the hyperbolic partition equation
The hyperbolic partition equation encodes the allowable transformations of the figure-eight knot complement, hyperbolically partitioning the 288 constants of Nature inside the Planck mass gap. It's 4 solutions
, 
, 
and 
—the hyperbolic partition constants—possess the following product, sum and quadrance.
= 0.0854245431533304 ...= 3.66756753485501 ...= -1.87649603900417 ... + 4.06615262615972 ...
= -1.87649603900417 ... - 4.06615262615972 ...The first of those quadrances is the fine structure constant 
.
In polar coordinates and are expressed as 
and 
, where:
= 4.47826244916751 ...
= 2.00316562310924 ...In addition to their product, sum, and quadrance, these hyperbolic partition constants possess the following algebraic-geometric symmetries.
