Cages are chained by greater-than signs and with equal signs; letters also indicate some cages with the same totals. Cage R1C456 contains two or three consecutive numbers, assumed not necessarily adjacent. All the other cages contain ‘singletons’, so no consecutive numbers within each of those cages.
Cages M at R8C1, R8C4 and R8C7 are all equal so must total 15. This also places 15(3) cages at R5C1, R5C3, R5C9, R6C2 and R7C5, also R34C3 = 15 = {69}, locked for C3. 15(3) = {159/168/249/258/357}, so only {168/249/357} for R8
Cages L less than cages M -> cages L = 12,13,14, R9C123 = 17,19,21 = {269/359/368/379/469/579} (cannot be {179} which clashes with cage M at R8C1), no 1
2,4 of {269/469} must be in R9C3 -> no 2,4 in R9C12
R7C123 = 9,11,13 (no restriction on ‘singletons’)
R7C123 cannot be {139} which clashes with cage M at R8C1, no 9 in R7C12
Cages K at least two greater than cages M = 17,18,19 -> R1C456 = 7,9,11, all of which can contain two or three consecutive numbers
R1C456 = {124/126/234/128/236/245}, no 7,9
R1C456 cannot be {124} because that would only leave {379} for both cages K
R1C456 cannot be {126/234} which clash with only valid 18(3) combinations {279/369/468}
-> cages K must total 17, R1C456 = 11
Cages K in R1 = {179/269/359/368}, no 4 -> R1C456 = {245}, locked for R1 and N2 -> cages K in R1 = {179/368}
Killer pair 6,9 in cage K at R1C1 and R3C3, locked for N1
Cage K at R4C5 = {179/359/368} (cannot be {269} which clashes with R4C3), no 2,4
Killer pair 6,9 in R4C3 and cage K, locked for R4
Cage K+1 at R1C5 = 18 = {279/468} (cannot be {369} because R1C5 only contains 2,4,5), no 1,3,5
Cages N at R2C6 and R2C9 = 16 = {169/259/268/358}, no 4,7
Cage N at R2C9 = {259/268/358} (cannot be {169} = {69}1 which clashes with cage K at R1C7), no 1
4 in N3 only in R3C78, locked for R3
4 in R3C78 -> no 3,5 in cage L at R3C6
Cage L = {147/246/148/247/149/248}
6 of {246} must be in R3C6 -> no 6 in R3C78
Cage K at R1C7 = {179/368} -> combined cage with cage N at R2C9 = {179}{268}/{179}/{358}/{368}{259} (cannot be {368}{268}/{368}{358}) -> 9 in R1C789 + R23C9, locked for N3
Cage N at R2C6 = {259/268/358} (cannot be {169} = 9{16} which clashes with cage K at R1C7), no 1
3 of {358} must be in R2C78 (cannot be 3{58} which blocks both cage K = {368} and cage N at R2C9 = {358} leaving no 3 in N3) -> no 3 in R2C6
3 in N2 only in R23C4, locked for C4
Hidden killer pair 1,7 in cage K at R1C7 and cage L at R3C6 for N3, cage K contains both or neither of 1,7 but cage L cannot contain all of 1,4,7 in R3C78 -> cage K at R1C7 = {179}, locked for R1 and N3
Cage K at R1C1 = {368}, locked for N1 -> R34C3 = [96]
9 in R4 only in cage K at R4C5 = {179/359}, no 8
Cage N at R2C9 = {268/358}, 8 locked for C9
Hidden killer pair 3,6 in R2C78 and R23C9 for N3, each can only contain one of 3,6 -> cage N at R2C6 = {268/358} with 3,6 in R2C78 -> R2C6 = 8, cage N at R2C9 = {268/358} with 3,6 in R23C9, no 3 in R4C9
Cage K+1 at R1C5 = {279} = [297]
Cage K at R4C8 = {269/359/368} (cannot be {179} which clashes with R1C8), no 1,4,7
