  The transition constant was introduced in our 1981 paper and denoted as
N(14). It is equal to the maximal degree of the ground fields of V-arithmetic
connected edge graphs with 4 vertices and of the minimality 14. This constant
is fundamental since if the degree of the ground field of an arithmetic
hyperbolic reflection group is greater than N(14), then the field comes from
very special plane reflection groups. In our recent paper (see also
arXiv:0708.3991), we claimed its upper bound 56. Using similar but more
difficult considerations, here we improve this bound. These results could be
important for further classification.
