This is a jigsaw killer; the Old Lace pattern in the 9th jigsaw nonet. It also has regular nonets.
I’ve given eliminations from placements in the jigsaw nonets; remember to make the eliminations from the regular nonets.
Prelims
a) R12C5 = {19/28/37/46}, no 5
b) R2C34 = {16/25/34}, no 7,8,9
c) R2C67 = {17/26/35}, no 4,8,9
d) R34C2 = {17/26/35}, no 4,8,9
e) R34C8 = {16/25/34}, no 7,8,9
f) R4C45 = {17/26/35}, no 4,8,9
g) R5C12 = {19/28/37/46}, no 5
h) R5C89 = {19/28/37/46}, no 5
i) R67C2 = {16/25/34}, no 7,8,9
j) R6C45 = {18/27/36/45}, no 9
k) R67C8 = {17/26/35}, no 4,8,9
l) R8C34 = {17/26/35}, no 4,8,9
m) R89C5 = {19/28/37/46}, no 5
n) R8C67 = {16/25/34}, no 7,8,9
o) 21(3) cage at R1C2 = {489/579/678}, no 1,2,3
p) 20(3) cage at R1C8 = {389/479/569/578}, no 1,2
q) 20(3) cage at R8C1 = {389/479/569/578}, no 1,2
1. 45 rule on NR1C1 2 innies R1C1 + R3C3 = 9 = {18/27/36/45}, no 9
1a. 9 in NR1C1 only in 21(3) cage at R1C2, locked for N1
1b. 21(3) cage = {489/579}, no 6
1c. R1C1 + R3C3 = {18/27/36} (cannot be {45} which clashes with 21(3) cage), no 4,5 in R1C1 + R3C3
1d. 8 in NR1C1 only in R1C1 + R3C3 and 21(3) cage, locked for N1
2. 45 rule on NR1C8 2 innies R1C9 + R3C7 = 10 = {19/28/37/46}, no 5
2a. 8,9 in NR1C8 only in R1C9 + R3C7 and 20(3) cage at R1C8, locked for N3
3. 45 rule on NR6C2 2 innies R7C3 + R9C1 = 10 = {19/28/37/46}, no 5
3a. 8,9 in NR6C2 only in R7C3 + R9C1 and 20(3) cage at R8C1, locked for N7
4. 45 rule on NR6C8 2 innies R7C7 + R9C9 = 16 = {79}, locked for NR6C8 and N9, clean-up: no 1 in R67C8
4a. 8 in NR6C8 only in 14(3) cage at R8C8, locked for N9
4b. 14(3) cage = {158/248}, no 3,6
4c. R8C67 = {16/34} (cannot be {25} which clashes with R67C8), no 2,5
4d. R34C8 = {16/34} (cannot be {25} which clashes with R67C8), no 2,5
4e. Killer pair 3,6 in R34C8 and R67C8, locked for C8, clean-up: no 4,7 in R5C9
5. 45 rule on R2 3 outies R1C258 = 21 = {489/579/678}, no 1,2,3, clean-up: no 7,8,9 in R2C5
6. 45 rule on C2 3 outies R258C1 = 21 = {489/579/678}, no 1,2,3, clean-up: no 7,8,9 in R5C2
7. Law of Leftovers (LoL) for R123 three outies R4C258 must exactly equal three innies R3C159, no 8,9 in R4C258 -> no 8,9 in R3C5
8. LoL for R789 three outies R6C258 must exactly equal three innies R7C159, no 9 in R6C258 -> no 9 in R7C5
8a. 8 in R6C258 and R7C159 only in R6C5 and R7C5 -> no 8 in R67C5, clean-up: no 1 in R6C4
8b. 7 in R6C258 only in R6C5 -> no 7 in R7C5
9. R2C67 = {17/26/35}, R34C8 (step 4c) = {16/34} -> combined cage R2C67 + R34C8 = {17}{34}/{26}{34}/{35}{16}, 3 locked for NR1C8, clean-up: no 7 in R1C9 + R3C7 (step 2)
9a. R1C9 + R3C7 (step 2) = {19/28} (cannot be {46} which clashes with R34C8), no 4,6
10. R8C34 = {17/26/35}, R8C67 (step 4b) = {16/34} -> combined cage R8C3467 = {17}{34}/{26}{34}/{35}{16}, 3 locked for R8, clean-up: no 7 in R9C5
11. Hidden killer triple 1,2,3 in R2C34, R2C5 and R2C67 for R2, R2C34 and R2C67 each contain one of 1,2,3 -> R2C5 = {123}, clean-up: no 4,6 in R1C5
11a. R1C258 (step 5) = {489/579}, 9 locked for R1, clean-up: no 1 in R3C7 (step 9a)
12. 45 rule on R8 3 outies R9C258 = 14
12a. 20(3) cage at R8C1 = {479/569/578} (cannot be {389} = {89}3, 8,9 locked for R8 => R9C8 = 8 (hidden single in R6C8) => R9C258 cannot be [338]), no 3 in R9C2
