Equal Books Koide's relation, its deviations in the other sectors, and tribimaximal mixing from a complete pass on the three-cube

The charged leptons obey Koide's relation, (me + mµ + mτ)/(√me + √mµ + √mτ)2 = 2/3, to eight parts per million. It is a balance: the square-root amplitudes put equal load into what the generations share and into what separates them. Every closed walk through the vertices of a three-cube steps one axis four times and the other two twice. Under two premises, that axis loads are generation modes with the four-stepped axis the common one, and that load counts steps, 4 = 2 + 2 is that balance. If charge conjugation conjugates a sector's matrix, a Majorana sector takes the walk's other structure; at leading order the two overlap in the tribimaximal pattern. One posting's fermion-core load splits as 2 ∓ √2; read as two Majorana neutrinos this gives ∆m231/∆m221 = 17 + 12√2 and a massless lightest state. Quark deviations fit half a unit per curved axis to two percent; the flux round the ring of axes is computed in every sector and unexplained.