c56 = +25(4)
Since max r6c4 = 4 -> Min r4c6 = 5
-> 9 cannot be in r456c7
-> 10(2)r8c9 cannot be {19}

4. r789c9 from [2{46}] or [4{28}]
If the former -> 22(4)r6c8 = [{578}2]
If the latter since r1c8 = 8 -> 22(4)r6c8 = [{567}4]
I.e., 22(4) = {57(28|46)}
Since r7c256 already contain three of (6789}
-> At most one of (6789} in r7c78
-> 5 in r7c78.

5. Outies n89 = r6c6 + r6c8 + r9c3 = +21(3)
r6c6 is from (689) and r6c8 from (678)
(79) cannot both go in r6c68, or both in r7c5678
-> One of r6c6 and rc68 is from (79) and the other from (68)
-> r9c3 is even.

r9c3 cannot be 2 since max r6c6 + r6c8 = +17
r9c3 cannot be 8 (puts r789c4 = {124})
r9c3 cannot be 4 (puts r6c68 = [98] puts 10(2)n9 = [46] leaves no place for 4 in n8)
-> r9c3 = 6
-> r6c68 from [96] or [87]
-> 6 in 23(3) in r7c56
-> 6 in n9 in r8

6. Whichever of (67) is in r6c8 cannot go in r9c7 in n9 since that would put r8c6 = 8
-> Whichever of (67) is in r6c8 goes in n9 in r8c7
Outies - Innies n9 -> r6c8 + r8c6 = r9c7 + 8
-> 9 cannot go in r9c7
-> 9 in n9 in r89c8
-> 9 in n6 in r456c9
-> 9 in n3 in r1c7

7. Remaining Outies n12 -> r4c2 + r4c4 = +12(2)
-> Min r4c2 = 3
Remaining Innies n47 = r4c2 + r6c3 + r7c3 = +8(3)
Can only be [3{14} or [5{12}]
[r4c2,r4c4] from [39] or [57]
Also given r9c3 = 6 and r4c2 + r4c4 = +12(2) -> Outies n47 = r4c4 + r6c4 = +11.
Must be [92] or [74]
-> Remaining Innies n5 = r6c4 + r6c6 = +14(2)
Whether [r4c2,r4c4] is [39] or [57] -> [r6c4,r6c6] = [68]

-> 23(3) = [869], 16(2) = [97], 22(4) = [7{58}2], 10(2)n9 = [64]

8. Also r1c8 = 6
-> 10(2)r3c8 = {28}
-> r7c78 = [85]
-> 7(2)n3 = {34}
-> r34c7 = {25}
-> 11(3)n6 = {146}

9. Since r6c4 from (24) -> r789c4 can only be {135}
-> 14(3)r3c4 is from [419] or [617] (Cannot be [437] since 7 in r4c4 puts 4 in r6c4)
-> HS 1 in n5/c6 -> r5c6 = 1
-> 11(3)n6 = [641]
-> 7(2)n3 = [43]
-> NS r9c7 = 3
-> Outies n9 -> r8c6 = 4
-> r89c8 = {19}

10. Also r123c6 = {235}
Also r7c3 = 1
-> r7c4 = 3
-> r7c1 = 4

11. Also 9 in n2 in r2c45
Innies - outies c1 -> r3c1 = r9c2
-> 9 in n1/r3 in r3c3
-> 9 in n7 in r89c1
-> 11(2)n7 = {38}
-> 20(4)n8 = [2873]
Since 2 already in r3 in r3c78 -> 2 not in r3c1 -> 2 not in r9c2
-> r9c1 = 2
-> r8c1 = 9
-> NS r9c2 = 5
-> r4c24 = [39]
etc.

