Nautilus: How are files sorted

GNU sort with the -g(--general-numeric-sort) option should be able to do the trick

sort -k5,5g -t '_'  <<!
beginning_num1_734_num2_1.363e+12_num3_800.pdf
beginning_num1_735_num2_7.453e+13_num3_800.pdf
beginning_num1_1007_num2_9.453e+12_num3_1200.pdf
!
beginning_num1_734_num2_1.363e+12_num3_800.pdf
beginning_num1_1007_num2_9.453e+12_num3_1200.pdf
beginning_num1_735_num2_7.453e+13_num3_800.pdf

Sorting is done in multiple passes. Each character has three (or sometimes more) weights assigned to it. Let's say for this example the weights are

         wt#1 wt#2 wt#3
space = [0000.0020.0002]
A     = [1BC2.0020.0008]

To create the sort key, the nonzero weights of the characters of a string are concatenated, one weight level at a time. That is, if a weight is zero, no corresponding weight is added (as can be seen at the beginning for " A"). So

       wt#1   -- wt#2 ---   -- wt#3 ---
" A" = 1BC2   0020   0020   0002   0008
       A      sp     A      sp     A

       wt#1   wt#2   wt#3
"A"  = 1BC2   0020   0008
       A      A      A

       wt#1   -- wt#2 ---   -- wt#3 ---
"A " = 1BC2   0020   0020   0008   0002
       A      A      sp     A      sp

If you sort these arrays you get the order you see:

       1BC2   0020   0008               => "A"
       1BC2   0020   0020   0002   0008 => " A"
       1BC2   0020   0020   0008   0002 => "A "

This is a simplification of what actually happens; see the Unicode Collation Algorithm for more details. The above example weights are actually from the standard table, with some details omitted.