arXiv2026
We show that in a self-consistent preon model, where Standard Model quarks and leptons are three-body composites confined at a metacolor scale Lambda_cr ~ 10^14 GeV, both leptoquarks and the Standard Model gauge group SU(3)_c x SU(2)_L x U(1)_Y emerge as structural predictions rather than inputs. Combining the preon content of a quark with that of a lepton gives exactly four distinct six-body bosonic leptoquark composites per generation, with electric charges Q = +2/3, -1/3, -1/3, -4/3 and a universal B-L = -2/3 fixed by the preon charge assignments. Their mass is of order Lambda_cr rather than of order the SM fermion masses, because the dynamical near-cancellation that produces light fermion masses is specific to three-body fermionic composites and does not extend to six-body bosonic ones. The fractional B-L = -2/3 forbids proton decay via single leptoquark exchange, requiring a dimension-12 operator and giving tau(p -> e+ pi0) ~ 10^58 years, consistent with the experimental bound > 2.4 x 10^34 years. It is shown that the SM gauge group emerges as a low-energy symmetry consistent with the Planck-scale boundary condition, and leptoquarks are required -- not merely permitted -- by the matching. The anomaly-matching argument extends to a tower of 3n-body composites, each level imposing consistency conditions on the next; we call this the vertical bootstrap and advance it as the organizing principle of the preon program.