Prelims

a) R12C1 = {19/28/37/46}, no 5
b) R2C78 = {16/25/34}, no 7,8,9
c) R34C8 = {19/28/37/46}, no 5
d) R67C2 = {79}
e) R8C23 = {29/38/47/56}, no 1
f) R89C9 = {19/28/37/46}, no 5
g) 11(3) cage at R5C7 = {128/137/146/236/245}, no 9
h) 7(3) cage at R6C3 = {124}
i) 23(3) cage at R6C6 = {689}
j) 26(4) cage at R1C3 = {2789/3689/4589/4679/5678}, no 1

1a. Naked pair {79} in R67C2, locked for C2, clean-up: no 2,4 in R8C3
1b. Naked triple {689} in 23(3) cage at R6C6, CPE no 6,8,9 in R89C6
1c. Caged X-Wing for 9 in R67C2 and 23(3) cage at R6C6, no other 9 in R67
1d. 45 rule on C1 1 outie R9C2 = 1 innie R3C1, no 7,9 in R9C2 -> no 7,9 in R3C1
1e. 45 rule on N5 4 innies R46C46 = 25 = {1789/2689/4579/4678} (cannot be {3589/3679} because R6C4 only contains 1,2,4), no 3
1f. R6C4 = {124} -> no 1,2,4 in R4C46
1g. Min R4C4 = 5 -> max R3C45 = 9, no 9 in R3C45
1h. Min R4C6 = 5 -> max R34C7 = 8, no 8,9 in R34C7
1i. 45 rule on N12 3(1+2) outies R1C7 + R4C24 = 21
1j. Max R4C24 = 17 -> min R1C7 = 4
1k. Max R1C7 + R4C4 = 18 -> min R4C2 = 3

2a. 45 rule on C9 1 outie R1C8 = 1 innie R7C9 + 4 -> R1C8 = {56789}, R7C9 = {12345}
2b. 22(4) cage at R6C8 = {2578/3478/3568/4567} (cannot be {1678} because R7C78 = {67/68/78/678 clash with R7C2 + R7C56, killer ALS block), no 1, clean-up: no 5 in R1C8
2c. R7C78 cannot be {67/68/78} -> one of 6,7,8 must be in R6C8 = {678}
2d. Killer quad 6,7,8,9 in R7C2 + R7C56 + R7C78, locked for R7
2e. 1 in R7 only in R7C134, CPE no 1 in R9C3
2f. 39(7) cage at R1C8 must contain 3, locked for C9, clean-up: no 7 in R1C8, no 7 in R89C9

3. 45 rule on N36 2(1+1) innies R1C7 + R6C8 = 1 outie R4C6 + 10
3a. Max R1C7 + R6C8 = 17 -> max R4C6 = 7
3b. Min R4C6 = 5 -> min R1C7 + R6C8 = 15, no 4,5,6 in R1C7
3c. 26(4) cage at R1C3 = {2789/3689/4589/4679/5678}
3d. 2 of {2789} must be in R1C345 (R1C345 cannot be {789} which clashes with R1C7) -> no 2 in R2C5
3e. 3 of {3689} must be in R1C345 (R1C345 cannot be {689} which clashes with R1C8) -> no 3 in R2C5

4. 45 rule on C789 2 innies R19C7 = 2 outies R48C6 + 2
4a. Max R48C6 = 13 -> max R19C7 = 15, min R1C7 = 7 -> max R9C7 = 8

5. 45 rule on N47 2(1+1) innies R4C2 + R9C3 = 1 outie R6C4 + 7
5a. Max R6C4 = 4 -> max R4C2 + R9C3 = 11, min R4C2 = 3 -> max R9C3 = 8
5b. R789C4 cannot be {124} = 7 (which clashes with R6C4) -> no 8 in R9C3

6. 45 rule on N89 3(2+1) outies R6C68 + R9C3 = 21
6a. Max R6C68 = 17 -> min R9C3 = 4
6b. R6C68 cannot be [97] = 16 (which clashes with R6C2) -> no 5 in R9C3
6c. Min R9C3 = 4 -> max R789C4 = 11, no 9 in R89C4

