[Math] Minimally inconsistent Sudoku puzzle

Question

A sudoku puzzle is a partially filled $9\times 9$ grid with numbers $1,\ldots,9$ such that each column, each row, and each of the nine 3×3 sub-grids that compose the grid does not contain two of the same number.

What is the minimal number of entries needed to produce an
inconsistent puzzle, i.e., a puzzle that can not be completed to one where there is a solution?

EDIT: Now that there is an example where 5 is attained, can one show that this is the least possible, i.e., that any non-trivial puzzle with 4 entries can be completed to a solution?

Answer 1

5?

123|   |   
   |4  |  
___|___|4__
   |   |   
   |   |   
___|___|___
   |   |   
   |   |   
   |   |