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 Z₂ 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 Λdark~ 200MeV. We establish a new structural connection: c (W) = b₂ (RHN) = q₁ 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 Rdark = 0. 208 is 7× larger than the SM ratio (: MDL doublet-pairing derivation of b₃'=37). The FIMP mechanism overproduces dark matter by 4. 84×10⁶ at λₛ ~ 10^-6; the leading resolution is asymmetric dark matter with η_χ ≈ (2/7) ηB+L, pre, where 2/7 = (Z₇ charge of dark baryon) / (Z₇ 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.