Neutrino Mass-Squared Ratio from the Braid Atlas

No parameter-free structural prediction of the neutrino mass-squared ratio currently exists in the literature. Texture models (Altarelli–Feruglio, Frampton–Glashow–Marfatia, A_4/S_4 flavor symmetries) predict this ratio with a small number of fitted parameters or a symmetry imposed by hand; none derive it from purely structural inputs with zero free parameters. We present such a prediction: m^2_21/ m^2_31 = 0.02936, matching the NuFIT 6.0 global fit (0.02951 0.00098) to 0.16 ($0.52 automatic. The prediction uses only the QCD colour rank N_c = 3 and the Braid Atlas right-handed neutrino b-values \5, 11, 19\. The seesaw exponent is 29/9 = N_c + _Koide, where _Koide = (N_c^2-1)/(4N_c^2) = 2/9 is the Lean-certified Koide phase determined by N_c=3 alone . This exponent admits three independent structural decompositions — in terms of Braid Atlas topology, the mirror-offset invariant , and SO(10)/SU(5) representation dimensions — all converging on 29/9. The integer 29 is the gauge/matter representation defect of the PSC-selected GUT group: (adj_SO(10)) - (spinor_SO(10)) = 45 - 16 = 29 (Lean-certified as seesaw\_index\_is\_gauge\_matter\_defect, zero sorry). The two-flavon Froggatt–Nielsen texture for the right-handed neutrino is (q_1, q_2) = (N_c, strand) = (3, 2), uniquely selected by the MDL criterion (Lean-certified: fn\_structural\_texture\_existence\_and\_uniqueness, zero sorry). The structural Dirac Yukawa scale E_D = v_H/(4N_c^2 - ) = v_H/29 places m_ [55, 75] meV within the Planck bound without a cosmological anchor. A null test confirms the prediction is not a coincidence: only $0.22 reproduce the target ratio within $1 Preregistered falsification tests for JUNO ($ 1 and Hyper-Kamiokande are listed. EPIC_052 update (2026-05-16): Phase 2 Lean certification complete — NeutrinoMassRatio.lean in ugp-lean, all 5 theorems zero-sorry: seesaw exponent 29/9 (fn_texture_gives_seesaw_exponent), M_R cancellation (seesaw_ratio_independent_of_MR), coarse ratio bound 0.029 < R < 0.030 (neutrino_mass_ratio_coarse_bound), tight bound |R − 0.02936| < 0.0001 (neutrino_mass_ratio_tight_bound, certified by norm_num on exact 74-digit integers for b in {5, 11, 19}), and NuFIT 1% comparison (neutrino_mass_ratio_within_1pct_of_nufit); prediction 0.02936 matches NuFIT 6.0 (0.02951) to 0.52 sigma.