7. R4C2 + R9C3 = R6C4 + 7 (step 5)
7a. Max R6C4 = 4 -> max R4C2 + R9C3 = 11, min R9C3 = 4 -> no 8 in R4C2
7b. R1C7 + R4C24 = 21 (step 1i), max R1C7 + R4C2 = 15 -> min R4C4 = 7 (since R4C24 cannot be [66])
7c. Min R4C4 = 7 -> max R3C45 = 7, no 7,8 in R3C45
7d. R4C2 + R9C3 = R6C4 + 7, R6C4 + R4C2 + R9C3 = [236/447/456] (cannot be [144] which clashes with R67C3 = {24}, cannot be [254] which clashes with R67C3 = {14}), no 1 in R6C4, no 6 in R4C2, no 4 in R9C3
7e. Naked triple {124} in 7(3) cage at R6C3, 1 locked for C3
7f. 15(4) cage at R7C4 = {1257/1347/1356/2346} (cannot be {1248} because R9C3 only contains 6,7), no 8
7g. R9C3 = {67} -> no 6,7 in R789C4
7h. 15(4) cage = {1257/1347/1356} (cannot be {2346} which clashes with R6C4), 1 locked for C4 and N8
7i. 15(4) cage = {1257/1356} (cannot be {1347} which clashes with R6C4 + R4C2 + R9C3 = [447]), no 4, 5 locked for C4 and N8
7j. Min R4C4 = 7 -> max R3C45 = 7, min R3C4 = 2 -> max R3C5 = 5

8. 45 rule on N1 2(1+1) outies R2C4 + R4C2 = 1 innie R1C3 + 7
8a. Max R2C4 + R4C2 = 14 -> max R1C3 = 7
8b. Min R1C3 = 2 -> min R2C4 + R4C2 = 9, max R4C2 = 5 -> min R2C4 = 4

9. 45 rule on N9 2(1+1) outies R6C8 + R8C6 = 1 innie R9C7 + 8
9a. Max R6C8 + R8C6 = 15 -> max R9C7 = 7

10. R46C46 (step 1e) = {2689/4579/4678}, R1C7 + R4C24 = 21 (step 1i)
10a. Consider candidates for R4C2 = {345}
R4C2 = {34} => R1C7 + R4C4 = 17,18 = [89/98/99], no 7 in R4C4 => R46C46 = {2689/4678} (cannot be {4579} = [7549]), no 5
or R4C2 = 5
-> no 5 in R4C6
10b. 13(3) cage at R3C7 cannot contain both of 6,7, R4C6 = {67} -> no 6,7 in R34C7
10c. R46C46 = {2689/4678}, 6 locked for C6 and N5
10d. 6 in N8 only in R789C5, locked for C5

11. R1C7 + R6C8 = R4C6 + 10 (step 3)
11a. R4C6 = {67} -> R1C7 + R6C8 = 16,17 = [88/97/98], no 7 in R1C7, no 6 in R6C8
11b. 19(4) cage at R1C6 cannot contain both of 8,9, R1C7 = {89} -> no 8,9 in R123C6
11c. 26(4) cage at R1C3 = {2789/4589/4679/5678} (cannot be {3689} which clashes with R1C78, ALS block), no 3
11d. 4 of {4589/4679} must be in R1C345 (R1C345 cannot be {589} which clashes with R1C7, cannot be {679} which clashes with R1C78, ALS block) -> no 4 in R2C5
11e. 5 of {4589/5678} must be in R1C345 (R1C345 cannot be {489} which clashes with R1C7, cannot be {678} which clashes with R1C78, ALS block) -> no 5 in R2C5

12. R1C7 + R4C24 = 21 (step 1i), R4C2 + R9C3 = R6C4 + 7 (step 5)
12a. R4C6 = {67} -> R1C7 + R6C8 = [88/97/98] (step 11a)
12b. Consider combinations for R46C46 (step 10c) = {2689/4678}
R46C46 = {2689}, R6C4 = 2 => R4C2 + R9C3 = [36] => R1C7 + R4C4 = 18 = [99]
or R46C46 = {4678} with R4C6 = 6 = [7648] => R1C7 + R4C2 = 14 = [95]
or R46C46 = {4678} with R4C6 = 7 => R1C7 + R6C8 = [98]
-> R1C7 = 9, clean-up: no 1 in R2C1, no 1 in R4C8
[Ed pointed out that after this placement, R3C3 becomes a hidden single for R3; don’t know how much difference this would make if it had been spotted.]