12b. Hidden killer pair 8,9 in R7C3 + R9C1 and 20(3) cage for NR6C2, 20(3) cage contains one of 8,9 -> R7C3 + R9C1 (step 3) must contain one of 8,9 = {19/28}, no 3,4,6,7
13. Hidden killer triple 1,2,3 in R34C2, R5C2 and R67C2 for C2, R34C2 and R67C2 each contain one of 1,2,3 -> R5C2 = {123}, clean-up: no 4,6 in R5C1
14. Old Lace property, because there are regular nonets, R37C5 must exactly equal R5C46 and R46C5 must exactly equal R5C37
14a. No 8,9 in R37C5 -> no 8,9 in R5C46
14b. No 8,9 in R46C5 -> no 8,9 in R5C37
14c. 5 in R5 only in R5C34567, R5C46 exactly equal R37C5 -> 5 must be in R37C5 + R5C357, locked for Old Lace, no 5 in R46C46, clean-up: no 3 in R4C5, no 4 in R6C5
14d. No 4 in R46C5 -> no 4 in R5C37
15. 8,9 in R2 must be in 21(3) cage at R1C1 and 20(3) cage at R1C8 (which only contains one of 8,9), 8,9 in C2 must be in 21(3) cage and 20(3) cage at R8C1 (which only contains one of 8,9) -> 21(3) must either be {489} or contain 9 in R2C2 -> no 5,7 in R2C2
16. 21(3) cage at R1C2 = {489/579}, 20(3) cage at R8C1 = {479/569/578}
16a. R258C1 (step 6) = {489/579} (cannot be {678} = {78}6 because 9 in 21(3) cage clashes with 20(3) cage = 6{59}), no 6, 9 locked for C1, clean-up: no 1 in R7C3 (step 12b)
17. R9C258 = 14 (step 12)
17a. Only valid permutation with 7 = [734] (because R8C5 = 7 (hidden single in R8) => R9C5 = 3) and, of course, R9C258 cannot be [662] and there’s no 3 in R9C8 -> no 6 in R9C5, clean-up: no 4 in R8C5
18. 45 rule on C8 3 outies R258C9 = 14
18a. Only valid permutation with 7 = [734] (because R5C8 = 7 (hidden single in C8), R5C9 = 3) and, of course, R258C9 cannot be [662] and there’s no 3 in R8C9 -> no 6 in R5C9, clean-up: no 4 in R5C8
19. 3 in R9 only in R9C34567, locked for NR6C5, no 3 in R6C5 + R7C46, clean-up: no 6 in R6C4
20. 8,9 in R5 only in R5C12 = [82/91], R5C5 and R5C89 = {19/28} -> no 1,2 in R5C5
21. When the 7(2) cages in the R28C28 ring are {16}, the 8(2) cages in the ring must be {35}. When 7(2) cage R8C67 = {34} the 7(2) cage R67C2 = {34} -> R67C2 = {16/34}, no 2,5
21a. R67C2 = {16} => R34C2 = {35} or R67C2 = {34} (locking cages), 3 must be in R3467C2, locked for C2, clean-up: no 7 in R5C1
22. 4 in R5 only in R5C456, locked for N5, clean-up: no 5 in R6C5
22a. 4 in R5C456, R5C46 = R37C5 (Old Lace) -> 4 must be in R357C5, locked for C5, clean-up: no 6 in R8C5
23. R9C258 = 14 (step 12) cannot be [635] (because 7 in R8C1234 clashes with R89C5 = [73]), no 6 in R9C2
23a. 6 in R9 only in R9C3467, locked for NR6C5, no 6 in R6C5 + R7C46, clean-up: no 3 in R6C4
24. Killer triple 1,2,7 in R12C5, R6C5 and R89C5, locked for C5, clean-up: no 1,6,7 in R4C4
25. Consider permutations for R4C45 = [26/35]
R4C45 = [26] => R6C45 = [81]
or R4C45 = [35], 3 placed for Old Lace => 3 in C5 only in R12C5 = [73] or R89C5 = [73] (locking cages), 7 locked for C5
-> no 7 in R6C5, clean-up: no 2 in R6C4
26. 7 in C5 only in R12C5 = [73] or R89C5 = [73] (locking cages), 3 locked for C5
27. Naked triple {456} in R347C5, locked for C5
27a. Naked pair {89} in R5C15, locked for R5, clean-up: no 1,2 in R5C89
