That in turn means that in our domain of programs a trillion bits long, exponentially more programs contain the compact subroutine than the literal print statement.
Are you sure this is right? There’s exponentially many different print statements. Do you have an argument why they should have low combined weight?
The number of N-bit print statements whose output starts with the n-bit Hamlet is exactly 2^(N-n). If K(Hamlet)=n/6, then there are at least 2^(N-n/6) programs whose output starts with Hamlet. Probably more.
EDIT: Ooops, I didn’t prove anything about the structuredness of the remaining N-n bits, so this is not too useful in itself.
Are you sure this is right? There’s exponentially many different print statements. Do you have an argument why they should have low combined weight?
The number of N-bit print statements whose output starts with the n-bit Hamlet is exactly 2^(N-n). If K(Hamlet)=n/6, then there are at least 2^(N-n/6) programs whose output starts with Hamlet. Probably more.
EDIT: Ooops, I didn’t prove anything about the structuredness of the remaining N-n bits, so this is not too useful in itself.