13. R1C7 = 9 -> R123C6 = 10 = {127/145/235}
13a. Consider combinations for R123C6
R123C6 = {127}, locked for C6
or R123C6 = {145} => R89C6 = {27/37} (cannot be {23} which clashes with R789C4), 7 locked for C6
or R123C6 = {235} => R89C6 = {47}, locked for C6
-> R4C6 = 6, clean-up: no 4 in R3C8
13b. R1C7 = 9, R4C6 = 6 -> R6C8 = 7 (step 12a), R67C2 = [97], R67C6 = [89], R7C5 = 6, clean-up: no 3 in R34C8, no 4 in R8C2
13c. R9C3 = 6 -> R789C4 = 9 = {135} (only remaining combination), locked for C4 and N8, clean-up: no 5 in R8C23, no 4 in R8C9
13d. R1C7 + R4C24 = 21 (step 1i), R1C7 = 9 -> R4C24 = 12 = [39/57], no 4
13e. 8 in R7 only in R7C78, locked for N9, clean-up: no 2 in R89C9

14. R123C6 (step 13) = {145/235} (cannot be {127} which clashes with R89C6, ALS block), no 7, 5 locked for C6 and N2
14a. Hidden killer pair 1,3 in R123C6 and R5C6 for C6, R123C6 contains one of 1,3 -> R5C6 = {13}
14b. Hidden killer pair 1,3 in R123C6 and R3C5 for N2, R123C6 contains one of 1,3 -> R3C5 = {13}
14c. 45 rule on N8 using R789C4 = 9, 1 remaining innie R8C6 = 1 outie R9C7 + 1 -> R8C6 + R9C7 = [21/43]
14d. R9C6 = 7 (hidden single in C6)
14e. 8 in N8 only in R89C5, locked for C5

15. 45 rule on N2 using R123C6 = 10, 2(1+1) outies R1C3 + R4C4 = 1 innie R2C4 + 5 -> no 5 in R1C3 (IOU)
15a. 26(4) cage at R1C3 = {2789/4679} -> R1C4 = {68}, R2C5 = 9, 7 locked for R1, clean-up: no 1 in R1C1, no 3 in R2C1
15b. Naked pair {68} in R1C48, locked for R1, clean-up: no 2,4 in R2C1
15c. R1C3 + R4C4 cannot total 12,13 -> no 7,8 in R2C4
15d. R1C45 = [87] (hidden pair in N2) -> R1C3 = 2, R1C8 = 6, clean-up: no 8 in R2C1, no 1 in R2C78, no 4 in R4C8
15e. Naked pair {14} in R67C3, locked for C3 and 7(3) cage at R6C4 -> R6C4 = 2
15f. R46C46 (step 10) = {2689} (only remaining combination) -> R4C4 = 9 -> R4C2 = 3 (step 13d), clean-up: no 1 in R3C8, no 8 in R8C3
15g. R4C4 = 9 -> R3C45 = 5 = [41], R2C4 = 6, R5C4 = 7
15h. R2C1 = 7 -> R1C1 = 3, R1C6 = 5
15i. R8C6 =4 (hidden single in C6), R9C7 = 3 (step 14c)
15j. R4C6 = 6 -> R34C7 = 7 = {25} (only remaining combination), locked for C7 -> R2C7 = 4, R2C8 = 3, R7C7 = 8, R1C9 = 1, clean-up: no 9 in R89C9
15k. R89C9 = [64]
15l. Naked pair {28} in R34C8, locked for C8 -> R7C89 = [52]
15m. R1C2 + R2C4 = [46] = 10 -> R2C23 = 9 = [18], R45C3 = [75], R5C2 = 2 (cage sum)

and the rest is naked singles.

I'll rate my WT for A361 at 1.5. I used fairly short forcing chains.]