This is Anti-kNight (AN), non-consecutive (NC). HATMAN commented that the value in R5C5 is in all four diagonal cages in the corner nonets; I didn't need to use that.
Prelims
a) 9(3) cage at R1C9 = {126/135/234}
b) 21(3) cage at R6C9 = {489/579} (cannot be {678} because of NC)
c) 20(3) cage at R7C3 = {389/479/569/578}, no 1,2
1. 45 rule on C5 3 innies R456C5 = 14
1a. 45 rule on C5 3 innies R5C456 = 16
1b. Total of two 15(3) cages and two hidden 14(3) and 16(3) cages = 60 with R5C5 used for all four cages, i.e. three extra uses -> R5C5 = 5 -> no 4,6 in R46C5 + R5C46 (NC)
1c. R5C5 = 5 -> R46C5 = 9 = {18/27}, no 3,9
1d. R5C5 = 5 -> R5C46 = 11 = {29/38}, no 1,7
1e. Killer pair 2,8 in R46C5 + R5C46, locked for N5
1f. R5C5 = 5 -> no 5 in R37C46 + R46C37 (AN)
2. 21(3) cage at R6C9 = {489/579}, 9 locked for C9
2a. 4 of {489} must be in R7C9 because of NC -> no 4 in R68C9, no 8 in R7C9
2b. 21(3) cage = {489/579} -> no 9 in R7C7 + R8C8 (N9 + AN)
2c. 18(3) cage at R7C7 = {378/468/567}, no 1,2
2d. 18(3) cage = {468/567} (cannot be {378} which clashes with 21(3) cage N9 + AN), no 3, 6 locked for N9
2e. 21(3) cage + 18(3) cage must contain 4, locked for N9
2f. 18(3) cage = {468/567} -> no 6 in R9C6 (R9 + AN)
2g. 15(3) cage at R9C6 = {159/249/348/357} (cannot be {258} which clashes with 18(3) cage N9 + AN)
2h. 4 of {348} must be in R9C6 -> no 8 in R9C6
2i. R8C9 = {89} (cannot be 5,7 which clash with 18(3) cage + NC)
2j. R8C9 = {89} -> no 9 in R7C9, no 8 in R8C8 + R9C9 (all NC)
2k. 8 of {468} must be in R7C7 -> no 4,6 in R7C7
2l. R9C8 = {12389} (cannot be 5,7 which clash with 18(3) cage + NC)
2m. 21(3) cage = {489/579} -> no 9 in R6C8 (AN)
2n. 15(3) cage = {159/249/348} (cannot be {357} = {57}3 which clashes with 18(3) cage + NC), no 7
2o. 18(3) cage = 8{46}/{567} -> no 7 in R7C8 + R8C7 (NC)
2p. Hidden killer pair 4,7 in 18(3) cage and R7C9 for N9, 18(3) cage contains one of 4,7 -> R7C9 = {47}
2q. 21(3) cage = {489/579}, R7C9 = {47} -> no 7 in R6C9
3. 16(3) cage at R1C5 = {169/349/367} (cannot be {178/268} which clash with R46C5), no 2,8
3a. 3,9 of {349/367} must be in R2C5 -> no 4,7 in R2C5
4. 12(3) cage at R5C1 = {129/138/147/246} (cannot be {237} which clashes with R5C46)
4a. 9 of {129} must be in R5C2 -> no 9 in R5C13
5. 15(3) cage at R7C5 = {168/249/267/348}
5a. 2 of {267} must be in R8C5 -> no 7 in R8C5
6. 15(3) cage at R9C6 (step 2n) = {159/249/348}
6a. Hidden killer triple 1,2,3 in R7C8, R8C7 and 15(3) cage at R9C6 for N9, 15(3) cage only contains one of 1,2,3 -> R7C8 = {123}, R8C7 = {123}, 15(3) cage contains one of 1,2,3 in R9C78 -> no 1,2,3 in R9C6
6b. R7C8 = {123} -> no 2 in R6C8 (NC)
6c. R8C7 = {123} -> no 2 in R8C6 (NC)
