Thanks Mike for a very challenging killer!
It starts fairly easily, which draws one into the puzzle, then gets really difficult.
At one stage I was thinking of giving up but then compared how far I'd got against Mike's state diagram which made me think what I'd been missing and I found steps 20e and 28, which was enough to get me going again. State diagrams like that can be helpful in providing hints while making one think how to reach the position. Thanks Mike!
The way I solved it, the later stages needed a bit more combination analysis and some contradictions but nothing particularly heavy. That includes step 39 which I don't think I used later but have left it in since I'd done it.
I'll go along with Afmob's rating of a hard 1.5.
Here is my walkthrough for A73 V1.5.
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 in N1 = 9{58/67}, 9 locked for N1
e) 8(3) cage at R3C1 = 1{25/34}, CPE no 1 in R6C1
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 in N7 = {126/135/234}, no 7,8,9
j) 19(3) cage at R8C4 = {289/379/469/478/568}, no 1
k) 19(3) cage in N9 = {289/379/469/478/568}, no 1
l) 6(3) cage in N9 = {123}, locked for N9
1. 45 rule on N1 3 innies R1C3 + R3C13 = 8 = 1{25/34}, 1 locked for N1
1a. R3C3 = {45} -> no 4,5 in R1C3 + R3C1
1b. 15(3) cage in N1 = {258/267/348} (cannot be {357/456} which clash with 22(3) cage)
2. 45 rule on N7 3 innies R7C13 + R9C3 = 22 = 9{58/67}, 9 locked for N7
2a. 14(3) cage in N7 = {158/167/248/347} (cannot be {257/356} which clash with R7C13 + R9C3)
3. 45 rule on C12 2 outies R28C3 = 9 = {36/45}/[72/81], no 2 in R2C3
4. 45 rule on C89 2 outies R28C7 = 7 = [43/52/61], R2C7 = {456}
4a. Max R2C7 = 6 -> min R23C8 = 12, no 1,2
5. 21(3) cage at R3C3 = {489/579} (cannot be {678} because R3C3 only contains 4,5), no 6
5a. R3C3 = {45} -> no 4,5 in R3C4 + R4C3
5b. R3C4 + R4C3 must contain 9, CPE no 9 in R4C4
6. 12(3) cage at R6C3, min R7C3 = 5 -> max R6C3 + R7C4 = 7, no 7,8,9
7. 45 rule on R89 2 outies R7C28 = 5 = {23}/[41], no 1,5,6 in R7C2
7a. 45 rule on R89 4 innies R8C2378 = 10 = {1234}, locked for R8, clean-up: no 3,4 in R2C3 (step 3), no 7,8,9 in R9C5
7b. 9(3) cage in N7 = {234} (only remaining combination), locked for N7, clean-up: no 8 in R2C3 (step 3)
7c. 1 in R8 locked in R8C78, locked for N9, clean-up: no 4 in R7C2 (step 7)
7d. Naked pair {23} in R7C28, locked for R7
7e. 1 in N7 locked in R9C12, locked for R9
7f. Min R8C6 + R9C7 = 9 -> max R9C6 = 8
8. 15(3) cage in N1 (step 1b) = {258/267} (cannot be {348} because R2C3 only contains 5,6,7), no 3,4, 2 locked in R23C2 for C2 and N1 -> R78C2 = [34], R8C3 = 2, R7C8 = 2, R2C3 = 7 (step 3), R23C2 = 8 = {26}, clean-up: no 5 in R2C7 (step 4), no 8,9 in R5C1, no 6 in R5C9
[I was going to do killer triple 2,3,4 in R23C2 and R78C2, locked for C2 until I realised that step 8 takes away the use of this nice move.]
