The Mirror Branch Braid Atlas: A Parameter-Free Dark Sector Classification from the Universal Generative Principle

The Universal Generative Principle (UGP) derives the Standard Model spectrum from a parameter-free arithmetic sieve at ridge n=10. The prime-lock mechanism that selects the SM lepton seed (1,73,823) simultaneously forces a mirror-branch seed (1,73,2137), predicting a complete dark sector with no free parameters. We derive the Mirror Branch Braid Atlas—the dark sector particle classification table. The electric charge Q=0 for all dark particles is derived from Braid Atlas topology, not assumed: the mirror Z_2 involution is an internal GTE arithmetic symmetry, not an SM gauge transformation. The dark sector gauge group is SU(3)_dark only—no dark SU(2)_L exists. Three generations of free dark leptons at 0.54MeV, 24.5MeV, and 3.60GeV coexist with confined dark quarks near Λ_dark~ 200MeV. We establish a new structural connection: c(W) = b_2(RHN) = q_1 in both branches—the first cross-sector structural unification in UGP Physics. The core results are machine-certified in Lean~4 ( .lean, .lean, .lean; zero sorry, zero custom axioms). The dark neutrino mass-squared ratio R_dark = 0.208 is 7× larger than the SM ratio ( : MDL doublet-pairing derivation of b_3'=37). The FIMP mechanism overproduces dark matter by 4.84×10^6 at λ_s ~ 10^-6; the leading resolution is asymmetric dark matter with η_χ ≈ (2/7)η_B+L,pre, where 2/7 = (Z_7 charge of dark baryon)/(Z_7 group order). The most accessible prediction is GTE-P7 at 211.9MeV—a Tier~1 target at Belle~II. The baryogenesis derivation and dark confinement scale are identified as primary open problems.