27b. R5C89 = [73], placed for NR3C9, no 3,7 in R46C6 + R3467C9
28. 20(3) cage at R1C8 = {479/569/578}
28a. 6,7 only in R2C9 -> R2C9 = {67}
29. R258C9 (step 18) = 14, R5C9 = 3 -> R28C9 = 11 = [65/74]
29a. 14(3) cage at R8C8 (step 4b) = {158/248}, 8 locked for C8
29b. R8C9 = {45} -> no 4,5 in R89C8
30. 8 in NR1C8 only in R1C9 + R3C7 (step 9a) = {28}, locked for NR1C8 and N3, clean-up: no 6 in R2C67
31. 7 in NR1C8 only in R2C679, locked for R2
31a. 21(3) cage at R1C2 = {489/579}
31b. 7 of {579} must be in R1C2 -> no 5 in R1C2
32. Consider placements for 6 in R2
6 in R2C34 = {16}, locked for R2 => R2C5 = {23}
or R2C9 = 6 => 7 in R2 only in R2C67 = {17}, locked for R2 => R2C5 = {23}
-> R2C5 = {23}, clean-up: no 9 in R1C5
33. R1C258 (step 11a) = {489/579}
33a. R1C5 = {78} -> no 7,8 in R1C2
34. 21(3) cage at R1C2 = {489} (only remaining combination), locked for NR1C1 and N1, clean-up: no 1 in R1C1 + R3C3 (step 1c), no 3 in R2C34
34a. Killer pair 1,5 in R2C34 and R2C67, locked for R2
35. R34C2 = {17/35} (cannot be {26} which clashes with R2C34), no 2,6
35a. Killer pair 1,3 in R34C2 and R67C2, locked for C2 -> R5C2 = 2, R5C1 = 8, both placed for NR3C1, no 2,8 in R3467C1 + R46C3, clean-up: no 2 in R7C3 (step 12b)
35b. R5C5 = 9, clean-up: no 1 in R89C5
35c. R6C5 = 1 (hidden single in C5) -> R6C4 = 8, 1 placed for NR6C5, no 1 in R7C46 + R9C3467, clean-up: no 6 in R7C2
36. R2C2 = 8 (hidden single in R2)
36a. R7C3 = 8 (hidden single in NR6C2), R9C1 = 2 (step 12b), placed for NR6C2, clean-up: no 7 in R3C3 (step 1c), no 6 in R8C34, no 8 in R8C5
37. 3 in R8 only in R8C34 = {35} or R8C67 = {34} (locking cages)
37a. Killer triple 3,4,5 in R8C34, R8C67 and R8C9, locked for R8
37b. 20(3) cage at R8C1 = {479/569}
37c. 4,5 only in R9C2 -> R9C2 = {45}
38. 3 in C2 only in R34C2 = {35} or R67C2 = {34} (locking cages)
38a. Killer triple 3,4,5 in R34C2, R67C2 and R9C2, locked for C2 -> R1C2 = 9, R2C1 = 4, R2C8 = 9
38b. R8C1 = 9 (hidden single in C1)
[Cracked, the rest is fairly straightforward. I was going to make this comment after step 33, but it’s probably more appropriate here.]
39. R9C258 = 14 (step 12) = [581] (only remaining permutation), 5 placed for NR6C2, 1 placed for NR6C8, R9C5 = 8 -> R8C5= 2, placed for NR6C5, no 2 in R7C46, R8C8 = 8, R8C9 = 5 (cage sum), placed for NR6C8, R12C5 = [73], both placed for NR1C3, no 3,7 in R1C3467 + R3C46, R8C2 = 6 (cage sum), clean-up: no 5 in R2C67, no 3 in R34C2, no 2 in R3C3 (step 1c), no 6 in R34C8, no 1 in R7C2, no 3 in R67C8, no 3 in R8C23
40. Naked pair {17} in R2C67, locked for R2 -> R2C9 = 6, R1C8 = 5 (cage sum)
41. R1C1 = 3 (hidden single in R1), R3C3 = 6
42. R7C1 = 1 (hidden single in R7), placed for NR3C1, no 1 in R4C3, R8C34 = [71]
42a. Naked triple {567} in R346C1, locked for NR3C1, no 5,6 in R46C3 + R5C4 -> R5C4 = 4, placed for NR3C1
42b. Naked pair {39} in R46C3, locked for C3 -> R9C3 = 4, placed for NR6C5, no 4 in R7C6
43. R3C8 = 3 (hidden single in R3), R4C8 = 4
44. 7 in N5 only in R46C6, locked for C6 -> R2C67 = [17], R7C7 = 9, R7C46 = [75], R5C6 = 6, placed for NR3C9, no 6 in R46C7, R4C5 = 5, placed for NR1C3, no 5 in R3C4, R4C4 = 3
and the rest is naked singles, without using the jigsaw nonets.