PRH | Essay | 7.3 • On Redundancy of Properties in Mathematical Objects

We propose a general principle about the role of apparently "redundant" properties in the definition of mathematical objects. If a property is unnecessary for the construction of the object but nonetheless impacts its behavior when modified, then the property is either fundamentally simple, or else our axiomatic understanding of the object is incomplete. We apply this principle to the role of the line $\Re s=\frac{1}{2}$ in the Riemann Hypothesis, and connect it to entropy considerations that measure how much non-random information primes actually contribute.