**Authors:** Thomas Evans

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.

**Comments:** 19 pages

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[v1] 18 Oct 2011

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