You don't need to solve the halting problem to prevent such access, not even close. You simply apply the same strategy as any other property you want to enforce

You don't need to solve the halting problem to prevent such access, not even close. You simply apply the same strategy as any other property you want to enforce - you prevent any use of the variable that can't be proven safe. You want to pass this in a call from the constructor to a function defined somewhere else where it might access a final/non-null able field that has not yet been initialized? Not allowed, only member functions that don't call other non-member functions allowed from the constructor. Of course, as I said, this ship has long sailed for general Java classes. It would be far too big of a breaking change to add such a limitation today. However, we know for sure this could have been done in Java: this is exactly how record and now value classes work: any call that could expose un initialized fields is in fact disallowed.