1 =  1
0
  0
1
  i =  i
0
  0
-i
  j =  0
-1
  1
0
  k =  0
i
  i
0
 
-1 =  -1
0
  0
-1
  -i =  -i
0
  0
i
  -j =  0
1
  -1
0
  -k =  0
-i
  -i
0


s1 =  0
1
  1
0
  s2 =  0
i
  -i
0
  s3 =  1
0
  0
-1
  Pauli matrices


s1 s2 s3    
s1 1 i -j    
s2 -i 1 k    
s3 j -k 1   s1 * s2 = i, s1 * s3 = -j, and so on


DARK
DARK
 
DARK
DARK
 
DARK
DARK
  -1 * -1
-1 * 1
 
-i * -i
-i * i
 
1 * i
1 * -i
= 1 * 1
= 1 * -1
 
= i * i
= i * -i

= -1 * -i
= -1 * i
= -1
= 1
 
= 1
= -1
 
= -i
= i
   
 
 
 
 
 
 
Dark multiplication rules

In the fourth line DARK -i * i = i * -i = -1 one recognizes the vacuum marble pair ( i   -i ) yielding -1, the backward time evolving vacuum as observed by us.

DARK   1
0
  0
1
  1
0
  0
1
 =  -1
0
  0
-1
  -1
0
  0
-1
 =  -1
0
  0
-1


      s1 s2 s3
    s1 -1 -i j
    s2 i -1 -k
DARK   s3 -j k -1


See also paragraphs
Dark multiplication rules at page 2 of EXPANSION OF THE UNIVERSE,
Matrices and the mapping on SU(3), page 9 of QQD