THE COMBINATION OF TRUE ELEMENTARY QUANTA
If all forms of substance are quantized, then in order for quarks to combine in stable structures, they must satisfy integer equations reflecting the quantization of matter and energy. We call those Diophantine (integer) equations the Conveyance Equations, because they convey the logical structure of reality into the space-time domain of our 3S-1t experience. Compound particle stability depends on the integer solution of the equation representing the combination of two or more particles to form a third particle. This family of Diophantine equations is represented mathematically by the expression
Σni=1 (Xn)m = Zm.
When n = 2 and m = 3, the expression becomes the equation
(X1)3 + (X2)3 = Z3
If we combine two cubes, two spheres, or any two regular polyhedrons to form a third regular three dimensional object of the same shape, we have
S(X1)3 + S(X2)3 = S(Z)3
where S is the shape factor. But S cancels out and we have
(X1)3 + (X2)3 = Z3
Which Fermat's Last Theorem tells us can have no integer solutions. However, when n = 3 and m = 3, the expression becomes the equation (X1)3 + (X2)3 + (X3)3= Z3, which does have integer solutions. This fact that the Conveyance Equation has no integer solutions when n = 2, but does when n = 3, explains why quarks are always found combined in threes. The combination of two quarks is asymmetric because when n = 2, because of their spin, they are unstable. But when n = 3, they can form stable structures.
Using (X1)3 + (X2)3 + (X3)3= Z3, we are able to find integer solutions that perfectly represent the combination of three quarks, two up quarks and one down quark to form a proton, and one up quark and two down quarks to form a neutron. Using experimental data we can then determine how many TRUE units of the third form (gimmel- most likely dark matter) are included to form stable atoms.
We choose the Hydrogen atom to start with because it is the simplest, most stable, and most abundant, even though very reactive, known element in the universe, and proceed to apply TRUE analysis to the elements of the Periodic Table.
When this is done, we find that all of the life-supporting elements and compounds are stable with the same high percentage of TRUE units of gimmel. This means that life is no accident, because no particle coming out of a big bang explosion could be stable without the proper amount of gimmel. Without symmetric stability, no physical universe could form.
Note: the details of the derivation of the stable forms of the elementary particles, atoms of the periodic table, and life supporting molecules are presented in a paper currently being peer reviewed for publication.