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A p-Adic Metric for Particle Mass Scale Organization with Genetic Divisors

Wagner, John S.

The concept of genetic divisors can be given a quantitative measure with a non-Archimedean p-adic metric that is both computationally convenient and physically motivated. For two particles possessing distinct mass parameters x and y, the metric distance D(x, y) is expressed on the field of rational numbers Q as the inverse of the greatest common divisor [gcd (x , y)]. As a measure of genetic similarity, this metric can be applied to (1) the mass numbers of particle states and (2) the corresponding subgroup orders of these systems. The use of the Bezout identity in the form of a congruence for the expression of the gcd (x , y) corresponding to the v{sub e} and {sub {mu}} neutrinos (a) connects the genetic divisor concept to the cosmic seesaw congruence, (b) provides support for the {delta}-conjecture concerning the subgroup structure of particle states, and (c) quantitatively strengthens the interlocking relationships joining the values of the prospectively derived (i) electron neutrino (v{sub e}) mass (0.808 meV), (ii) muon neutrino (v{sub {mu}}) mass (27.68 meV), and (iii) unified strong-electroweak coupling constant ({alpha}*{sup -1} = 34.26).