The complexified exceptional Jordan algebra yields fermion mass ratios via a diagonal-action theorem on Sym^3(3) representations after triality breaking, with a universal eigenvalue spectrum fixed by the Jordan cubic.
Quark structure and octonions
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The Standard Model gauge group is characterized as a subgroup of Spin(10) via two suitably aligned commuting complex structures on R^10 encoded in orthogonal pure spinors whose sum is pure, described efficiently with octonions.
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Fermion mass ratios from the exceptional Jordan algebra
The complexified exceptional Jordan algebra yields fermion mass ratios via a diagonal-action theorem on Sym^3(3) representations after triality breaking, with a universal eigenvalue spectrum fixed by the Jordan cubic.
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Octonions, complex structures and Standard Model fermions
The Standard Model gauge group is characterized as a subgroup of Spin(10) via two suitably aligned commuting complex structures on R^10 encoded in orthogonal pure spinors whose sum is pure, described efficiently with octonions.