The Riemann hypothesis is false. I have a few independent negations by direct counterexample and they are presented in papers with varying degrees of rigor. In this "quick" proof, I present a fully rigorous proof upon an unproven proposition. Obvioulsy, this fails to negate RH due to the unproven proposition but it concisely states the method I use. In a longer paper, I do it without that proposition's assumption and in a *much* longer paper I start with Euclid's Elements, assume nothing else, and then show that RH is consequently false. That paper is linked below and if I can post the PDF, I will post it.
Fractional Distance: The Topology of the Real Number Line with Applications to the Riemann Hypothesis
>https://vixra.org/abs/2111.0072
Recent analysis has uncovered a broad swath of rarely considered real numbers called real numbers in the neighborhood of infinity. Here we extend the catalog of the rudimentary analytical properties of all real numbers by defining a set of fractional distance functions on the real number line and studying their behavior. The main results of are (1) to prove with modest axioms that some real numbers are greater than any natural number, (2) to develop a technique for taking a limit at infinity via the ordinary Cauchy definition reliant on the classical epsilon-delta formalism, and (3) to demonstrate an infinite number of non-trivial zeros of the Riemann zeta function in the neighborhood of infinity. We define numbers in the neighborhood of infinity as Cartesian products of Cauchy equivalence classes of rationals. We axiomatize the arithmetic of such numbers, prove all the operations are well-defined, and then make comparisons to the similar axioms of a complete ordered field. After developing the many underlying foundations, we present a basis for a topology.
