[1] **viXra:1110.0055 [pdf]**
*submitted on 18 Oct 2011*

**Authors:** Thomas Evans

**Comments:** 19 pages

It is the underlying purpose of the author throughout this and subsequent related
papers to consider the examination of conjectures such as the Birch-Swinnerton-Dyer
conjecture, the Riemann Hypotheses, as well as a number of other misunderstood or
unacknowledged phenomena. It is the author's hope that through such considerations,
both autonomous and presented herein, that it may become evident that the introduction
of fundamental, new practices is a necessity to any advancement in the directions of the
aforementioned. This represents the first in a series of eight (8) papers regarding these
materials. Throughout the remaining 7 the author presents, to a much greater degree of
rigor, the basic theory of analytic gauge functions, associated phenomenology, and there
from a solution to the (two) above conjectures. This paper facilitates an introduction to
the theory of analytic gauges. In the first section the author presents a re-examination of
the concepts of geometries of connections. Very briefly introduced are the basic concepts
of analytic numbers, analytic fields, analytic gauge functions, etc.

**Category:** Set Theory and Logic