The binomial constructor encodes the general two-part structure maintained by the complement of the hyperbolic figure eight knot, and its coherent external transform space—defined by the volume of the 24-dimensional unit hypersphere, or the density of the Leech lattice. Where = the external geometric action of each transform,
= the external boundaries that action takes place on—expressed in Planck constants,
= the internal geometric action, and
= the internal inversion boundary of the minimal hyperbolic structure.
Where = the Planck length,
= the Planck mass, and
= the Planck charge.
Every constant of Nature is coherently maintained by this bi-part structure, using one of the hyperbolic partition equation's simple (one-dimensional) transforms. Those transforms include: two polar expressions (expressed in powers of and
), and 6 Cartesian expressions—the 2-part products, the 3-part products, the 2-part sums, the 3-part sums, the 2-part quadrances, and the 3-part quadrances.
Check the Constants of Nature page to see which simple transform each constant uses.