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 0.54 MeV, 24.5 MeV, and 3.60 GeV coexist with confined dark quarks near Lambda_dark ~ 200 MeV. 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 (MirrorWindingNumber.lean, EWBosonRHNConnection.lean, DarkBraidAtlas.lean; zero sorry, zero custom axioms). The dark neutrino mass-squared ratio R_dark = 0.208 is 7x larger than the SM ratio (conditional on the structural gap theorem). The FIMP mechanism overproduces dark matter by 4.84e6 at lambda_s ~ 1e-6; the leading resolution is asymmetric dark matter with eta_chi ~ (2/7) eta_{B+L,pre}, where 2/7 = (Z_7 charge of dark baryon)/(Z_7 group order). The most accessible prediction is GTE-P7 at 211.9 MeV---a Tier 1 target at Belle II. The baryogenesis derivation and dark confinement scale are identified as primary open problems.