7. 17(3) cage at R5C7 = {179/269/368/467} (cannot be {278} which clashes with R5C46)
7a. 4 of {467} must be in R5C8 -> no 4 in R5C79
8. 4,6 in N5 only in 15(3) cage at R4C4 = {456} or 15(3) cage at R4C6 = {456}
Because of the symmetry of candidates in these 15(3) cages and in R46C5 and R5C46 it doesn’t matter where 4,6 are place at the start of a forcing chain, so consider the forcing chain with R4C4 = 4, R6C6 = 6 -> no 3 in R5C4 (NC), no 8 in R5C6 (step 1d), no 7 in R6C5 (NC), no 2 in R4C5 (1c), R4C6 + R6C4 = {19/37}
Consider candidates for R4C6
R4C6 = {13} => R6C4 = {79} => no 8 in R5C4 (NC) no 3 in R5C6 (step 1d) => R4C6 = 3 (hidden single in N5), R6C4 = 7
or R4C6 = {79} => no 7,8 in R4C5 (NC) => R4C5 = 1, R6C5 = 8 (step 1c) => no 3 in R5C6 (NC) => R6C4 = 3 (hidden single in N5), R4C6 = 7
-> R4C6 + R6C4 = {37}
Similarly for other placements of 4,6
-> R46C46 = {3467}, locked for N5, R5C46 (step 1d) = {29}, locked for R5 and N5, R46C5 = {18}, locked for C5
8a. Naked pair {18} in R46C5 -> no 1,8 in R5C37 (AN)
8b. Naked pair {29} in R5C46 -> no 2,9 in R37C5 (AN)
9. 12(3) cage at R5C1 = {138/147}, no 6, 1 locked for R5 and N4
9a. 1 in R5C12 -> no 1 in R37C12 (AN)
9b. 6 in R5 only in 17(3) cage at R5C7, locked for N6
9c. 17(3) cage = {368/467}
9d. 4 of {467} must be in R5C8 -> no 7 in R5C8
9e. R8C9 = {47} -> {467} = [746] (AN), no 7 in R5C9
9f. 6 in R5C789 -> no 6 in R3C8 (AN)
10. 15(3) cage at R7C5 = {249/267}, no 3, 2 locked for N8
10a. 4 of {249} must be in R7C5 -> no 4 in R89C5
10b. 2 of {267} must be in R8C5 -> no 6 in R8C5
10c. 2 in R789C5 -> no 2 in R8C37 (AN)
10d. 3 in C5 only in 16(3) cage at R1C5, locked for N2
10e. 16(3) cage = {349/367}
10f. 3 of {367} must be in R2C5 -> no 6 in R2C5
10g. 9 of {349} must be in R2C5 -> no 9 in R1C5
10h. 3 in R123C5 -> no 3 in R2C37 (AN)
11. 17(3) cage at R5C7 (step 9c) = {368} (cannot be {467} = [746] which clashes with 21(3) cage at R6C9 because of AN for R5C8 + R8C9 and NC for R67C9), locked for R5 and N6
11a. Naked triple {368} in 17(3) cage -> no 3,8 in R37C8 (AN)
11b. Naked triple {147} in 12(3) cage at R5C1, locked for N4
11c. Naked triple {147} in 12(3) cage at R5C1 -> no 4,7 in R37C2 (AN)
12. 21(3) cage at R6C9 (step 2) = {489/579} = [579/948]
12a. 18(3) cage at R7C7 (step 2f) = {468/567}
12b. Killer pair 7,8 in 21(3) cage and 18(3) cage, locked for N9
12c. 15(3) cage at R9C6 (step 2n) = {159/249}, no 3, 9 locked for R9
12d. R8C7 = 3 (hidden single in N9), R5C7 = 6
12e. R8C7 = 3 -> no 4 in R8C68, no 2 in R9C7 (NC), no 3 in R6C6 (AN) -> no 7 in R4C4 (cage sum)
12f. 2 in N9 only in R79C8, locked for C8
12g. R5C7 = 6 -> no 7 in R46C7 (NC), no 6 in R3C6 (AN)
12h. 4 in N9 only in R79C9, locked for C9
