Why does one finite group unify these?
PSL(2,7) is the automorphism group of the Fano plane and the symmetry group of the Klein quartic. It is the smallest non-trivial finite simple group whose order is twice that of the smallest non-cyclic simple group, A₅. In the Merkabit framework, every measurable physical structure that requires three ternary closure with binary verification reduces to PSL(2,7) somewhere along its derivation chain. The "five faces" are the five places this reduction has been made explicit and falsifiable.
The fifth face — matter–antimatter asymmetry — is the most recent and currently in development. The architectural finding: the asymmetry parameter η_B = 6.1×10⁻¹⁰ emerges from the same loop-obstruction trichotomy of B₃₁ that produces the Yang–Mills mass gap. Five distinct hard problems; one finite group of order 168.