Let us explore the consequences of the plausible assumption 
. By (6.3), we
expect that 
, where the O constant is uniform in
. Thus the region 
, being the product of two intervals of lengths 1 and
and 
disks of radius 
, has volume 
. Since the points of 
are distributed with density
, and assuming 
is in general
position, there are 
points of
in 
. If 
is sufficiently large, it is thus possible to
push through the argument of .2 for d = 4 and the birthday paradox argument of
.3 for d = 6 to conclude that the orbit of 
should be finite.
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