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"Phenomenological formula for CKM matrix and its physical interpretation"

This paper was mentioned in "Koide sum rules" thread, but not discussed much. But to me, this looks like a big deal.

Here's the "numerology":

Square roots of experimental quark masses, MeV

down: 2.1679 9.7980 64.6529

up: 1.4832 35.7771 416.5333

Unit-length vectors built of those (IOW: divided by norm)

down: 0.0331 0.1498 0.9882

up: 0.0035 0.0856 0.9963

CKM matrix:

0.97435 -0.2287 0.005641

0.2286 0.9712 -0.06700

0.009846 0.06652 0.9977

Kohzo Nishida says that (normed_sqrt_up_masses) = CKM * (normed_sqrt_down_masses)

0.0036 0.0868 0.9962

Match with experimentally known value for "down mass vector" is eerily good.

Square roots of masses of quarks seems to be definitely linked to CKM matrix. And again, like in Koide rule, we have square roots of masses. Hmmm.

I'm no specialist (and thus would like specialists to chime in), but to me this says "mass" is a square of something, or some complex value multiplied by its complex conjugate.

What theories can give something like this?