Are *all* Sudoku configurations solvable?

Factual Questions
12

Perhaps a more interesting question is, “what is the minimum number of numbers that can exist on a Sudoku grid that gives a puzzle with no solution?” Let me propose this:




X X X | X X X | X X X
X X X | X X X | X X X
X X X | 1 X X | X X X
---------------------
X X 1 | X X X | X X X
X X X | X 2 X | X X X
X X X | X X X | 1 X X
---------------------
X X X | X X 1 | X X X
X X X | X X X | X X X
X X X | X X X | X X X

(It’s even symmetric!) Is that minimal?