The transform space is the set of coherent transformations available to the minimal arena—the hyperbolic figure-eight knot. Its measure is equal to both the volume of the 24-dimensional unit hypersphere ( 
), and the density of the Leech lattice ( 
). Here, 
= 120, the factorial of 
, and 
= 44, the number of derangements of objects.
The divisors of this space ( , , 35, 18, 32, and 8 ) define its coherent structure. The first divisor introduces the 120–cell structure. The remaining divisors ( 44, 35, 18, 32, and 8 ) define the quantized powers of the Planck constants: the division boundaries that connect the transform space. The 120-cell encodes relationships among the convex regular polytopes of the first 4 dimensions. The highest-power component of this structure is determined by the product of the hyperbolic figure-eight knot's twisted zeros.
The constructive zeros of the hyperbolic figure-eight knot are:
Swap either side to produce a pair of twisted zeros.