A Curious Effect of Benford's Law for Bijective Numeration

We assume that the probability mass function Pr(Z)=(2Z)^-2 is at Newcomb-Benford Law's root and the origin of positional notation. Under its tail, we find that the harmonic (global) Q-NBL for bijective numeration is Pr(b,q)=(q Hb)^-1, where q is a quantum (1≤q≤b), Hn is the nth harmonic number, and b is the bijective base. Under its tail, the logarithmic (local) R-NBL for bijective numeration is Pr(r,d)=Log(r+1,1+1/d), where d≤r ≪ b, being d a digit of a local complex system’s bijective radix r. We generalize both lows to calculate the probability mass of the leading quantum/digit of a chain/numeral of a given length and the probability mass of a quantum/digit at a given position, verifying that the global and local NBL are length- and position-invariant in addition to scale-invariant. In the framework of bijective numeration, we also prove that the sums of Kempner’s series conform to the global Newcomb-Benford Law and suggest a natural resolution for the precision of a universal positional notation system