the binomial constructor
binomial constructor equation

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 A_external = the external geometric action of each transform, B_external = the external boundaries that action takes place on—expressed in Planck constants, A_internal= the internal geometric action, and box symbol = the internal inversion boundary of the minimal hyperbolic structure.

box symbol equation

Where l_p = the Planck length, m_p = the Planck mass, and q_p = 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 zhe_r and zhe_theta), 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.

2-part products 1 and 2
3-part products 1
2-part sums plus
3-part sums plus
2-part quadrances plus 1
3-part quadrances plus 1
2-part products 3 and 4
3-part products 2
2-part sums minus
3-part sums minus 1
2-part quadrances minus 1
3-part quadrances minus 1
2-part sums plus 3
3-part sums plus 2
2-part quadrances plus 3
3-part quadrances plus 2
2-part sums minus 3
2-part sums minus 2
2-part quadrances minus 3
3-part quadrances minus 2

Check the Constants of Nature page to see which simple transform each constant uses.