After {{#bindImplicitColumns}}we have -

The columns for PersistentClass(B).getIdentifier().getColumns() -

1. Column(code)
2. Column(cost)
3. Column(id)
4. Column(type)

The columns for ToOne(A.b) -

1. Column(b_code)
2. Column(b_cost)
3. Column(b_id)
4. Column(b_type)

And as I mentioned, the type details are correct.