Cage L at R3C6 = 1{48}/6{24} = 12,13 -> cage L at R9C4 and R9C7 = 12,13 -> R9C123 = 19,21 = {379/469/579}, no 2,8, 9 locked for R9 and N7
Cage M at R8C1 = {168/357}, no 2,4
2 in N7 only in R7C123, locked for R7
Cage M = 15, R9C123 = 19,21 -> R7C123 = 9,11 containing 2 = {126/234/128/245} (cannot be {236} which clashes with cage M), no 7
Cages L at R9C4 and R9C7 = 12,13 = {138/246/148/157} (cannot be {147/247} which clash with R9C123)
One of them must contain 8 for R9 -> cages L at R9C4 and R9C7 = {138/246} (cannot be {157} which clashes with {138/148} and cannot be {148} which clashes with {138/246}), no 5,7 -> cages L = 12
R9C123 = {579} (hidden triple in R9), 5,7 locked for N7 -> cage M at R8C1 = {168}, locked for R8 and N7 -> R7C123 = {234}, 3,4 locked for R7
Cage M at R7C5 = {159/168}, no 7, 1 locked for R7
45 rule on N8 1 innie R7C4 = 1 outie R7C7 + 3 -> R7C4 = {89}, R7C7 = {56}
1 in R7 only in R7C56, locked for N8
Cage L at R9C4 = {246}, locked for R9 and N8
Cage M at R8C4 = {357}, locked for R8, 5 locked for N8
Naked triple {189} in R7C456, 8,9 locked for R7
Cage M at R5C1 = {249/258/357} (cannot be {159/168} because R7C1 only contains 2,3,4), no 1
3 of {357} must be in R7C1 -> no 3 in R56C1
Similarly cage M at R6C2 = {249/258/357} (cannot be {159/168} because R7C2 only contains 2,3,4), no 1
3 of {357} must be in R7C2 -> no 3 in R6C23
9 of {249} must be in R6C2 -> no 4 in R6C2
Cage M at R5C9 = {159/168/258/357} (cannot be {249} which clashes with R8C9), no 4
R8C9 = 4 (hidden single in C9)
Cage K at R4C8 = {359/368} (cannot be {269} which clashes with R8C8), no 2, 3 locked for C8 and N6
Cage M at R5C9 = {159/168/249/258}, no 7
R7C8 = 7 (hidden single in R7)
R1C9 = 7 (hidden single in C9)
Killer pair 8,9 in R19C8 and cage K at R4C8, locked for C8 -> R8C8 = 2, R8C7 = 9, R1C78 = [19], R9C8 = 1 (hidden single in C8) -> R9C79 = [83]
R2C7 = 3 (hidden single in C7), R2C6 = 8 -> R2C8 = 5 (cage sum)
R3C8 = 4 (hidden single in C8), R3C7 = 2 -> R3C6 = 6 (cage sum)
R23C9 = [68] -> R47C9 = [25], R23C4 = [13]
R7C7 = 6 -> R7C56 = [81], R7C4 = 9
R4C6 = 9 (hidden single in R4) -> R4C57 = [17/35]
Cage at R2C1 must be less than 15 and cannot be {257} which clashes with cage M at R5C1 -> no 2 in R2C1
2 in C1 only in cage M = {249/258}, no 3,7
Cage at R2C1 must contain 1 (cannot be {357} which totals 15), locked for C1
Cage M at R5C3 = {168/258} (cannot be {357} = 3{57} which clashes with R8C4), no 3,4,7
Hidden killer pair 2,6 in cage M and R9C4 for C4, cage M cannot contain both of 2,6 -> R9C4 = {26} and cage M must contain one of 2,6 in R56C4, no 2 in R5C3
Cage M at R5C1 = {249/258}, cage M at R6C2 = {249/258/357} -> killer pair 5,9 in R56C1 and R6C23, locked for N4
Naked pair {18} in R58C3, locked for C3 -> R1C3 = 3
Naked pair {68} in R18C1, locked for C1
R7C2 = 3 (hidden single in R7) -> cage M at R6C2 = {357}, R6C23 = {57}, locked for R6 and N4 -> R6C7 = 4
R4C1 = 3 (hidden single in C1), R4C5 = 1, R4C6 = 9 -> R4C7 = 7 (cage sum), R4C248 = [458]
Naked pair {29} in R56C1, 2 locked for C1 and N4 -> R7C1 = 4
Cage M at R5C3 = {168} -> R5C3 = 1, R56C4 = {68}, 6 locked for C4 and N5
and the rest is naked singles.