>One of the properties that π is conjectured to have is that it is normal
conjectured
Glad to see one of my pet points of pedantry come up. No non-constructed irrational number has never been proven to be normal or disjunctive.
You must be fun in RL.
Chaitin's constant does not count? Depends on your definition of constructed, but contrary to "easy" normal numbers such as Champernowne's constant, it's not defined by its sequence of digits.