8a. Naked pair {26} in R23C2, locked for C2 and N1
8b. R3C3 = 4 (step 1 or as hidden single in N1), R3C4 + R4C3 (step 5) = {89}, CPE no 8 in R4C4
9. 12(3) cage at R6C3 = {138/156/345}, no 9
10. R7C13 + R9C3 (step 2) = 9{58/67}
10a. 6 of {679} must be in R7C3 -> no 6 in R7C1 + R9C3
11. 19(3) cage at R6C1 = {289/379/478/568} (cannot be {469} because 4,6 only in R6C1)
11a. 2,3,4,6 only in R6C1 -> R6C1 = {2346}
12. 8(3) cage at R3C1 = 1{25/34}
12a. 2,4 only in R4C1 -> R4C1 = {24}
13. 13(3) cage at R1C3 = {139/148/157/238/346} (cannot be {247/256} because R1C3 only contains 1,3)
13a. 7 of {157} must be in R1C4 -> no 5 in R1C4
14. 45 rule on C89 4 innies R2378C8 = 17 = {1259/1268/2348/2357} (cannot be {2456} because R8C8 only contains 1,3)
14a. 3 of {2348/2357} must be in R8C8 -> no 3 in R23C8
14b. 18(3) cage in N3 = 4{59}/4{68}/[648]/[657]
14c. 13(3) cage in N3 = {139/148/157/238/256} (cannot be {247/346} which clash with 18(3) cage)
14d. R1C89 = {13} clashes with R1C3 -> no 9 in R2C9
14e. Hidden killer pair 1,2 in N3 for 13(3) cage and R1C7 + R3C79 -> R1C7 + R3C79 must contain 1 or 2
14f. 45 rule on N3 3 innies R1C7 + R3C79 = 14 = {149/167/239/248/257} (cannot be {158} which clashes with 13(3) cage and with 18(3) cage)
15. 45 rule on C1234 1 outie R5C5 = 1 innie R6C4 + 3, no 1,2,3 in R5C5, no 7,8,9 in R6C4
16. 45 rule on C6789 1 outie R4C5 = 1 innie R6C6 + 4, no 1,2,3,4 in R4C5, no 6,7,8,9 in R6C6
17. 1 in R7 locked in R7C45, CPE no 1 in R6C4, clean-up: no 4 in R5C5 (step 15)
18. 45 rule on R12 3 outies R3C258 = 17 = {269/278/368} (cannot be {179/359} because R3C2 only contains 2,6), no 1,5, clean-up: no 9 in R2C8 (step 14b)
18a. Killer pair 8,9 in R3C4 and R3C58, locked for R3
19. Hidden killer triple 1,2,3 in R3C1, R3C25 and R3C679 for R3 -> R3C679 must contain one of 1,2,3
19a. Min R3C67 = {15} = 6 -> max R4C7 = 6
19b. Hidden killer pair 6,7 in R3C258 and R3C679 for R3 -> R3C679 must contain one of 6,7
19c. R3C679 must contain 5, one of 1,2,3 and one of 6,7
20. R1C7 + R3C79 (step 14f) = {167/257} (cannot be {149/248} because 4,8,9 only in R1C7, cannot be {239} because R3C79 = {23} clashes with R3C258), no 3,4,8,9, 7 locked for N3
20a. R3C79 cannot be {67} (step 19c) -> no 1 in R1C7
20b. 18(3) cage in N3 (step 14b) = 4{59}/4{68}/[648], 4 locked in R2C78, locked for R2 and N3
20c. 3 in N3 locked in 13(3) cage = {139/238}, no 5,6
[Alternatively killer pair 5,6 in R1C7 + R3C79 and 18(3) cage]
20d. 13(3) cage at R1C3 (step 13) = {139/148/157/238/346}
20e. 4 of {346} must be in R1C4 -> no 6 in R1C4
21. Hidden killer pair 1,3 in R1C3 and R56C3 for C3 -> R56C3 must contain one of 1,3
21a. 45 rule on N4 3 innies R456C3 = 2 outies R37C1 + 6
21b. Min R37C1 = 6 -> min R456C3 = 12 = {138} clashes with R1C3
21c. Min R37C1 = 8 -> min R456C3 = 14 = {158} clashes with R4C2
21d. Min R37C1 = 9, no 5 in R7C1
22. R7C13 + R9C3 (step 2) = 9{58/67}
22a. R79C3 must contain 5 or 6, hidden killer pair 5,6 in R56C3 and R79C3 -> R56C3 must contain one of 5,6
22b. Combining steps 21 and 22a, R56C3 = {1356}, no 8,9
23. Hidden killer triple 7,8,9 in R4C3, R5C12 and R6C2 -> R6C2 = {789}
23a. 19(3) cage at R6C1 (step 11) = {289/379/478}, no 6
24. 6 in N4 locked in R56C3, locked for C3, clean-up: no 7 in R7C1 (step 2)
24a. R7C13 + R9C3 (step 2) = {589} (only remaining combination), locked for N7, 5 locked in R79C3 for C3
[Alternatively 6 locked in R56C3 (step 24) -> no 5 in R56C3 (step 22a).]
