Traces of the Riemann zeta function on the complex plane.

In this revision [v.12], I have corrected some inaccuracies and improved some parts, which may have been difficult to understand. I also deleted what was section 14, the reason being that I now find it superfluous and potentially misleading.
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Given for example the formulation $\zeta(s)=\sum_{n \ge 1}\frac{1}{n^s}$, at each increment of (n) a new point on the complex plane is defined. Starting from the origin of the complex plane, the traces in question are formed of the vectors connecting these points.
The traces resulting from the zeta function of Riemann, can be divided into two parts.
The first part of the traces tends to move away from the origin, it develops in a convoluted way reaching variable distances.
The two parts behave like two arms of a mechanism that makes them both rotate, clockwise if the coefficient of the imaginary part of (s) is positive. The second arm is the extension of the first, its rotation is in synchrony with that of the first arm, to which is added.
The rotation of the two arms cyclically brings the free end of the second arm, to pass where the origin of the complex plane is located, but intercepts it only if the lengths of the two arms compensate.
In this article I highlight that the Riemann hypothesis is true for the reason that, only if the real part of (s) is 1/2 it is possible to compensate the lengths, of the two parts of the trace.
The second part of the trace, is characterized by the presence of particular polygonal spirals that follow one another, always better formed. Seen the similarity with clothoids I called them “pseudo-clothoids”.
Given a complex number (s), I call (a) the real part and (b) the coefficient of the imaginary part, then s=a+b*i.
The value of (b) is the engine of the rotations, only if a=1/2, the value of (b) results neutral with respect to the distances, between the two origins of the pseudo-clothoids.