  We conjecture that for all regular lattices $b(n)$ is asymptotically of the
form in eq.(A1).
  \begin{equation}\label{A1} \tag{A1}
  (-1)^{n+1} * b(n) \sim \exp{( k_{-1} n + k_{0} ln(n) + \frac{k_{1}}{n} +
\frac{k_{2}}{n^{2}}...)} \end{equation} We restrict testing this to lattices
for which we know the first 20 Mayer series coefficients, the $b(n)$. This
includes the infinite number of rectangular lattices, one for each dimension,
the tetrahedral lattice ( in this one case we know only the first 19
coefficients ), and the (bipartite) body centered cubic lattices, in dimensions
3 through 7. In this paper we will detail results for the rectangular lattices
in dimensions 2,3,5,11,and 20, for the tetrahedral lattice, and for the body
centered cubic lattices in dimensions 3,4, and 5. These are all bipartite,
unfortunately we do not have an example of a non-bipartite regular lattice for
which we know enough of the $b(n)$ to work with. For the triangular lattice,
regular and non-bipartite, we know the first 14 $b(n)$. We feel this is not
enough terms to make any judgement, hopefully someone may compute more terms.
We work with an 'approximation' that keeps the first four terms, in $k_{-1},
k_{0}, k_{1}, k_{2}$, in the exponent in eq.(A1). Agreement will be striking.
At the end of Part 1 there is a discussion of computations in the present work
relevant to conjectures rising from the Yang-Lee Edge Singularity.
