The full reasoning can be found below the Sudoku.
Apr 23 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C2 can only be <4>
R5C7 can only be <6>
R6C4 can only be <2>
R8C6 can only be <3>
R5C2 can only be <8>
R5C3 can only be <2>
R6C2 can only be <3>
R5C5 can only be <4>
R8C5 can only be <1>
R5C8 can only be <9>
R4C8 can only be <2>
R6C6 can only be <8>
R6C8 can only be <1>
R4C4 can only be <5>
R4C6 can only be <6>
R7C5 can only be <2>
R8C4 can only be <4>
R2C6 can only be <2>
R2C4 can only be <3>
R8C1 can only be <8>
R1C9 is the only square in row 1 that can be <2>
R1C2 is the only square in row 1 that can be <9>
R7C7 is the only square in row 7 that can be <8>
R9C1 is the only square in row 9 that can be <2>
R9C3 is the only square in row 9 that can be <3>
R1C3 can only be <5>
R1C8 can only be <7>
R8C9 is the only square in row 8 that can be <7>
R9C9 is the only square in row 9 that can be <9>
R9C8 is the only square in row 9 that can be <4>
Squares R3C3 and R3C9 in row 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <46>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R3C1 - removing <4> from <347> leaving <37>
Squares R3C3 and R3C9 in row 3 and R7C3 and R7C9 in row 7 form a Simple X-Wing pattern on possibility <6>. All other instances of this possibility in columns 3 and 9 can be removed.
R2C9 - removing <6> from <146> leaving <14>
The puzzle can be reduced to a Bivalue Universal Grave (BUG) pattern, by making this reduction:
R2C1=<47>
These are called the BUG possibilities. In a BUG pattern, in each row, column and block, each unsolved possibility appears exactly twice. Such a pattern either has 0 or 2 solutions, so it cannot be part of a valid Sudoku
When a puzzle contains a BUG, and only one square in the puzzle has more than 2 possibilities, the only way to kill the BUG is to remove both of the BUG possibilities from the square, thus solving it
R2C1 - removing <47> from <147> leaving <1>
R2C2 can only be <6>
R2C9 can only be <4>
R1C1 can only be <3>
R7C1 can only be <4>
R2C8 can only be <5>
R8C2 can only be <5>
R3C3 can only be <4>
R2C5 can only be <7>
R8C8 can only be <6>
R3C7 can only be <3>
R3C9 can only be <6>
R7C3 can only be <6>
R3C1 can only be <7>
R1C7 can only be <1>
R7C9 can only be <1>
R9C7 can only be <5>
R9C2 can only be <1>
R3C5 can only be <5>
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