Golomb's Randomness postulates
They make sense as a starting point, for pseudorandomness.

R1. This is a strict balancedness condition, the difference is 1, in case $N$ is odd and zero is impossible.

R2. If you have an i.i.d. and unbiased binary source, the run length distribution is geometric, which in a finite length segment should follow the profile given in R2, due to the law of large numbers.

R3. Having an autocorrelation $C(t)$ of the form
$$
C(t)=N I\{t=0\}+ f(t) I\{t \neq 0\}
$$
where $I$ is the indicator function, with $f(t)$ small in absolute value is a feature of an i.i.d. independent sequence.
By parseval $|f(t)|\leq 1$ is possible for odd lengths. Golomb chooses this off peak correlation function $f(t)$ as constant so phase information is not leaked.

Of course he also knew that algbraic structures, in particular cyclic difference sets, allowed one to mechanise this two level correlation.