24b. R7C67 = {89} clashes with R7C1 -> no 4 in R6C7
25. Naked triple {589} in R127C1, locked for C1, clean-up: no 7 in R5C2
25a. 5 in C1 locked in R12C1, locked for N1
26. 12(3) cage at R6C3 (step 9) = {138/156/345}
26a. 5 of {156/345} must be in R7C3 -> no 5 in R7C4
27. 19(3) cage at R8C4 = {289/379/469/478/568}
27a. 2,3,4 of {289/379/469/478} must be in R9C4 -> no 7,9 in R9C4
28. R123C5 = {129/138/147/156/237/246/345}
28a. 6 of {156} must be in R3C5, 4 of {246} must be in R1C5 -> no 6 in R1C5
29. 6 in R1 locked in R1C67, locked for 14(3) cage -> no 6 in R2C6
29a. 14(3) cage = {167/356}, no 2,4,8,9
29b. 1 of {167} must be in R2C6 -> no 1 in R1C6
30. R123C5 = {129/147/156/237/246/345} (cannot be {138} which clashes with R12C6), no 8
30a. 8 in N3 locked in R123C4, locked for C4
31. 19(3) cage at R8C4 = {289/379/469/478/568}
31a. 8 of {568} must be in R9C3 -> no 5 in R9C3
32. R7C3 = 5 (hidden single in C3)
33. R1C7 + R3C79 (step 20) = {167/257}
33a. R1C7 = {567} -> R3C79 must contain 1 or 2
33b. R3C679 must contain one of 1,2,3 (step 19) -> no 1,2,3 in R3C6
33c. 12(3) cage at R3C6 = {147/156/237/246} (cannot be {345} because 3,4 only in R4C7)
33d. 7 of {147/237} must be in R3C6 -> no 7 in R3C7
33e. 3,4 of {237/246} must be in R4C7 -> no 2 in R4C7
34. 13(3) cage at R1C3 (step 13) = {139/148/157/238/346}
Hidden killer pair 2,4 in N2 for R12C4 and R123C5 -> R123C5 must contain at least one of 2,4 -> R123C5 = {129/147/237/246/345} (cannot be {156} which doesn’t contain 2,4)
34a. 4 of {345} must be in R1C5 -> no 5 in R1C5
35. 45 rule on N9 3 innies R7C79 + R9C7 = 20 = {479/569/578}
35a. 5 of {569/578} must be in R9C7 -> no 6,8 in R9C7
36. 45 rule on N5 3 outies R5C37 + R7C5 = 12 = [38/65]1/[17/35/62]4/[15]6/[14/32]7/{13}8/[12]9, no 6,9 in R5C7
37. 45 rule on R5 3 outies R4C456 = 17 = {179/269/278/359/368/458/467}
Some permutations are eliminated by R4C5 = R6C6 + 4 (step 16)
37a. {269} must have 9 in R4C5 = [296/692]
37b. {359} must have 5 in R4C5 = [359]
37c. {458} must have 5 in R4C5 = [458]
37d. -> no 5 in R4C46
38. R7C79 + R9C7 (step 35) = {479/569/578}
38a. Hidden killer pair 4,6 in R7C456 and R7C79 for R7 -> R7C456 must have at least one of 4,6
38a. 45 rule on N8 2 outies R9C37 = 3 innies R7C456 + 2
38b. Max R9C37 = 17 -> max R7C456 = 15
38c. Only remaining permutation with 9 in R7C456 = {149} => R7C1 = 8 => R7C79 = {67} clashes with R7C79 + R9C7
38d. -> no 9 in R7C56
38e. 9 in N8 locked in R8C456, locked for R8
39. 15(4) cage at R6C4 = {1239/1248/1257/1347/1356/2346}
39a. R6C456 + R7C5 = {234}6 clashes with R6C1
39b. R6C456 + R7C5 = {236}4 => R6C3 = 1 => R7C4 = 6 -> no 1 in R7
39c. -> cannot be {2346}
39d. -> 15(4) cage = {1239/1248/1257/1347/1356}
40. 13(3) cage at R1C3 (step 13) = {139/148/157/238/346}
40a. Cannot be {157} because R3C4 = 8 => 9 must be in R123C5 and cannot then place 4 for N2
