Octonion Flavour Assignments

The 8D spatial extension of the S³ framework introduces an octonion structure. The G₂ automorphism group of the octonions contains SU(3), giving a geometric origin for quark flavour.

While describes our observable 3D universe, the full spatial universe is embedded within an 8-dimensional space. The only normed division algebras are the reals , complex numbers , quaternions , and octonions . The 8D space is geometrically isomorphic to .

G₂ Automorphism

The three quark generations (u/d, c/s, t/b) are hypothesised to correspond to three independent embeddings within . The 7 imaginary basis vectors of the octonions translate into 7 quark/antiquark states which decompose as under action.

Basis Assignment

Currently, the explicit assignment of basis vectors to specific flavours is open. Solving this would not only eliminate free parameters from quark masses, but it could directly solve the MeV proton/neutron mass splitting via symmetry breaking.

Integrity Status: Open [O]

The geometric potential of the octonion mapping is profound, but the exact assignments remain an open and critical research area.

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