The challenge page says that “You may choose any mapping between the state vector domain D to the distribution domain (i.e. the discretization) as long as it is continuous”.

I’m not sure I understand how a mapping couldn’t be continuous. Could you elaborate a bit on this, or give an example of a forbidden mapping?

Does that mean that, for a discretization x_0, …, x_{2^n}, it is valid as long as x_i < x_{i+1} holds? Or is it necessary but not sufficient?