40b. -> 13(3) cage = {139/148/238/346}, no 5,7
40c. {139} can be 1{39} or 3{19}
If 1{39} => R3C4 = 8 => R123C5 = 4{26} (step 34) => R123C6 = {157} = [715] (step 29a), R1C7 = 6 clashes with R34C7 = {16}
If 3{19} => R3C4 = 8 => R123C5 = 4{26} (step 34) => R123C6 = {357} = [537] (step 29a), R1C7 = 6 -> cannot place 7 in N3
40d. -> no {139}, no 1,3,9 in R12C4
41. 13(3) cage at R1C3 = 1[48]/3{28}/3[46]
41a. If 1[48] => R3C4 = 9 => R123C5 = {237} (step 34) -> no 3 in R1C6
41b. If 3{28}/3[46], R1C3 = 3 -> no 3 in R1C6
41c. -> no 3 in R1C6
41d. R123C5 (step 34) = {129/147/237/345} (cannot be {246} which clashes with R12C4), no 6
42. 14(3) cage at R1C6 (step 29a) = {167/356}
42a. 3 of {356} must be in R2C6 -> no 5 in R2C6
43. 13(3) cage at R1C3 = 1[48]/3{28}/3[46]
43a. If 1[48] => R3C4 = 9 -> R123C5 cannot be {129}
43b. If 3{28} -> R123C5 cannot be {129}
43c. If 3[46] => R3C4 = 8 => R123C5 = {129} (only place for 9) => R123C6 = {357} = [537] (step 29a), R1C7 = 6 -> cannot place 7 in N3
43d. -> R123C5 cannot be {129}
43e. -> R123C5 (step 34) = {147/237/345}, no 9
44. R3C4 = 9 (hidden single in N2), R4C3 = 8, R9C3 = 9, R7C1 = 8
44a. R1C2 = 8 (hidden single in N1), R2C4 = 8 (hidden single in N2)
44b. R3C8 = 8 (hidden single in R3), R2C78 = 10 = {46}, locked for R2 and N3 -> R23C2 = [26]
44c. R1C6 = 6 (hidden single in R1)
45. 13(3) cage in N3 = {139} (only remaining combination), locked for N3
45a. 9 locked in R1C89, locked for R1 -> R12C1 = [59], R1C7 = 7, R2C6 = 1 (step 29a), R2C9 = 3, R2C5 = 5, R13C5 = [43] (step 43e), R3C1 = 1, R1C34 = [32], R4C2 = 5, R4C1 = 2, R5C2 = 9, R5C1 = 3, R6C12 = [47], R9C2 = 1, R3C6 = 7, clean-up: no 5 in R5C89, no 7 in R5C5, no 6 in R6C4 (both step 15), no 4 in R7C4 (step 9)
46. R3C6 = 7 -> R34C7 = 5 = [23], R3C9 = 5, R8C78 = [13]
47. R9C3 = 9 -> R89C4 = 10 = [64/73], no 5, no 6 in R9C4
48. Naked pair {67} in R8C14, locked for R8 -> R8C9 = 8, R8C5 = 9, R8C6 = 5, R9C5 = 2
49. Killer pair 1,6 in R5C3 and R5C89, locked for R5 -> R5C5 = 8, R6C4 = 5 (step 15)
50. Naked pair {16} in R6C35, locked for R6 -> R6C8 = 9, R6C9 = 2, R1C89 = [19], R6C6 = 3, R4C5 = 7 (step 16), clean-up: no 6 in R5C8
and the rest is naked singles
Near the end I also noticed 45 rule on R12 4 innies R2C2378 = 1 outie R3C5 + 16, but never got to find out if it was useful.
Mike's analysis and alternative path after step 9 of Afmob's original walkthrough was interesting. I look forward to reading Mike's further posts about Grouped Swordfish. I did one use an ordinary Swordfish, a 3 row and 3 column X-Wing, in a walkthrough almost a year ago. Therefore I could understand what Mike said about the Grouped Swordfish in this puzzle and also agree with his comment that it would be difficult to spot; something that's probably easier for a software solver to spot.