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Unfortunately, no such method currently exists. I don't have a proof for its nonexistence, as there's no mathematical proof that can't exist (yet), but none have yet been discovered. The only way we currently know to verify a Sudoku has no errors is by solving it and checking for impossibilities.

To reason why, consider that if such a method existed, Sudoku solvers wouldn't implement the deductive methods that they currently employ - they would simply need to guess a number then check to see if it's right.

(Slightly) more formally, the proposition you'd be trying to prove is: "The sudoku is solvable." There are really only two approaches you could take to prove that it's solvable:

  • Proof by contradiction: "The sudoku can't be solvable because it leads to an impossible state."
  • Direct proof: "By [some mathematical process], the Sudoku can be classified as "solvable" or 'unsolvable.'"

The first can always be executed - it's just guess and check until you exhaust all possibilities or encounter a valid solution. The second is a yet-unsolved unsolved mathematical problem.