the hyperbolic partition equation
The hyperbolic partition equation encodes how the two-layer system coherently partitions within its mass gap—the normalized Planck mass. It's 4 solutions 
, 
, 
and 
define the hyperbolic partition constants—which possess the following product, sum and quadrance (sum of squares).
= 0.0854245431533304 ...= 3.66756753485501 ...= –1.87649603900417 ... + 4.06615262615972 ...
= –1.87649603900417 ... – 4.06615262615972 ...The first of those quadrance parts is the fine structure constant 
.
In polar coordinates and are expressed as 
and 
, where:
= 4.47826244916751 ...
= 2.00316562310924 ...Vieta relations: , , and .
