An experimental study of the monotonicity property of the Riemann zeta function

In 1970, based on newly available empiric evidence, a remarkable monotonicity property for $\mathrm{\mid }\zeta (z)\mathrm{\mid }$ was conjectured by R. Spira. The $\zeta$-monotonicity property can be written as follows: $$\mathrm{\mid }\zeta (x_2+yi)\mathrm{\mid }<\mathrm{\mid }\zeta (x_1+yi)\mathrm{\mid }\text{for any }{x}_1<x_2\le 0.5\text{ and }6.29<y\mathrm{.}$$ In this work we present an experimental study of the monotonicity conjecture, in the course of which new properties of $\zeta (z)$ are discovered. For instance, the spectrum of semi-limits $\lambda (z)\subset \mathbb{R}$ and the core function $C(z)$, which serves as a non-chaotic simplification of $\zeta (z)$ to the left of the critical line