12i. Naked pair {38} in R5C89 -> no 3,8 in R3C9 (AN)
13. 21(3) cage at R6C9 (step 12) = [579/948]
13a. 15(3) cage at R7C5 (step 10) = {267} (cannot be {249} = [492] which clashes with 21(3) cage) -> R8C5 = 2, R79C5 = {67}, locked for C5 and N8
13b. R8C5 = 2 -> no 1 in R8C46 (NC), no 2 in R9C3 (AN)
13c. Naked pair {67} in R79C5 -> no 6,7 in R8C3 (AN)
13d. R2C5 = 9 (hidden single in C5) -> no 8 in R2C46 (NC), no 9 in R1C37 + R3C3 (AN)
13e. Naked pair {34} in R13C5, locked for N2, no 4 in R2C37 (AN)
13f. 1 in R8 only in R8C13, locked for N7
14g. 9 in N3 only in R13C8, locked for C8
14h. Naked pair {12} in R79C8, locked for C8 and N9
14i. 9(3) cage at R1C9 = {135/234} (cannot be {126} because R2C8 only contains 3,4,5), no 6, 3 locked for N3
15. 18(3) cage at R7C7 (step 2f) = {468/567} = [567/765/864]
15a. Consider combinations for 21(3) cage at R6C9 (step 2) = {489/579} = [579/948]
21(3) cage = [579] => 18(3) cage = [864] => no 8 in R5C8 (AN) => R5C89 = [38]
or 21(3) cage = [948] => R5C89 = [83] => no 7 in R46C8 (NC) => R4C9 = 7 (hidden single in N6)
-> 7 in R47C9, locked for C9, 8 in R58C9, locked for C9, 18(3) cage = [756/765/864]
15b. R23C9 = {26} (cannot be {25} which clashes with 9(3) cage at R1C9, cannot be {56} because of NC), locked for C9 and N3
[Now it gets a lot easier]
15c. 9(3) cage = {135} (only remaining combination), locked for N3, no 4 in R13C8 + R2C7 (NC)
15d. R2C7 = {78} -> no 7,8 in R1C7 + R2C6 (NC)
15e. R1C7 = 4, R13C5 = [34], no 2 in R1C4, no 2,5 in R1C6 (NC)
15f. R2C8 = 3 (hidden single in N3), R5C89 = [83]
15g. R2C7 = 8 (hidden single in N3) -> R7C7 = 7, R79C5 = [67], R79C9 = [45], R1C9 + R3C7 = [15], R9C67 = [49], R9C8 = 2 (cage sum), R4C9 = 7, R68C9 = [98], R7C8 = 1
15h. Naked pair {59} in R8C46, locked for R8 and N8
15i. Naked pair {38} in R7C46, locked for R7 and N8 -> R9C4 = 1
15j. 1 in N2 only in R23C6 -> no 2 in R23C6 (NC)
15k. R5C6 = 2 (hidden single in C6), R5C4 = 9, R8C46 = [59]
15l. R5C6 = 2 -> no 3 in R4C6 (NC) -> R4C6 = 6, R6C4 = 4 (cage sum), R6C6 = 7 -> R4C4 = 3, R7C46 = [83]
15m. R4C4 = 3 -> no 2 in R3C4 + R4C3 (NC), no 3 in R3C2 (AN)
15n. R6C4 = 4 -> no 3 in R6C3 (NC), no 4 in R5C2 (AN)
15o. R7C4 = 8 -> no 9 in R7C3 (NC), no 8 in R6C2 (AN)
15p. R8C4 = 5 -> no 4 in R8C3 (NC), no 5 in R7C2 (AN)
16. R7C3 = 5 -> R8C2 + R9C1 = 15 = [78]
16a. R8C2 = 7 -> no 6 in R9C2 (NC) -> R9C23 = [36], R8C13 = [41]
16b. 12(3) cage at R5C1 = [714]
16c. R5C1 = 7 -> no 6 in R6C1 (NC)
16d. R5C2 = 1 -> no 2 in R46C2 (NC)
17. R2C4 = 2 (hidden single in N2), R2C39 = [76], R1C36 = [28]
17a. R2C6 = 5
17b. R2C2 = 4 -> R1C1 + R3C3 = 8 = [53]
17c. R1C1 = 5 -> no 6 in R1C2 -> R1C2 = 9
and the rest is naked singles, without using anti-knight or non-consecutive.